Some energy units, definitions, and conversions

Contents of this page

Power
Energy
Energy content of fuels
Energy density of some batteries
Comparisons, weight-for-weight
Compressed air and flywheels
Energy from falling water
Energy and boiling water
CO2 released per kWh
Miscellaneous
Metric system multipliers
Index

Many of my pages are concerned with energy.
This page provides readers with the relationships between some of those units, some definitions, and some values.

Created as a separate page 2005/06/09, modified 2009/03/13
Feedback welcome; email daveclarkecb@yahoo.com

Also see Wind power glossary for terms particularly relating to wind power.

Units of Power

Units of the power
1 Watt	= 1 Joule per second (J/sec)
1 kilowatt (kW)	= 1000 watts
1 megawatt (MW)	= 1000kW
1 gigawatt (GW)	= 1000MW
1 terawatt (TW)	= 1000GW

Units of energy

Units of energy
1 Watt hour (Wh)	= a flow of 1W for 1 hour (or equivalent)
1 kilowatt hour (kWh)	= a flow of 1kw for 1 hour (or equivalent)
1 megawatt hour (MWh)	= 1000kWh
1 gigawatt hour (GWh)	= 1000MWh
1 terawatt hour (TWh)	= 1000GWh
1 kilojoule (kJ)	= 1000 Joules
1 megajoule (MJ)	= 1000kJ
1 gigajoule (GJ)	= 1000MJ
1 Watt second	= 1 Joule (J)
1 Watt hour (Wh)	= 3600 Joules or 3.6 kilojoules
1 kilowatt hour (kWh)	= 3.6 megajoules
1 megawatt hour (MWh)	= 3.6 gigajoules
1 MJ	= 0.278 kWh
1 calorie (c)	= 4.19002 Joules

Note 1 calorie is (approximately) the amount of heat required to raise the temperature of one ml of water by 1 degree Celsius. This unit is less used than it was. Note that it is one thousandth of the Calorie used in nutrition (capital 'C').
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Energy content of some fuels

Many of the figures in this table were taken from the Australian Bureau of Agricultural and Resource Economics (ABARE), energy definitions (http://www.abareconomics.com/pdf/ENERGYDEFINITIONS.pdf; unfortunately no longer available).
Another source I have used is Xtronics.

1 Tonne of oil equivalent (TOE) is defined as being 41.868GJ
By definition a TOE is the amount of energy produced by burning a tonne (metric ton) of oil. In practice, of course, this depends on the composition of the oil.

Fuel	Wh/kg	MWh/tonne	MJ/L	MJ/kg	Source
Propane	13 800	13.8	25.4	49.6	ABARE and Xtronics
Petrol (automotive gasoline)	12 900	12.9	34.2	46.4	ABARE and Xtronics
Kerosene	12 800	12.8	37	46.1	ABARE
Heating oil	12 800	12.8	37.3	46.2	ABARE
Ethanol	8 200	8.2	23.4	29.6	ABARE and Xtronics
Methanol	5 500	5.5	15.6	19.7	ABARE
Coal	2 800 to 8 300	2.8 to 8.3	-	10 to 30	ABARE and others
Energy in air-seasoned firewood	4 400	4.4	-	approx. 16.0	ABARE and others
Hydrogen	39 000	39	-	142	Several, including Hypertextbook
Bagasse	2 700	2.7	-	9.6	ABARE

Notes
Coal varies from 10 for wet lignite (brown coal) to 30 for high quality coking (black) coal.

While hydrogen has a very high energy content per kilogram, it is very light in weight, even when highly compressed or liquefied. It therefore does not have a high energy content per litre of space required to store it. Also, as all the systems used to store hydrogen weigh much more than the hydrogen they store, the useful energy per kilogram of storage system is low. The best current hydrogen storage systems can manage only about 3MJ/L or 4MJ/kg (4GJ/tonne). See The Industrial Physicist.
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Energy density of some batteries

Battery type	Energy density			Cycles
Battery type	Wh/kg	kJ/kg	MJ/kg	Cycle life is to 80% initial capacity
Nickel-cadmium	45-80	160-290	0.16-0.29	1500
NiMH	60-120	220-430	0.22-0.43	300 to 500
Lead-acid	30-50	110-180	0.11-0.18	200 to 300
Lithium-ion	110-160	400-580	0.40-0.58	300 to 500
Lithium-ion-polymer	100-130	360-470	0.36-0.47	300 to 500
Reusable alkaline	80	290 (initially)	0.29	50 (to 50% capacity)
Taken from Battery University, What is the best battery?

Compressed air and flywheels can also be used for energy storage

Xtronics gives the figures below:

Energy source	Energy density
Energy source	Wh/kg	kJ/kg	MJ/kg
Compressed air	34	122	0.12
Flywheel	120	432	0.43

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Energy from falling water
Or energy needed to lift water

The relevant equation is E=mgh; where, using the SI metric system (kg,m,sec);

E is energy in Joules
m is the mass in kilograms
g is the acceleration by gravity = 9.8m/sec/sec
h is the fall (or lift) in metres

100% efficiency is assumed
Energy from a kilogram of water falling 1m or energy needed to lift 1kg of water 1m	9.8 Joules
Energy from a kilolitre of water falling 1m (1kL of water = 1 tonne approx.)	9800 Joules
	9.8 kilojoules
Energy from a megalitre of water falling 1m	9800kJ
	9.8MJ
	2.7kWh
Energy from 100ML of water falling 100m (typical of values involved in hydropower)	27GWh
Power from a litre of water per second falling 1m	9.8 Watts
Power from a kilolitre of water per second falling 1m	9.8KW
Power from a megalitre of water per second falling 1m	9.8MW

Energy and changing the state of water

Energy required to convert one litre of boiling water to steam	2300kJ or 0.64kWh
From Engineering Toolbox. These figures are approximate and depend on the pressure; they assume a pressure about that at sea level.

It takes about seven or eight times as much energy to convert boiling water to steam as is needed to melt the same mass of ice and about a fifth as much energy to raise the temperature of water from freezing point to boiling point as is needed to boil it all away.

Comparing flammable fuels, weight-for-weight, with batteries and compressed air as energy sources

Energy densities of batteries are much lower than the amount of energy that can be obtained from burning the same weight of flammable fuel - compare with Energy content of fuels, above.

Compressed air can also be used as a source of energy. How much useful energy you can get from a tank of compressed air depends on the pressure inside the tank, the size of the tank, and the efficiency of the compressed air engine. The effective energy density for compressed air as an energy source depends on these factors in addition to the weight of the tank.

To be fair, there are two more factors that should be considered in this comparison:

The weight of the fuel tank containing the fuel (particularly important in the case of hydrogen);
The figures given for batteries are for the useful energy that they can provide, while the methods of getting useful energy from flammable fuels are usually only about 30% efficient.

However, even taking these factors into consideration, flammable fuels typically provide around 10MJ/kg while batteries yield less than 0.5MJ/kg.

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CO2 released per kWh

Carbon dioxide released per kWh of electricity generated For fossil fuelled power stations Approximate values
Natural gas	= 0.45kg
Oil	= 0.5kg
Black coal	= 0.8kg
Brown coal	= 1.2kg

How do you calculate the amount of CO₂ released from burning one kilogram of carbon?

The carbon dioxide (CO₂) molecule is made up of one atom of carbon and two atoms of oxygen. Carbon has an atomic weight of 12, the atomic weight of oxygen is 16. Therefore, when one kg of carbon combines with oxygen we have 12 mass units of carbon and 32 units of oxygen being converted into 44 units (12 + 16 + 16 = 44) of carbon dioxide.

1kg of carbon becomes 1 x 44/12 = 3.7kg (approximately) of CO₂.

Burning 1kg of petrol (gasoline for USians)

Petrol is composed of a mix of short-chain hydrocarbons; I will use heptane for my calculations. A molecule of heptane is composed of seven atoms of carbon and 16 atoms of hydrogen. In atomic weights, 7 x 12 = 84 for the carbon, 16 x 1 = 16 for the hydrogen; so the molecular weight of heptane is about 100, 84% of which is carbon. So burning one kilogram of heptane (or petrol) would release 84% of 3.7kg = 3.1kg of CO2.

Miscellaneous

Volume
1 barrel (oil)	= 158.987L

Some multipliers used in the SI metric system

A capital M must be used for 'mega' to distinguish it from the lower-case 'm' for milli (one thousandth). Generally capitals are used for multipliers and lower case for dividers.

Don't ask me why the abbreviation for kilo (one thousand) is lower case; that's just how it is.

The abbreviations for Watt and Joule are usually capitalised because they are peoples' names.
Comparative costs of energy in oil, electricity, and firewood are discussed on my Sustainability page.

For a full list see Wikipedia

10ⁿ	Prefix	Symbol	Decimal Equivalent	Language
10¹⁸	Exa	E	1 000 000 000 000 000 000	Billion billion
10¹⁵	Peta	P	1 000 000 000 000 000	Million billion
10¹²	Tera	T	1 000 000 000 000	Trillion
10⁹	Giga	G	1 000 000 000	Billion
10⁶	Mega	M	1 000 000	Million
10³	kilo	k	1000	Thousand
10^-3	milli	m	0.001	Thousandth
10^-6	micro	µ	0.000001	Millionth

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On this page...
Barrel
Calorie
calorie
Carbon into carbon dioxide
CO2 released per kWh
Comparisons, weight-for-weight
Compressed air and flywheels
Energy and boiling water
Energy and melting ice
Energy
Energy content of fuels
Energy density of some batteries
Energy from falling water
GJ
GWh
Gigajoule
Gigawatt
Gigawatt hour
Kilojoule
Kilowatt
Kilowatt hour
kJ
kW
kWh
MJ
MWh
Megajoule
Megawatt
Megawatt hour
Metric system multipliers
Miscellaneous
Power
TWh
Terawatt
Terawatt hour
Top
Watt
Watt hour
Watt second
Wh