Tag Archives: science

Never Tell Me the Watts! Energy and Power Use in the Star Wars Universe

As is quickly becoming my favorite holiday season tradition, a new film in the Star Wars franchise is about to be upon us with the release of Episode VIII- The Last Jedi on December 15! Star Wars has officially been in the cultural consciousness for over 40 years, and as someone who has grown up at any point during those 4 decades, I am a huge fan. Among the many great aspects of a series so long-lasting and deep with rich canonical story-telling, be it through films, books, or video games, is the prevalence of debate it offers for the real-life implications of a fictional universe. Star Wars is the at the pinnacle of such analyses and debates– from economists calculating the cost to build the Death Star (an analysis even cited in an Official White House document) to scientists debating the reality of lightsabers— so it only seems right that this blog dives into the real-life energy implications of various notable Star Wars scenes.

Because Star Wars is so entrenched in pop culture, especially among young boys and girls who eventually become scientists, mathematicians, and engineers, many of these topics have already been explored from academic, scientifically rigorous, and painfully detailed perspective. As such, I chose to allow these crusaders of over-analysis do the digging for me and just cite their work instead of doing the number crunching on my own. Not only would it seem that the hours and immense attention to detail these people have poured into these questions would come to a much close answer to the ‘truth’ than my patience would allow me, but it also allows me to spend my anticipatory re-watch of the entire series without diligent note taking!



So strap in and take a tour of a galaxy far, far away as it relates to energy.

Preliminary notes

A couple important preliminary notes about the calculations cited and used below:

  • Certain questions have been analyzed be numerous people across various fields leading to competing answers to the Star Wars questions. For this exercise, I’m choosing to identify the conclusions that I find to use the greatest scientific rigor and attention to detail, as well as those that show their work and cite their sources. My goal was to find the closest to the ‘true’ answer as possible, but if you find a different number or calculation to be more accurate then I welcome the gloriously nerdy debate in the comment section below!

Source

  • It is also necessary to state that almost every data point going into the below calculations are estimates and approximations. Many of the numbers needed for the calculations simply aren’t provided in the source material, so these mathematical Jedi have resorted to options like determining size of equipment by comparing it to the known size of a human standing adjacent, analyzing the known energy required to melt certain earthen material and assuming the materials in the Star Wars universe are the same or similar materials, or even slowing down clips of the movies to get a frame-by-frame rate of speed.  All that’s to say that the resultant numbers are estimates– diligently arrived-at estimates– but estimates nonetheless that do as good a job as possible at determining the relative order of magnitude. So take them with a grain of salt (which is better than a grain of sand, which is course and rough and irritating, not to mention it gets everywhere).
  • And lastly, with that grain of salt comes another huge one– I know these are movies. They are fictional, the directors often care more about how cool a scene looks instead of how it might break the law of physics, and the small details we analyze were probably not overly scrutinized for adherence to reality. These things don’t matter, but who cares? They are fun to think about and talk about and add depth to one of the greatest sagas in pop culture– so don’t strain yourself thinking too hard about them!

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Power required for uses of the Force

Emperor Palpatine’s Force lighting

Description: A number of times throughout the saga, we see Palpatine use his Force lighting, a unique aspect of his Force abilities. In the conclusion of Episode VI- Return of the Jedi, he uses the Force lightning on Luke after Luke once again refuses to join the Emperor on the Dark side and replace Darth Vader as his apprentice (click here for a YouTube link to the scene in question).

Calculation: This calculation is a rather tough one, but we do gain several clues from the scene, as pointed out by Joshua Brown.

The first clue is Luke’s reaction while being struck with the Force lighting, as he is able to call out in a plea for help, and though he is in obvious agony the attack is not fatal. Based on the science of the effect of electricity on the human body, this reaction from Luke would suggest he was experiencing between an AC-3 or AC-4 injury from the Force lighting.  Given the evidence that the longest continuous length of time that Luke was being struck exceeded 10 seconds, the below chart would suggest the current coursing through Luke’s body likely didn’t exceed 30 milliamps (mA).

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With the current of the Force lighting in Luke’s body established, the other piece of data we would need is the resistance of Luke’s body– which we can assume is about 100,000 Ohms, the upper limit for the internal resistance of the human body (Luke is a trained Jedi, after all).

Referencing our high school physics textbooks, we’ll remember that power equals current squared times resistance. Plugging in a current of 30 mA and a resistance of 100,000 Ohms gives a Force lighting power of 90 Watts.

Real World Comparison: To put that power in perspective, 90 Watts is about the upper limit for power adapters for Macbook laptops. Surely you don’t want that much electricity coursing through your body, but it’s also an amount of power we routinely carry around in our backpacks.

This amount of power might not seem like much, but watch the scene again and consider whether it truly looked like the Emperor was using all his strength to kill Luke– or was he instead using just a portion of his powers to torture Luke as a message to Luke and/or Darth Vader? It also does end up being a deadly amount of power, as it serves as enough to knock out the electronics of Darth Vader’s life-supporting suit and causes his death.

Darth Vader Force choking and throwing into the ceiling a Rebel trooper

Description: Among the many aspects of Darth Vader that makes him such a menacing presence is his combination of raw power and his tendency to use that power to intimidate those weaker than him. This combination is displayed each time he uses the Force to choke a subordinate or adversary without ever laying a finger on them. This power was on display in the final scene of Rogue One, as he laid waste to a number of Rebel troopers who stood between him and the stolen plans for the Death Star, with one poor trooper being lifted and slammed against the ceiling in a fit of rage (one of the biggest on-screen payoffs in Star Wars films, in my opinion, which can be watched here).

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Calculation: Rhett Allain, a physics professor, analyzes this scene for Wired to determine the power of this demonstration of the Force. Allain has to make a couple of assumptions and educated guesses– namely that the Rebel trooper is the size of an average man (1.75 meters tall and 70 kilograms in mass) and that the gravity inside the ship is the same as gravity on Earth at 9.8 Newtons/kilogram.

With that information, Allain then uses a video tracker on the scene to determine that the trooper is lifted up to a height of about 1.5 meters in 0.46 seconds at a constant speed of about 3.3 meters per second.

Time once again to employ the high school physics text book to find that the total work done is calculated as the change in kinetic energy (0.5 times mass times velocity squared) plus the change in potential energy (mass times gravity times height). Plugging in the values listed gives a total work done of 1,410 Joules, which when divided by a time of 0.46 seconds gives the total power output of 3,065 Watts.

Real World Comparison:  To put the power output of 3,065 Watts, or about 3.1 kilowatts (kW), in perspective– consider that 3.1 kW equates to about 4.1 horsepower. Commonly found outboard engines for small motorboats, such as this one, are rated at 4 horsepower as well– so at a moment’s notice Darth Vader is summoning the strength of a small motorboat. While that again doesn’t sound particularly scary, the clip shows the effect that this amount of power output can have when put in the wrong (robotic) hands.

Yoda lifting an X-Wing out of the swamp

Description: In Episode V- The Empire Strikes Back, Luke visits the planet of Dagobah to train with Master Yoda. Seeing the small stature and confusing training tactics, Luke begins to doubt the power of Yoda and question whether he is benefiting at all by being there.

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Disappointed by Luke’s insolent attitude and lack of faith in the training process, Yoda provides one of the greatest raw feats of Force strength we’re shown in the films– lifting Luke’s crashed X-Wing ship out of the swamp and into the air using the Force alone (again, the scene in question can be found on a YouTube video).

Calculation: Randall Munroe tackles the question of how much power Yoda outputs in this scene in his ‘What If?’ series. Munroe starts with a series of important assumptions, namely that:

  • The X-Wing is about 12,000 pounds (based on the weight of an F-22 fighter jet and the relative lengths of an F-22 and an X-Wing, Munroe scales the weight of an F-22 down to the proportional weight of the X-Wing), and
  • The gravity on Dagobah is 90% the gravity on Earth (according to sources on the highly detailed, extensive, and canonically accurate website Wookiepeedia).

Munroe then also broke down the video of the scene on a frame-by-frame basis, determining that Yoda lifted the X-Wing to a height of 1.4 meters in 3.6 seconds.

By plugging all these numbers into the equation power = mass times gravity times height divided by time, we find a power output of 19,228 Watts.

Real World Comparison: Sticking with the horsepower comparison, this power of about 19.2 kW equates to about 26 horsepower. What’s the first hit on Google when looking for a vehicle that’s 26 horsepower?

Riding lawnmowers!

Sense in you much fear, do I?

Summary
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Energy Associated with Star Wars Weapons

Lightsaber

Description: Lightsabers are the first and foremost among weapons you think of when you think of Star Wars, possibly of sci-fi in general. They are weapons mastered by Jedi and replicated by kids everywhere for the last 40 years. Lightsabers really don’t need any introduction, but the scene that is used to calculated the power of a lightsaber possibly does– as our best data points for lightsaber power use come from an early scene in Episode I- The Phantom Menace.

Source

In the scene in question, Qui-Gon Jinn uses his lightsaber to get through a thick, metal door– first he makes a significant cut in the door, and then he sticks his lightsaber into the door for a period of time that allows it to melt a hole in the door (here is a clip of that scene that is for some reason repeated for an entire hour). This quick scene was enough to send Star Wars sleuths to the whiteboards to calculate the power output.

Calculation: For this calculation, we again to look to Rhett Allain at Wired who uses this scene to determine the power needed for a light saber.  This calculation is the most complicated yet, so I would urge you to read the full article to learn more. But in summary, Allain uses the color that the door changes to as it heats up, the dimensions of the cut that Qui-Gon cuts initially,  an assumed set of material characteristics for what this door was likely made out of, and the total time taken to make that cut. Put them all together using equations that would require your graduate-level physics books this time, and you get a power requirement of 28 kilowatts.

Real World Comparison: Rather than looking to the power outputs of an engine, it seemed useful this time to compare this power output to as similar a type of weapon as possible. As it turns out, Lockheed Martin created a laser weapon system for the U.S. Army that is rated at a comparable 30 kW. This Advanced Test High Energy Asset (ATHENA) system has proven capable of shooting down outlaw drones and disabling a truck from a mile away.

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Considering the Jedi are carrying around that kind of power in a handheld weapon, you can understand the awe they inspire while expertly and effortlessly wielding lightsabers.

Blaster

Description: While lightsabers get all the buzz, Han Solo is famously quoted as saying that those “ancient weapons are no match for a good blaster at your side.” For the non-Force sensitive players in the Star Wars universe, blasters are the go-to firearm and are thus the most commonly used weapon in the galaxy, according to Wookieeepedia.

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To determine the energy of a single blaster bolt, the team at Ebates analyzed an escape scene in Episode IV- A New Hope where Princess Leia takes a blaster and shoots a hole through a metal grate for her, Luke, Han, and Chewbacca to crawl through. Not only does Leia succeed in winning the audiences heart by showing that this Princess is no damsel in distress (toward the end of this YouTube clip), but she also gives us the evidence needed to estimate the destructive energy of a single blaster bolt.

Calculation: According to the numbers crunched by eBates, the shot with the blaster created a hole about 3 feet in diameter in the metal grate, seemingly by vaporizing the metal.  Estimating the dimensions and density of the metal that was vaporized (about 54 kilograms) and knowing the energy needed to vaporize a kilogram of iron (6.34 Megajoules) leads to a rough conclusion that the blaster shot yeilded about 342 Megajoules.

Real World Comparison: Because the result of the blaster bolt here appeared to be a literal ‘blast’ of energy, it would be useful to know what would be required to yield the same explosive blast in the real world. Luckily, a unit of such destructive energy is standardized by the gram of TNT and is directly convertible to and from joules (one kilogram of TNT yields 4.184 Megajoules).  Thus for our lovely Princess to have blasted through the iron gate with the same energy of the blaster, it would have required about 82 kilograms of TNT.

Star Destroyer’s turbolaser

Description: The devoted fans at StarDestroyer.net took on the question of the energy from a shot by the empire’s domineering Star Destroyers.  In terms of military might (outside of the megaweapons to be discussed next), the Star Destroyer certainly stands as one of the most intimidating shows of military force in any galactic fleet.

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In one particular scene of Episode V- The Empire Strikes Back, a single blast from the turbolaser of the Star Destroyer is shown to clear asteroids right from its path. This show of firepower gives us a good idea of exactly how much destructive energy is contained in these blasts (watch in action in this YouTube clip).

Calculation: This calculation is another fairly in-depth and complicated one, so I would again recommend reading their entire write-up of the topic in full. However, the basic gist is that one bolt was able to instantaneously melt an asteroid (composed of the average asteroid composition) that measured on the order of 20 meters in diameter. Knowing the science behind the melting of such an asteroid leads to the calculation that the energy in a single turbolaser blast is 30 Terajoules or 30 million Megajoules.

Real World Comparison: A single shot of the Star Destroyer’s turbolaser has the destructive energy of 30 terajoules, which for context is about half the total energy released by the bomb dropped on Hiroshima to end World War II. Given that the Star Destroyer was releasing dozens of these shots over the course of its chase of the Millenium Falcon, you would understand why those being pursued might ‘have a bad feeling about this.’

Original Death Star’s superlaser

Description: The Death Star is the Ultimate Weapon of the Empire, the presence of which alone was enough to inspire fear and garner compliance from every corner of the galaxy. That fear is well-deserved because this awe-inspiring weapon was created to have the power to completely destroy planets.

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That’s not some sort of hyperbole, as we saw in the scene of Episode IV- A New Hope when the Empire demonstrates the power and unleashes the Death Star to destroy Princess Leia’s home planet of Alderaan. This show of force gives us the information we need to estimate how much destructive power is unleashed with the superlaser of the Death Star (watch the clip here, trigger warning for anyone who may have had friends or family on the planet formerly known as Alderaan).

Calculation:  Our friends at StarDestroyer.net also did the analysis on how much firepower was behind this blast from the Death Star. These calculations might be the most scientifically detailed yet, so definitely check out the full analysis. In the end, they used three different methods to estimate the energy of the weapon (calculating the surface escape velocity that would be required for planetary destruction, the constant gravitational binding energy that would need to be overcome, and the variable gravitational binding energy that would need to be overcome). Each of these calculation methods resulted in a final figure betweeen 2.2 x 10^32 and 3.7 x 10^32 joules. This range is a wide one in terms of an exact answer, but they are all in the same order of magnitude and thus inspire confidence in their approximate accuracy. For the sake of argument, we’ll go right in the middle and assume the energy of the Death Star is 3 x 10^32 joules, or 3 x 10^26 Megajoules.

Real World Comparison: We’re up at a level of energy that doesn’t have any real Earthly comparisons, as the total annual world energy consumption is on the order of 10^14 Megajoules– many orders of magnitude less than a single shot from the Death Star.

Instead we have to go, rather appropriately, into space. The 3 x 10^26 Megajoules of energy used to destroy Alderaan is equivalent to the total energy output of the Sun over the course of about 9 days.

Starkiller Base’s superweapon

Description; In the first film of the latest Star Wars trilogy, Episode VII- The Force Awakens, the Death Star gets completely outclassed as a weapon. The First Order takes the idea of a planet-sized battle station capable of wiping out a planet and inspiring fear-based obedience and cranks it up to 11, as their Starkiller Base is a superweapon built into a mobile planet that is capable of wiping out an entire star system.

 Source

In this scene that shows the first ever shot from the superweapon, the massive scale of the destructive energy being unleashed is evident and is used to wipe out five planets like they were never there– something never before seen in the Star Wars universe. The energy needed for this weapon is literally siphoned from the energy/plasma of a nearby star and then unleashing it in one blast. As you can imagine, this amount of energy is almost unthinkable.

Calculation: Jason Haraldsen, a physics professor, tackles the science behind Starkiller Base in a piece he wrote from the Huffington Post. Despite his conclusions that there are a number of aspects of Starkiller base that would be scientifically impossible (for one, Starkiller Base and its weapon are hosted on an ice planet– yet the harvesting of energy directly from a star does not end up overheating the planet or even melting the snow on it?) Haraldsen calculates the amount of energy that is needed to charge up the superweapon by converting the mass of the nearby star into pure energy. Keeping things way oversimplified, just converting the mass of the star to energy using E = mc^2 results in an energy output of 2 x 10^41 Megajoules.

Real World Comparison: If the Death Star’s energy required us to go from the Earth to the Solar System, Starkiller Base forces us to go on a galactic scale to find an energy equivalent. The 2 x 10^41 Megajoules of Starkiller Base’s superweapon is equivalent to the energy released by 1,000 supernovas. Talk about unlimited power!

Summary

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Conclusion

Do the filmmakers put as much attention into the minute details as we fans do in splicing apart and analyzing those details? Probably not. But that’s fine because the debate can be fun and educational and open up our eyes a bit about the comparable calculations in the real world. While thankfully it seems unlikely that any ill-intended human will create a sinister weapon as destructive as the Death Star or Starkiller Base, let us not forget that sci-fi can and has influenced the imaginations in the real world– from President Reagan’s Star Wars missile defense initiative to the ever-increasing presence of droid-like robots in our life.  So pay attention to any new inventions while you’re watching The Last Jedi, and let me know in the comments if you have any other Star Wars (or pop culture in general) energy-related questions you’d like to read about next!

Sources and additional reading

Ask Us: NASA

BP Statistical Review of World Energy

Death Star Firepower: StarDestroyer.net

How Many Batteries Would It Take to Power a Lightsaber? Or the Death Star? infographic journal

How strong is the Emperor’s lightning attack?

In Which We Literally Calculate the Power of the Force: Wired

Lockheed Martin’s laser weapon takes down 5 drones in live-fire demonstration: New Atlas

Power Source for a Lightsaber: Wired

Supernovae: Hyperphysics

The Physics Behind the Starkiller Base in Star Wars: The Force Awakens: Huffington Post

Turbolaser Firepower: StarDestroyer.net

US Army gets world record-setting 60-kW laser: DefenseNews

What was the yield of the Hiroshima bomb? Warbird Forum

Worker Deaths by Electrocution: NIOSH

Yoda: What if?

About the author: Matt Chester is an energy analyst in Washington DC, studied engineering and science & technology policy at the University of Virginia, and operates this blog and website to share news, insights, and advice in the fields of energy policy, energy technology, and more. For more quick hits in addition to posts on this blog, follow him on Twitter @ChesterEnergy.  

Deconstructing Units of Energy into Pizza, Fly Push Ups, and Grenades

When looking at energy use in everyday life situations, it is easy to overlook what the units used actually mean. When getting the electric bill in the mail, most people will simply compare the kilowatt-hours from last month to this month and note if their bill has gone up or down. When buying a new energy-efficient dryer, you know the fewer watts used the less energy it will be. The same mental comparisons are used all the time by people who do not have to deal with energy extensively– such as with the horsepower of a car or the calories in a sandwich.

However, it is all too common for people to forget the real significance of and differences between various units of measure related to energy and power use once they pass their high school physics class. Newscasters will constantly use kilowatts and kilowatt-hours as if they’re interchangeable (they’re not). Writers will misrepresent statistics online as if the difference between megawatts and gigawatts are not massive (they are).



For those of us that work in the energy industry, these numbers are much more tangible and easy to understand. However that does not describe a majority of citizens who are having these statistics thrown at them all the time, so this article will serve as a reference and allow you to re-up your energy statistics literacy.

The Basics

Energy vs. Power

The cardinal sin when dealing with energy units is confusing energy and power, a mistake that is unfortunately one of the most common as well. Even in mainstream news articles, it is not uncommon to see the total energy used for something to be listed in watts or vice versa (e.g., this article quotes the rate of energy use of a soccer stadium in kilowatts per hour, which you will shortly understand to be nonsensical if taken literally). So clearing up the confusion here is top priority.

The technical definitions of energy and power, according to the Energy Information Administration (EIA), are as follows:

Energy: The capacity for doing work as measured by the capability of doing work (potential energy) or the conversion of this capability to motion (kinetic energy)

Power: The rate of producing, transferring, or using energy, most commonly associated with electricity

Put simply, energy is the total work that is done while power is the rate at which that work is done. This concept can still be a bit tricky, so the easiest way to keep it straight is through metaphors. As one example, you can think of the relationship between energy and power as water flowing from a hose to a bucket. The volume of water that has been added to the bucket at any given point is comparable to the total energy use, while the rate that the water is flowing from the hose into the bucket can be considered the power. Another useful metaphor is to consider power to be the speed a car travels along a highway, while the total distance traveled would be the total energy. The main point is to think of power as a rate that is occurring with time (gallons of water per second, miles per hour) while the energy can then be thought of as that rate multiplied by the amount of time to get the total quantity (gallons of water per second times total seconds = total gallons of water, miles per hour times total hours = total miles driven).

To bring it to real world applications of energy and power, think of a light bulb in the lamp of your living room. The light bulb might be rated at 60 Watts, which is the power rating. 60 Watts is the rate of energy use of the bulb, and if you leave it operating for 2 hours then the total energy use is 60 Watts times 2 hours or 120 Watt-hours. Watt-hours, often divided by 1,000 to be expressed in kilowatt-hours, are the total energy use you will see come up on your monthly power bill (for more real-world applications of power and energy calculations, see the recent blog post on the energy used in various Thanksgiving turkey cooking methods).

Once you understand the difference between energy and power, you will start to see them used improperly all too often.

SI units vs. Imperial units vs. every other type of unit

To anyone who has to deal with the variety of units available to measure the same quantity, it can seem very confusing and unnecessary. Certainly it would be easier if everything and everyone used the same units and no conversion was needed. Unfortunately, that is not the world we live in for a variety of reasons– everyone has seen or heard how hard it has been to try to get the metric system adopted in the United States.

The reality is that there are many different units because these units originated at different times, by different people/industries, for different uses. The development of the metric system during the French Revolution was the first attempt to create internationally agreed upon units. Prior to that time, the world was a much larger place and it was not uncommon for units that even carried the same name to vary in actual measurement depending on where you were and who you asked. As science and trade expanded with the ever-shrinking global stage, units became more and more standardized until the International System of Units (SI) was created in the mid-20th century. These units are standard and widely accepted across the scientific landscape, no small victory for unit standardization.

Even with that success, however, many industries were already set in their way. For example, even though the automotive industry could use the widely accepted wattage to describe the power of an engine, people already understood horsepower in the context of a car. Because of the inertia and history of units like this, the implementation of the SI system did not take off in all sectors. While this may have been the easiest choice for those industries, it leaves the layperson with an alphabet soup of units and abbreviations to wrap their head around. Hopefully this article will do a small part to clearing that all up.

Prefixes

Another important part of the tangled web of units, particularly among SI and metric units, is the use of standard prefixes. Prefixes are used to take a standard unit and modify it by a power of ten. A familiar example would be the difference between a meter and a kilometer. Kilo- is the standard prefix for a multiplier of 10^3 or 1,000, which is why a kilometer equals 1,000 meters. These types of prefixes, summarized in the table below, can be applied across all sorts of units and the meaning is always the same– look at the power of ten multiplier and apply it to the unit.

The prefixes at the extreme of either end (such as yotta- and yocto-) are rarely used because they are so large/small that they are not needed to describe real, tangible energy/power quantities you’ll come across. The ones that are commonly used include giga-, mega-, kilo-, milli-, and micro-, and in fact some of the units described in the below tables will have those prefixes because the power-of-ten-adjusted units are more commonly used in certain applications than their base units.

Units to know

Energy

With all that background out of the way, we can look at 24 various units used to measure energy. Some of these are more common and will be familiar to most people, others are more niche and relate to specific industries or fields of study, while others still are rarely used but are still interesting to consider. Again keep in mind you may run across more units made up of the measures below combined with one of the prefixes above– simply use the prefix multiplier to modify the designated unit in the below table.

This first table will list these energy-measuring units, from smallest to largest, along with the manner in which they are typically used, the qualitative fundamental equivalence by definition, and the standard quantitative reference.

Table 2: Units of Energy Across Industries and Applications

UnitAbbreviationTypical useFundamental equivalenceStandard Reference
electronvolteVUsed by astronomers to measure energy of electromagnetic radiation, as well as to describe the difference in atomic/molecular energy states.

Also used by particle physicists to measure mass (based on E=mc 2 )
Amount of energy one electron acquires from accelerating through one volt1.602 x 10^ -19 Joules
RydbergRyUsed by chemists and physicists to claculate the energy levels in that are absorbed or emitted as photons as electrons move between energy levels of a hydrogen atomGround-state energy of an electron in the Bohr model for the hydrogen atom13.605693009 eV
HartreeEhUsed in calculating energy of molecular orbitsThe electic potential energy of the hydrogen atom in ground state (and thus double E h )27.211 eV
ergergNot commonly used today, but can still be found in old European scientific papersAmout of energy used when a force of one dyne is exerted over one centimeter 100 nanojoules
jouleJUsed in electricity, mechanics, thermal energy, and other basic sciences on a small scaleAmount of energy transferred to an object when a force of one newton acts on the object in the direction of its motion through a distance of one meter (i.e., one Newton-meter)As the SI unit of measurment for energy, considered the base use unit of all energy and is the common reference for other units of energy
foot-pound forceft*lbUsed to describe muzzle energy of a bullet in small arms ballistsAmount of energy transferred to an object when applying one pound of force over a distance of one foot1.35581795 Joules
thermochemical calorie**cal thUsed in chemistry to describe the energy released in a chemical reactionAmount of heat/energy needed to raise the temperature of 1 gram of water 1 o C (at 17 o C)4.8140 Joules
gram calorie**calUsed in chemistry to describe the energy released in a chemical reactionAmount of heat/energy needed to raise the temperature of 1 gram of water 1 o C (from 14.5 to 15.5 o C)4.8155 Joules
British thermal unitBTUUsed as a common unit of energy content by industry and analysts to compare energy sources or fuels on an equal basisAmount of heat/energy needed to raise the temperature of one pound of water by 1 o F1,055 Joules
Watt-hourWhUsed commonly in electrical applications Amout of energy used when one Watt of power is expended for one hour3,600 Joules
food Calorie, or kilocalorie**kcalIn common practice, nutritional calories are referring to these kilocalories (or Calorie, capitalized) as a means to measure the relative heating/metabolizing energy contained within a foodAmount of heat/energy needed to raise the temperature of 1 kilogram of water 1 o C (from 14.5 to 15.5 o C)1,000 thermochemical calories
gram of TNTg of TNTUsed to compare the relative size of explosions based on their release of energyAmout of energy in the explosive yield of one gram of Trinitrotoluene (TNT)4,184 Joules
(The real use of a gram of TNT would result in a range of energy outputs between about 2,700 and 6,700 Joules, so the actual conversion was somewhat arbitrarily defined as 4,184 Joules or exactly 1 kilocalorie)
megajoulesMJUsed to describe the energy content of liquefied petroleum gas (LPG) and natural gas in the context of gas heaters in buildingsOne million times the amount of energy transferred to an object when a force of one Newton acts on the object in the direction of its motion through a distance of one meter (i.e., one Newton-meter)1.0 million Joules
horse-power hourhphUsed in railroad industry to describe a performance-use basis when companies lend locomotives to others (e.g., Railroad A lent Railroad B a 4,000 horsepower locomotive to use for 2 hours, Railroad B now owes Railroad A a payback favor of 8,000 horsepower-hours)Amount of work that can be done (or energy that can be expended) by a horse over one hour2.686 x 10^6 Joules
kilowatt-hourkWhThe common unit of measure used as a billing unit for electricity delivered to consumersAmount of energy if a constant power of one kilowatt is transmitted for one hour3.6 x 10^6 Joules
kilogram of hard coalkg of hard coalUsed within the coal industry to compare the energy output of other fuel types to the output of a standard measure of coalAmount of energy emitted when burning one kilogram of coal7,000 kilocalories
ThermthmUsed by natural gas companies to convert volume of gases to its equivalent ability to heatAmount of heat energy from burning 100 cubic feet of natural gas100,000 BTU
gasoline gallon equivalentGGEUsed to compare the cost of gasoline with other fuels that are sold in different units for internal combustion enginesAmout of energy equivalent to that found in one liquid gallon of gasoline5.660 pounds of natural gas
gigajoulesGJUsed on a global scale to compare the amount of energy used by different nations over given time periodsOne billion times the amount of energy transferred to an object when a force of one Newton acts on the object in the direction of its motion through a distance of one meter (i.e., one Newton-meter)1.0 billion Joules
ton of TNTton of TNTUsed to describe the energy released in an explosionAmount of energy released in the detonation of a metric ton of TNT4.184 Gigajoules
barrels of oil equivalentBOEUsed by oil and natural gas companies (and analysts of those industries) that have access to both fuel types to describe the overall energy content of their reserves in a simple, single numberAmount of energy equivalent to that found in a barrel of crude oil (42 gallons); for natural gas, the conversion is to about 6,000 cubic feet of natural gas5.8 million BTU*
Ton of coal equivalentTCEUsed to describe very large amounts of energy output on a national or global scale with coal as the reference pointAmount of energy generated from burning one metric ton of coal0.697 tonne of oil equivalent (according to World Coal Association)
0.700 tonne of oil equivalent (according to International Energy Agency)
tonne of oil equivalentTOEUsed to describe very large amounts of oil or natural gas, either in terms of trade and transportation or natural production/consumptionAmount of energy equivalent to that found in one tonne (i.e., a metric ton, or 1,000 kilograms) of crude oil7.33 BOE (according to SPE)
41.868 GJ (according to OECD)
10.0 kcal (according to IEA)*
quadquadUsed by the Department of Energy and others in the field to discuss the total energy production and use across the globeEqual to exactly 10 15 BTU, i.e., one quadrillion BTU (quad for short)1,000,000,000,000,000 BTU

*These values are approximate because different grades of oil/gas have slightly different energy equivalents, and thus different agencies/bodies sometimes use slightly different measures of them.

**It’s important to note the difference between calories and Calories– Calories with a capital C are the nutrtional Calories everyone is familiar with counting on diets. These Calories are actually known as kilocalories and are 1000 thermonuclear calories, so do not mix up Calories and calories…

To make some more sense of this array of units, both massively large and incomprehensibly small, the following table puts the units into some more context. In this table, you’ll find a real-world example of what can be done with a single unit of that energy measurement, how many Joules it equates to for comparison’s sake, and the multiplier needed to get from the previous unit of energy to that one.

Click to enlarge

Power

The same exercise can be done for units of power (or rate of energy over time), as there are just as many different units for various industries, applications, and technical necessities. For power, we’ll focus on 17 of the more commonly used units– though remember you might come across all of them modified by the previously discussed prefixes.

Again, this first table will list all the power-measuring units, from smallest to largest, along with the manner in which they are typically used, the qualitative fundamental equivalence by definition, and the standard quantitative reference.

Table 4: Units of Power Across Industries and Applications

UnitAbbreviationTypical useFundamental equivalenceStandard Reference
erg per seconderg/sNot commonly used today, but in old scientific papers could be used to express power on an atomic scaleAmout of power used when a force of one dyne is exerted over one centimeter in one second100 nanowatts
milliwattmWUsed to measure the power needed by very small electrical components, such as small lasers to read CDsEqual to one thousandth of a Joule per second, or the work/power needed to hold an object's velocity constant at one meter per second against a constant force of one thousandth of a Newton0.001 Watts
dBmdBmUsed as a measure of power in wires in radio, microwave, and fiber-optic networksdBm is measured as the decibals relative to one milliwatt on a logarithmic scale, where the dBm of a power P in millwatts equals 10 x log(P)Not applicable because of the log-based scale. While 1 dBm is about 1.3 milliwatts, 50 dBm is 100 Watts and -50 dBm is 10 nanowatts.
Foot-pounds per minuteft*lb/minCommonly used as a mesaure of power in the foot-pound-second (FPS) unit system, which was the most common scientific unit system in English publications until the mid-1900s. The work done to apply a force of one pound-force over a linear dispalcement of one foot over the course of a minuteConsidered the base use unit for power in the FPS system, others reference the foot-pound per minute
kilowatt-hour per yearkWh/yEnergy consumption of some household appliances is often expressed based on the kilowatt-hours used over the course of a year given certain assumptions (kWh/y of a washing machine based on 180 standard cleaning cycles). While this may appear to be an energy unit and not a power unit, the time component of hour of kWh and the year cancel out to leave you with a measure of power-- which is what this measure really is, an understandable way to compare the power rating of various appliances Based on the assumptions given by the particular appliance label, each additional kWh/y is another expected kilowatt-hour to show up on your power bill over the course of an entire year with typical appliance use1 kilowatt-hour per year divided by 8,760 hours per year, or about 0.114 Watts
British Thermal Units per hourBTU/hOften used as the power rating for furnaces and other large heating systemsAmount of power needed to raise the temperature of one pound of water by 1 o F over the course of an hour1,055 BTU/hr divided by 3,600 seconds/hr, or 1055/3600 Joule/second which equals about 0.293 Watts
WattWUsed as the basic measurement of electrical power in small household-sized applicationsEqual to one Joule of energy per second, or the work/power needed to hold an object's velocity constant at one meter per second against a constant force of one NewtonAs the SI unit of measurement for power, considered the base use unit of all power and is the common reference for other units of power
kilocalories per hourkcal/hUsed to measure the metabolic rate of the human body, that is the amount of Calories your body will burn per hour doing various activities (e.g, exercising, sleeping, etc.)The amount of work needed to increase the temperature of one liter of water by 1 o C over the course of an hour1,000 calories per hour
calories per secondcal/sUsed by chemists when describing the rate of heat/energy transfer in chemical reactionsAmount of power needed to raise the temperature of 1 gram of water 1 o C (at 17 o C) over the course of 1 second4.184 Watts
Metric horsepowerPSUsed for advertising in the same applications as mechanical horsepower but in countries who use the metric system (often leading to confusion and mixing up the units, though the official horsepower ratings of engines are typically conservative enough that it's not overpromising power0Equal to the power required to raise a mass of 75 kilograms over a distance of one meter in one second75 kilogram*meters per second
Mechanical HorsepowerhpUsed to measure the output shaft of an engine, turbine, or motor in applications from cars and trucks down to chain saws and vacuum cleanersWhen invented by James Watt (inventor of the steam engine), it was derived by calculating the average work a pony at a coal mine could do in a minute and then increasing that by 50 percent33,000 foot pounds per minute
Electrical horsepowerhp(E)Used in the United States for the nameplace power output capacity of electrical motorsIntended to be equivalent in use to the mechanical horsepower, but is defined as exactly 746 Watts746 Watts
kilowattkWTypically used to describe power output of engines, motors, and other machinery. The work done to apply a force of one thousand pounds-force over a linear dispalcement of one foot over the course of a minute1,000 Watts
Tons of refrigerationTRUsed to rate the power of commercial refrigeration systemsThe power needed to freeze a short ton of water at 0 o Cover a 24 hour period12,000 BTU/hr
Boiler horsepowerhp(S)Used to denote a boiler's capacity to deliver steam to a steam engineEqual to the thermal energy rate required to evaporate 34.5 pounds of fresh water at 212 o F in one hour33,475 BTU/h
megawattMWUsed to describe the power used by very large electical equipment and vehicles, such as warships, super colliders, electric trains, or large commercial buildingsThe work done to apply a force of one million pounds-force over a linear dispalcement of one foot over the course of a minute1,000,000 Watts
gigawattGWDenotes the power output of large power plants and electrical capacity on a national scaleThe work done to apply a force of one billion pounds-force over a linear dispalcement of one foot over the course of a minute1,000,000,000 Watts

Again, a useful way to make sense of all these power units is to give them more meaningful context. The next table shows some of the real world examples of these different levels of power output, converts them all to Watts for the sake of comparison, and the multiplier between two consecutive units.

Click to enlarge

Conclusion

Armed with the knowledge of these units of energy and power, you’ll be well prepared to tackle statistics anew– you’ll have useful context for how much energy was in the recent 5,000 barrel oil spill on the Keystone Pipeline (using the above information, we can calculate that 5,000 barrels of oil is over 30,000 Gigajoules– or equivalent to the average annual electricity consumption of over 700 American households), or you’ll also have not so useful (but fun!) context for the energy content of a gallon of gasoline (the same as over 127 slices of large cheese pizza or 30 kg of TNT).  Either way, being literate in your scientific and energy-related units will make you a more informed consumer of the news– if only everyone editing the news could do the same and stop using ‘Watts per hour’!

Sources and additional reading

A Megajoule or MJ Probably Isn’t What You Think: Elgas

Aqua-calc: Conversions and Calculations

Arkansas State Energy Profile: Energy Information Administration

Ask Trains from December 2007: Trains Magazine

Atomic Units: Nature

Barrel of Oil Equivalent: Investopedia

Blast effects of external explosions: Isabelle Sochet

Bluetooth range and Power: Electronics Stack

Brief history of the SI: National Institute of Standards and Technology

British Thermal Units (BTU): Energy Information Administration

By gum! Chewing to power your hearing aid: CNBC

Calorie: Encyclopedia Britannica

Choose the right charger and power your gadgets properly: Wired

Coal conversion statistics: World Coal

Coal equivalent: European Nuclear Society

CODATA Recommended Values of the Fundamental Physical Constraints

Conversion factors: Organization of Petroleum Exporting Countries

Electron Volt: Universe Today 

Elephants: San Diego Zoo

Energies in Electron Volts: Hyper Physics

Energy Conversion Calculators: Energy Information Administration

Energy Examples: Genesis Now

Energy Units: APS Physics

Energy Units and Conversions: Dennis Silverman

erg: WhatIs.com

Eu Energy Labels: What does kWh/Annum mean?

Exploding Laptop Batteries

Foot-Pound Force Per Minute: eFunda

Frequently Asked Questions: Energy Information Administration

Glossary: Energy Information Administration

Horsepower-hour: Collins Dictionary

Horsepower: Encyclopedia Britannica

How Hard Does It Hit? Jim Taylor

How Horsepower Works

How Many Calories Are Burned By Coughing? LiveStrong

How Many Calories Do You Burn Doing Everyday Activities?

How Many Flies Would It Take To Pull A Car? Neatorama

How much electricity does a solar panel produce? Solar Power Rocks

How much energy do my household appliances use? Energy Guide

Is it really worth my time to eat that last grain of rice?

Joule: techopedia

Launching satellites: Science Learning Hub

Measuring energy: IEEE 

Metric Conversions

Nanotechnology Introduction: Nanotechnology Now

NIST Guide to the SI: National Institute of Standards and Technology

Nonconventional Source Fuel Credit

One Calorie is Equivalent to One Gram of TNT In Terms of Energy: Today I Found Out

Papa John’s Nutritional Calculator

Physical Phenomena: University of Sydney

Physlink

Projectiles, Kinetic/Muzzle Energy and Stopping Power

Report of the British Association for the Advancement of Science

Rydberg: Wolfram Research

Rydberg Constant: National Institute of  Standards and Technology

Rydberg Unit of Energy: Energy Wave Theory

The Adoption of Joules as Units of Energy: FAO

Tonne of coal equivalent: Business Dictionary

Tonne of oil equivalent: Organization for Economic Cooperation and Development

Turning sweat into watts: IEEE

Understanding Energy Units: Green Building Advisor

Unit Conversion Factors: Society of Petroleum Engineers

Unit converter: International Energy Agency

USB Flash Drives: AnandTech

watt-hour (Wh): WhatIs.com

What’s a hartree? National Institute of Standards and Technology

What is a Joule? Universe Today

What is a GJ? Natural Resources Canada

What is a Ton of Refrigeration: Power Knot

What is a Watt, Anyway? Building Green

What is a Watt Hour? SolarLife

What is resting metabolic rate?

Why Do We Use a Dumb Unit to Measure Explosions? Gizmodo

About the author: Matt Chester is an energy analyst in Washington DC, studied engineering and science & technology policy at the University of Virginia, and operates this blog and website to share news, insights, and advice in the fields of energy policy, energy technology, and more. For more quick hits in addition to posts on this blog, follow him on Twitter @ChesterEnergy.