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.  

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