'Watts' the mystery? The energy units that power our lives

Energy is a complex subject, loaded with many specialized terms and a confusing array of units and inconsistent abbreviations. For example, natural gas reserves and production are usually measured in cubic feet, but natural gas is usually traded in terms of British thermal units, and it shows up on your power bill in terms of therms.

As a longtime energy journalist, I don't want to know how much of my life has been wasted puzzling over unit conversions. But it's a topic about which we all need to become more conversant. So, let me save you some trouble with a short primer on fundamental energy units and conversions. It's not a comprehensive guide, but once you get familiar with these terms, hopefully you can read and convert them like a pro. Bookmark and refer back to this primer, and never be confused again!

Units you need to know

Some fuels are discussed in volumetric units, such as tons (or the metric tonne) or barrels. Others are referenced in terms of heat (thermal) values. (Heat values can actually get quite complicated with various "low heating values" and "high heating values" for different grades of fuels, but we won't go there in this primer.) Here are the most common units (listed alphabetically):

• barrel: Oil reserves are usually measured in barrels, which are equivalent to 42 US gallons. Barrels are abbreviated "bbl." Sometimes barrels are given as barrels of oil equivalent (boe) when a quantity of liquid fuel is biofuel or oil mixed with natural gas liquids or something else. A thousand boes are sometimes abbreviated as kboe; a million barrels as Mb or Mboe; and a billion barrels (one gigabarrel) as Gb or Gboe.
  Similar to the Btu conventions described below, millions of barrels are often abbreviated MMBbl by energy experts, and MBtu by non-experts. There are even more variations to describe production rates. All of the following are used to mean "million barrels per day": mb/d, MMBbl/d, mbpd, Mbd, mbd, Mboe/d and mboe/d. There are probably more I can't think of right now. All I can say is: it sucks. Just try to understand the context of the figure you're reading and do a simple spreadsheet reality check when in doubt. Years ago, I used to use mbpd to express this measure, but I switched to mb/d for consistency with other units. I wish all other energy journalists would follow my lead, because of course I'm right.

• Btu or BTU: A basic heat unit is the British thermal unit, variously abbreviated as BTU or Btu. It's the amount of energy needed to cool or heat one pound of water by one degree Fahrenheit, and is approximately the amount of heat put off by burning a single wooden match. One thousand Btu are often abbreviated MBtu, following the Roman convention of using M for one thousand. One million Btu are then stupidly abbreviated as MMBtu (for "thousand thousand BTU"). Don't ask me why, especially when so many other energy units use "k" for thousand (following the metric system convention) and "M" for million. Very large (like, global) amounts of energy are sometimes stated in quadrillion Btu, or "quads."
• calorie: A calorie is roughly the amount of energy needed to raise the temperature of one gram of water by one degree Celsius. When you read the labels on a food product, the "calories" shown are actually kilocalories (kcal), which are equal to 1,000 calories.
• joule: Another basic unit of heat commonly used internationally is the joule, abbreviated J. It is equal to an electric current of one ampere through a resistance of one ohm for one second. A kilojoule (kJ) is 1,000 joules, a megajoule (MJ) is 1,000 kilojoules, a gigajoule (GJ) is 1,000 megajoules, and a terajoule (TJ) is 1,000 gigajoules. After that, the units are petajoule (PJ), exajoule (EJ), zettajoule (ZJ), and yottajoule (YJ) ... and that's a yotta joules! At the global scale, energy is often stated in exajoules (10¹⁸ joules).
• kWh: The kilowatt-hour is the most common measure of electrical energy, and represents 1,000 watt-hours (Wh). A watt-hour is the amount of energy produced by a one-watt source running for one hour. A megawatt-hour (MWh) is one million Wh or 1000 kWh, a gigawatt-hour (GWh) is 1,000 MWh, and a terawatt-hour (TWh) is one trillion Wh, or 1,000 GWh.
• Mcf: Natural gas production is often measured volumetrically in cubic feet (cf). Thousand cubic feet (Mcf) is the most common unit (another case where "M" stands for thousand, not million.) Larger amounts of gas are million cubic feet (MMcf), billion cubic feet (bcf or Bcf) and trillion cubic feet (tcf or Tcf). Internationally, these units are often expressed in terms of cubic meters instead of feet.
• therm: Natural gas is often represented on utility bills in therms (th or thm). A therm is 100,000 Btu. 
• toe and MToe: Often used to measure coal, or to compare different fuels, these units stand for "tonnes of oil equivalent" and "million tonnes of oil equivalent," respectively. They represent the equivalent heat value of a fuel, in terms of oil. One standard toe is about 40 MMBtu, but in reality different grades of crude oil contain different amounts of heat energy. So be careful if you're comparing (for example) the energy in an MToe of Bakken light, sweet crude to the energy in an MToe of diluted bitumen from tar sands.
• tonne: Coal is often measured in by weight in metric tonnes, which are equivalent to 2204.62 pounds. (So one metric tonne is about 1.1* tons.) The heat value of coal can vary widely by the type of coal; for example, 1.5 tonnes of hard coal and 3 tonnes of lignite are each roughly equivalent to 1 toe of oil.
• watt: A watt is a unit of power* equal to one joule per second. Multiply volts with amps and you get watts. A kilowatt (kW) is 1,000 watts, a megawatt (MW) is 1,000 kilowatts, a gigawatt (GW) is 1,000 megawatts, and a terawatt (TW) is 1,000 gigawatts.

Common unit conversions

The number of units is dizzying. Fortunately, there are standard formulas for converting all units to other units. Just plug them into a spreadsheet and do some simple multiplication or division.

Here are some of my favorite rules of thumb. They're easy-to-remember, round numbers, so they're handy for doing some quick math in your head, but they're not suitable for detailed calculations.

• 1 barrel of oil is about 6 GJ
• 7 barrels of oil is about 1 toe
• 1 toe is about 42 GJ
• 1 quad is about equal to 1 exajoule
• 1 therm of natural gas is about 100 cf, or 100,000 Btu
• 1 Mcf of natural gas is roughly 1 MMBtu

Here are some more specific common unit conversions:

• 1 boe = 5.8 MMBtu
• 1 toe = 41.868 GJ = 39.68 MMBtu
• 1 mb/d = 2 quad/year
• 1 calorie = 4.1900 J
• 1 Btu = 251.9958 calories = 1,055.87 J
• 1 kWh = 3.6 x 106 J = 3,412 Btu
• 1 quad = 1.055 EJ

Converting electricity and heat units

Converting electricity to and from heat units can be a very confusing business.

If the electricity is produced from a fossil fuel, then represented in (for example) oil equivalent, the actual amount of fossil fuel consumed to make the electricity would be converted to oil equivalent (a combustion equivalent).

Similarly, if the electricity is not produced from a fossil fuel, then it would be converted to a fossil fuel unit using a combustion equivalence.

But if the source of the electricity is unknown, and you're just converting units, or if you're just looking at a total quantity of fuel consumed (for example, natural gas) without knowing how much of it was used for electricity generation and how much of it was used for something else, then you'd use the heat value equivalent of electricity, not the combustion equivalent.

For example, electricity produced from solar would be converted to Mtoe on the basis of how much oil would have to be burned in a modern thermal power station with 38 percent conversion efficiency to make the equivalent amount of electricity. By that calculation, one Mtoe of oil produces about 4,400 GWh (or 4.4 TWh) of electricity. But using a straight conversion of the heat units, one Mtoe of oil is equivalent to 12 TWh of electricity.

So if you find your calculations seem to be off by around a factor of 3, that might be your problem.

Converting fuels

For some quick fuel conversions of different fuels, here's a handy table (courtesy Dr. Tad Patzek). To find the comparative heat value of one fuel to another, look up the first fuel in the left-hand column, and get its Btu value. Then find that value in the top row, and look down the corresponding column to find the Btu equivalence of the other fuel.  

Other conversion resources

There are many unit conversion calculators online, like this one from the U.S. Energy Information Association (EIA). (Don't be ashamed to find yourself in the Energy Kids section of the EIA's site. It's a great place to learn about energy, even for adults and energy journalists!)

A comprehensive online resource is Unit Juggler. Its energy converter should do for most purposes.

The American Gas Association also has a good, simple page on measuring natural gas. 

A handy Excel file of conversion factors is included in the next-to-last tab, "Approximate conversion factors," of the Historical data workbook included in the BP Statistical Review of World Energy. That workbook is my go-to source when I need to compare different kinds of energy usage over recent history.

If you don't find what you need at those resources, just Google around a bit.

Power vs. energy

Power is a rate. Energy is a quantity. Put another way, you have the energy in your legs to walk up three flights of stairs, but not the power to leap to the top of a building.

This distinction can be particularly hard to conceptualize with electricity, since it's invisible. With electricity, it's often helpful to think of water metaphors. Volts are like water pressure. Amps are like the diameter of a hose. Watts are like the rate of the water flow.* 

Units like kW are measures of power. Units like kWh are measures of energy (like a cup of water). Power multiplied by hours gives you units like kWh. If you run a 1-kW generator for one hour, it will generate 1 kWh of energy.

Capacity vs. generation

Capacity is a measure of how much power a power plant can put out.

Generation is a measure of how much energy a power plant actually produces.

Capacity factors

The actual generation of a power plant depends on how often it runs. No power plant runs 100 percent of the time, so its actual generation is always lower than its "nameplate" power rating. To denote the amount of energy a power plant actually generates, compared to the energy it would generate if it ran full-time, we use a capacity factor.

A 1-MW plant with a 50 percent capacity factor would have the same energy output as a 2-MW plant with a 25 percent capacity factor.

For example, to calculate the energy output of a 1.5-MW wind turbine with a 30 percent capacity factor, you'd multiply the turbine's nameplate power rating by its capacity factor and the number of hours in a year:

1.5 x 0.30 x 24 x 365 = 3,942 MWh

Capacity factors tend to be fairly consistent from place to place for conventional generators, but for renewables like wind and solar, they can vary widely from place to place, and from machine to machine.**

There can be big differences between technologies too; for example, solar photovoltaic (PV) and concentrating solar thermal (CSP) systems. Making the question even more complicated, solar plants with storage capability can run when the sun is down, giving them even higher capacity factors.

The National Renewable Energy Laboratory (NREL) Transparent Cost Database has some aggregate data on capacity factors that can be useful as rules of thumb, but if you're doing careful analysis, you have to check the vintage of the data (some of it is quite old). In a sector evolving as quickly as renewables, data even one year old can be out of date.

The EIA recently started publishing monthly and annual data for utility-scale fossil fuel generators and non-fossil fuel generators, but even those data are U.S. averages. Actual capacity factors for specific wind or solar systems can vary widely. And, as I explained last July, the benefits of a specific renewable generator also vary widely from place to place, depending on what other kinds of local power it displaces.

Unfortunately, finding location- and system-specific data can be frustratingly difficult. But it's important if you're doing a detailed calculation. For example, a 2012 Lawrence Berkeley National Laboratory (LBNL) survey of U.S. utility-scale solar plants installed in 2010 found capacity factors ranging from 13.8 percent to 30.2 percent.

Capacity factors are often misinterpreted, and old capacity factor data is often the cause of incorrect conclusions about the economics and potential of renewable power systems. 

Go forth and multiply

Once you get the hang of energy units, you'll find that it's pretty straightforward stuff. You won't need any more advanced skills than basic arithmetic. Don't be afraid to pop open a spreadsheet and run some simple calculations, especially when in doubt. But mind your decimal places! Many an energy conversion goes awry at the comma or the "point."

If you have any unit questions this little primer hasn't answered, suggestions for other energy primers you'd like to see, or if (gasp) you found an error in this one, just drop me a line in the comments.

* Corrected from original

** In the original version, a comment about the increasing efficiency of renewable power collectors was inserted here. That was confusing. It has been removed. --Chris Nelder

Photo: zebbie/Flickr

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This post was originally published on Smartplanet.com