musingsheader image
Helpful? 0

Understanding Energy Units

Don't confuse energy and power — it's important to know the difference between Btu and Btu/h, as well as kW and kWh

Posted on Jun 22 2012 by Martin Holladay, GBA Advisor

If you’ve ever been confused by the difference between 500 BtuBritish thermal unit, the amount of heat required to raise one pound of water (about a pint) one degree Fahrenheit in temperature—about the heat content of one wooden kitchen match. One Btu is equivalent to 0.293 watt-hours or 1,055 joules. and 500 Btu/h, you probably can use a handy cheat sheet to explain energy units. As a guide through the thorny thickets of energy, power, and the units used to measure them, I’ve assembled some questions and attempted to answer them.

What’s the difference between energy and power?

Energy is the amount of heat or work that can be obtained by burning a certain amount of fuel. Energy is measured in a variety of units, including kilowatt-hours (kWh), Btu, and joules. A quantity of energy can also be expressed in terms of barrels of oil, gallons of gasoline, or cords of firewood.

A unit of energy can be bought or sold. For example, electricity is usually sold by the kWh. Your electric bill includes a monthly tally of the number of kWh you used. If you are charged $80 for 800 kWh, then each kWh costs you 10¢.

A Btu (British Thermal Unit) is the amount of heat necessary to raise one pound of water by 1 Farenheit degree. A joule is the work done by a force of one newton for a distance of one meter.

Power is different from energy. Power is the rate at which energy is burned or used (or, more precisely, the rate at which energy is converted from one form to another). In other words, power is a measure of how quickly work can be performed; Power = Energy/Time, and Energy = Power × Time. Power is measured in watts, kilowatts, horsepower, Btu/h, tons of cooling, and foot-pounds/minute.

Appliances are usually rated by their power consumption. When we talk about a 100-watt light bulb, we are describing it by its power rating. Furnaces also have power ratings — for example, a furnace can be rated at 40,000 Btu/h. If the power rating is high, the appliance uses energy at a fast rate; if the power rating is low, it uses energy at a slow rate. So we can say that a 20-horsepower tractor is more powerful than a 12-horsepower tractor; we can also say that a 2,000-watt hairdryer is more powerful than a 1,000-watt hairdryer.

If you turn on a 1,000-watt hairdryer for one hour, you’ve used a kilowatt-hour. While it’s possible to buy a kilowatt-hour, you can’t buy a kilowatt.

When dealing with electricity, Power (in watts) = Current (in amperes) × Voltage. One watt is the power from a current of 1 ampere flowing through 1 volt. (An ampere is the unit used to measure the flow of electricity, or current. Amperes measure the rate of electron flow.)

Lots of people are confused by energy and power units. Don’t be one of them — or you'll risk ending up on the Power and Energy Hall of Shame. Remember, there is no such thing as kilowatts per hour or watts per hour.

Can you provide some analogies to clarify these energy units?

Yes. Here’s one: energy is a measurable quantity and can therefore be compared to distance. In this analogy, power (which is a rate) is like speed.

I especially like plumbing analogies, because I was a plumber before I was an electrician. If you are comparing electricity to piped water, here’s how the analogy works:

  • Kilowat-hours (energy) are like gallons of water.
  • Kilowatts (power) are like gallons per minute.
  • Voltage is like water pressure.
  • Wire gauge is like pipe diameter.

A tap that delivers a generous flow of water is like an appliance using a lot of watts. A tap delivering a trickle of water is like an appliance using few watts.

So, if you need 10 gallons of water per minute, you can deliver it with a fat pipe operating at low pressure, or with a skinny pipe operating at high pressure. Similarly, you can obtain 1,000 watts of electric heat from a low-voltage appliance with a large-gauge wire or from a high-voltage appliance with a small-gauge wire.

How do I convert energy units?

Here are some handy conversion factors for energy units:

1 kWh = 3,413 Btu
1 kWh = 3,600,000 joules
1 joule = 1 watt-second
1 Btu = 1,055 joules
1 Therm = 100,000 Btu = 29.3 kWh
1 calorie = 4.184 joules
1 Btu = 252 calories

Note: Try to avoid using the abbreviation MBtu, since this unit has two definitions. One MBtu can mean either 1,000 Btu or 1,000,000 Btu; that’s reason enough to stay away from MBtu.

How do I convert power units?

Here are some handy conversion factors for power units:

1 watt = 1 joule/second
1 watt = 3.413 Btu/h
1 Btu/h = 0.2931 watt
1 kW = 1,000 watts
1 megawatt (MW) = 1,000,000 watts
1 kW = 3,413 Btu/h
1 ton of cooling = 12,000 Btu/h
1 horsepower (electric) = 746 watts

What’s the energy content of common fuels?

A gallon of propane isn't equivalent to a gallon of fuel oil, because fuel oil packs more Btu per gallon than propane. To compare different fuels, use this handy guide.

Natural gas: 1,000 Btu/cu. ft.
Propane: Between 91,333 Btu/gallon and 93,000 Btu/gallon
Fuel oil: Between 138,700 Btu/gallon and 140,000 Btu/gallon
Kerosene: Between 120,000 Btu/gallon and 135,000 Btu/gallon
Gasoline: Between 114,000 Btu/gallon and 125,000 Btu/gallon
Coal: 25,000,000 Btu/ton
Seasoned dense hardwood firewood: Between 21 and 26 million Btu/cord
Seasoned pine firewood: Between 14 and 16 million Btu/cord

Here are some useful conversion factors used for measuring natural gas:
1 ccf (“centi- cubic feet”) = 100 cubic feet
1 cubic foot of natural gas = 1,000 Btu = 0.01 Therm
1 Therm = 1 ccf of natural gas = 100,000 Btu = 29.3 kWh

What about air pressure units?

The question is a little off-topic, but why not address it anyway? Here are some conversion factors:

1 atmosphere = 14.7 lb./sq. in. = 760 mm. of mercury = 406.78 in. of water = 101,325 Pascals
1 Pascal = 0.00401 in. of water
1 lb./sq. in. = 6,894.76 Pascals
1 lb./sq. ft. = 47.88 Pascals

According to the formula in Meteorology Today by C. Donald Ahrens, wind speed in miles per hour multiplied by itself and then by 0.004 gives the wind’s pressure in pounds per square foot.

What about converting units used to measure fan performance?

Here are some conversion factors:

1 cubic foot/minute (cfm) = 0.472 liter/second
1 liter/second = 2.12 cfm
1 liter/minute = 0.03531 cfm
1 cubic meter/hour = 0.588 cfm

What’s the difference between “site energy” and “source energy”?

Site energy is the amount of electricity and fuel consumed at a building. For example, in one year a house might require 12,000 kWh of electricity and 500 gallons of fuel oil. These quantities represent the amount of site energy consumed by the house; if we convert both types of energy to Btu, the house used 40,956,000 Btu + 69,500,000 Btu = 110,456,000 Btu of site energy.

Source energy is a calculation of the amount of fuel required to produce the energy consumed at a given site. Of all of the fuels, electricity has the biggest discrepancy between site energy and source energy — that is, the biggest “site/source ratio” — because most fuel-burning power plants require 3 or more units of fuel to produce 1 unit of electricity. (The energy that isn’t converted to electricity is lost as waste heat.) Different power plants have different conversion efficiencies, so calculating source energy can be tricky; the site/source ratio for electricity varies by state and even by time of day.

When primary energy (for example, fuel oil or natural gas) is consumed at a house, the conversion to source energy must account for losses that occur during storage, transport, and delivery of the fuel to the building. The site/source ratios for natural gas and fuel oil burned in a building are much lower than the site/source ratio for electricity produced at a fuel-burning power plant.

In the case of the house that uses 110,456,000 Btu of site energy each year (the example given above), it might require 40,080 kWh of coal (in other words, 136,793,000 Btu of coal) to generate 12,000 kWh of electricity for the house. Moreover, it might require 70,195,000 Btu of energy to deliver 69,500,000 Btu of fuel oil to the house. So the house in this example used 136,793,000 Btu + 70,195,000 Btu = 206,988,000 of source energy. That’s considerably more source energy than site energy.

The Energy StarLabeling system sponsored by the Environmental Protection Agency and the US Department of Energy for labeling the most energy-efficient products on the market; applies to a wide range of products, from computers and office equipment to refrigerators and air conditioners. program assumes the following site/source ratios (based on national averages): grid electricity, 3.34; natural gas, 1.047; and fuel oil and propane, 1.01. In other words, it takes 1.047 units of source energy to deliver 1 unit of natural gas to a building.

Another source provides the following site/source ratios for the U.S.: grid electricity, 3.365; natural gas, 1.092; fuel oil, 1.158; propane, 1.151.

Average energy use per person

A nonprofit group in Switzerland, the 2,000-Watt Society, has calculated that the current level of worldwide energy use amounts to 2,000 watts per capita. This is the total amount of energy used continuously, on average, by one person, as long as the person is alive. The amount includes energy used for industry, commercial buildings, residential buildings, municipalities, and transportation — everything.

Per capita energy use in the U.S. is significantly above the world average, of course. The average American uses about 12,000 watts — six times the world average. In Bangladesh and sub-Saharan Africa, on the other hand, the figure is well under 500 watts per person.

It’s hard to understand the quantity of the energy used by a typical U.S. family, but here’s a mental exercise that helps: how big a photovoltaic(PV) Generation of electricity directly from sunlight. A photovoltaic cell has no moving parts; electrons are energized by sunlight and result in current flow. array would be needed to provide all of the energy used by the average American?

Let’s assume the American lives in Chicago. A person using 12,000 watts requires 288 kWh/day or 105,120 kWh/year. In Chicago, that much energy could be produced by a 90-kW PVPhotovoltaics. Generation of electricity directly from sunlight. A photovoltaic (PV) cell has no moving parts; electrons are energized by sunlight and result in current flow. array. The cost to install such a PV system would be about $405,000. A family of three would require an array costing $1.2 milllion.

Of course, this PV array would produce enough energy to cover every aspect of one’s life, including one’s transportation and a personal share of the energy used for U.S. manufacturing.

Last week’s blog: “Joe Lstiburek Discusses Basement Insulation and Vapor Retarders.”

Click here to follow Martin Holladay on Twitter.


Tags: , , , , , , , ,

1.
Fri, 06/22/2012 - 10:14

Energy tech....mmmm.....MORE! And found Hall of Shame error...
by Dustin Harris

Helpful? 0

Hall of Shame has explanation of HowStuffWorks.com error, but that seems to have an error itself:
"resulting in a respectable average capacity factor of 43% (2,633 TWh / (675,000 MW * 8760 hrs/yr)".

According to my math, this works out to units of "per hour" rather than dimensionless...or was this another error they were highlighting and I'm simply confused?

We seem to often fall into forgivable shortcuts that are technically inaccurate, such as writing kw-hr rather than kw.hr, but I always find the common "measure X will save Y gigawatts by the year Z" hard-to-interpret & really irritating.


2.
Fri, 06/22/2012 - 11:53

Hall of Shame math
by Cramer Silkworth, PE

Helpful? 0

Dustin,

I think Hall of Shame's math works fine, (TWh/yr)/(MW x hrs/yr) fully cancels (once you adjust the Tera- and Mega- to the same units). Though I get 44.5%, not 43%....but anyway.

Now if you'll excuse me, I need to go turn on my "8,000 Btu" air conditioner... :)


3.
Fri, 06/22/2012 - 12:58

Edited Fri, 06/22/2012 - 12:58.

KW per Hour
by Alex A

Helpful? 1

Martin wrote that "there is no such thing as kilowatts per hour"

Technically there is such a thing... kilowatts per hour is a unit of change in power over time. So if, for example, your wind farm went from 4 MW to 2 MW over 2 hours, you could say it lost capacity at a rate of 1 MW per hour.

That's definitely "a thing," It's just not what people usually mean when they mistakenly say "KW per hr."


4.
Fri, 06/22/2012 - 13:24

Response to Alex A
by Martin Holladay, GBA Advisor

Helpful? -1

Alex,
You're right -- KW/h is a measure of acceleration, like m/sec² (meters per second squared).


5.
Fri, 06/22/2012 - 13:28

Unit of electrical charge, amp-hour
by aj builder, Upstate NY Zone 6a

Helpful? 0

Martin, another useful blog thanks. Small correction needed. Nix Amp-hour from your intro to energy unit terms. It is to do with units of electrical charge. Amp-hours your readers know about are ratings on car batteries and can help determine energy within the battery if one knows the voltage of the battery such as a 1 volt battery or a 12 volt battery.

For example; a higher voltage battery with the same amp-hour rating holds more energy than a lower voltage battery, so knowing amp-hours is not knowing energy amounts if the voltage is not known.

Might be best just to strike amp-hour from your second paragragh....

I hope I am explaining this close to right... been close to wrong too often!


6.
Fri, 06/22/2012 - 13:36

Response to AJ
by Martin Holladay, GBA Advisor

Helpful? 0

AJ,
Thanks for noticing my error! As soon as I read your comment, I realized you were right.


7.
Sat, 06/23/2012 - 22:27

Voltage
by shane claflin

Helpful? 0

If voltage is water pressure... is amperage viscosity of fluid or is it the other way around?


8.
Sun, 06/24/2012 - 05:51

Response to Shane Claflin
by Martin Holladay, GBA Advisor

Helpful? 1

Shane,
It's just an analogy, so there is no correct or incorrect answer to your question. Amperage is the quality of the electric current that causes the conductor to get hot. I can't think of a direct correlation that works with my plumbing analogy -- but I'm open to suggestions.


9.
Sun, 06/24/2012 - 09:25

to Cramer Silkworth, PE: you changed units...
by Dustin Harris

Helpful? 0

You changed units from TWh / (MW *hrs/yr) to TWh/MWh....

But I was wrong as well: the answer comes out in units of years rather than 1/years (as I said) rather than dimensionless (as they said)...


10.
Sun, 06/24/2012 - 09:32

Martin: amperage analog
by Dustin Harris

Helpful? 0

Wouldn't amperage (coulombs per second) be analogous to gallons per minute? Each is flow, is limited by capacity of the conductor, and is reduced by internal friction that converts energy to heat. Further, each increases with pressure/voltage and each gallon/coulomb carries more energy with higher pressure/voltage.


11.
Sun, 06/24/2012 - 10:39

Edited Sun, 06/24/2012 - 10:40.

Response to Dustin Harris
by Martin Holladay, GBA Advisor

Helpful? 0

Dustin,
My house has two types of wiring: 12 VDC and 120 VAC. My motto is, "A watt is a watt is a watt." But it isn't true that "an amp is an amp is an amp."

10 amps at 120 volts is a lot more power (1,200 watts) than 10 amps at 12 volts (120 watts). So the gallons per minute analogy doesn't hold. As I said in my earlier example, if I want 10 gpm, I don't really care if it comes at high pressure through a thin tube or low pressure through a fat tube. But if I want to make toast with a toaster, 10 amps at 120 volts is going to work a lot better than 10 amps at 12 volts.


12.
Sun, 06/24/2012 - 11:57

Viscosity would be like
by aj builder, Upstate NY Zone 6a

Helpful? 0

Viscosity would be like resistance


13.
Mon, 06/25/2012 - 09:06

amperage
by shane claflin

Helpful? 0

amperage could be turbidity of water :)


14.
Mon, 06/25/2012 - 11:20

Edited Mon, 06/25/2012 - 11:24.

Martin, I think we are using different units...
by Dustin Harris

Helpful? 0

I think our difference stems from our watts analogy.
gallons = coulombs & voltage = pressure, thus
gpm=amps
gpm X pressure = watts

I believe you are using gpm while I am using gpm X water pressure.

Imagine running a power distribution system of pipes and water. The power delivered would be gallons/minute (amps) times pressure (volts). You wouldn't really care (as far as watts goes) how if it is 1 gpm at 100psi or 10 gpm at 10psi....but the plumbing would need to be far larger to deliver the same watts at 10psi than at 100psi, just as you need fatter wire for 1000watts at 12 volts (80amps) than at 120 volts (8amps).


15.
Mon, 06/25/2012 - 11:43

Response to Dustin Harris
by Martin Holladay, GBA Advisor

Helpful? 0

Dustin,
Analogies are a kind of poetry, not mathematics, so I don't know if there is a single answer to this analogy disagreement.

However, I'm still don't think I agree with your suggestion, "Wouldn't amperage be analogous to gallons per minute?" Depending on the voltage, a fixed amperage results in either low power (few watts) or high power (many watts). Watts are what I want when I turn on my toaster.

When I am filling my bathtub, what I want is gallons per minute. As long as I'm getting so many gallons per minute, I'm happy.


16.
Mon, 06/25/2012 - 16:30

Edited Mon, 06/25/2012 - 21:58.

GPM is analogous to amps but
by aj builder, Upstate NY Zone 6a

Helpful? 0

GPM is analogous to amps but we are straying off topic just a bit.

Just thinkin Martin, don't be filling that tub, with amps.... stick to the GPMs...


17.
Tue, 06/26/2012 - 10:52

Watts
by Pat Murphy

Helpful? 0

You note that a person using 12,000 watts, which I must acknowledge that I don't understand since I only consume kWhs, would have to pay $405,000 to get that from PV. I would appreciate a more detailed analysis of that, for example how my 1,000 kwH per year and my 500 gallons of gasoline per are calculated and how they relate to 12,000 watts.


18.
Tue, 06/26/2012 - 11:16

Edited Fri, 02/15/2013 - 10:32.

Response to Pat Murphy
by Martin Holladay, GBA Advisor

Helpful? 0

Pat,
Q. "You note that a person using 12,000 watts, which I must acknowledge that I don't understand since I only consume kWhs."

A. To convert watts to kW, you divide by 1,000, so 12,000 watts = 12 kW. In 24 hours, an American who uses 12,000 watts (12 kW) is using 288 kWh (12 kW x 24 hours). Each month, that person uses about 8,928 kWh (288 kWh x 31 days). Each year, that person is using 105,120 kWh (288 kWh x 365 days).

Q. "For example, how [is] my 1,000 kwH per year and my 500 gallons of gasoline per year calculated and how [do] they relate to 12,000 watts?"

A. Gasoline has about 120,000 Btu/gallon, so your 500 gallons of gasoline are equivalent to 60,000,000 Btu. Since 3,413 Btu = 1 kWh, your 500 gallons of gasoline are equivalent to 17,580 kWh. If you want to combine your annual electrical consumption (1,000 kWh) and your gasoline consumption (17,580 kWh), you get a total of 18,580 kWh.

As an American, you are consuming 105,120 kWh/year. If 18,580 kWh represents your automobile budget and your residential electricity budget -- that's less than average -- then the rest (86,540 kWh) is your share of the energy used by the U.S. military, Coca-Cola, Archer Daniels Midland, the offices of the State of California, your local public library, Amtrak, John F. Kennedy airport, WalMart, and so on...


19.
Tue, 06/26/2012 - 17:09

MMMMMMMMMBtus
by Kohta Ueno

Helpful? 0

Martin--nice column as always!

Try to avoid using the abbreviation MBtu, since this unit has two definitions. One MBtu can mean either 1,000 Btu or 1,000,000 Btu; that’s reason enough to stay away from MBtu.

This MBtu vs. MMBtu system has long driven me nuts, and I agree we should try to get away from it. Just to keep the readers informed of the back story--they are not using M = mega = 1,000,000 times (which would analogously use k = kilo = 1000 times). Instead, they are using it as Roman numeral M = 1000, as in "this film was produced MCMXXXLIV"). So in this system, MBtu = 1000 Btu. However, if you use the metric prefix kBtu = MBtu = 1000 Btu. Argh!

To make it worse, the IP system uses the terminology MMBtu, which is 1,000,000 Btu. As in M times M = 1000 x 1000 = 1,000,000. Argh!

So if you interpret things poorly, an MBtu = kBtu, and an MMBtu = MBtu. Argh!

Also, in case anyone was interested, John Straube and I wrote a piece on explaining Site and Source Energy (Building Science Digest 151: Understanding Primary/Source and Site Energy.


20.
Wed, 06/27/2012 - 06:58

Argh indeed
by Martin Holladay, GBA Advisor

Helpful? 0

Kohta,
Thanks for the further details on MBTU and MMBTU.

As far as I can tell, MBTU stands for "muddled British Thermal Units."


Register for a free account and join the conversation


Get a free account and join the conversation!
Become a GBA PRO!