# Some energy units, definitions and conversions

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.

The important concepts of energy and power, and the difference between them, are explained briefly in my Wind power glossary; it also includes terms particularly relating to wind power.

Created as a separate page 2005/06/09, last edited 2021/02/15
Contact: David K. Clarke – ©

## Power

Units of the power
1 milliwatt (mW)= 0.001 Watts
1 Watt (W)= 1 Joule per second (J/sec)
1 kilowatt (kW)= 1000 Watts
1 megawatt (MW)= 1000kW
1 gigawatt (GW)= 1000MW
1 terawatt (TW)= 1000GW
1 horsepower= 0.7457kW
Human power output – approximate
From Wikipedia August 2016
Trained cyclist400 Watts – for an hour or so
Adult of average fitness50-150W for an hour
Healthy, well fed labourer75W for 8 hours

## Energy

Units of energy
1 milliwatt hour = a flow of 1mW for 1 hour (or equivalent)
1 Watt hour = a flow of 1W for 1 hour (or equivalent)
1 kilowatt hour = a flow of 1kw for 1 hour (or equivalent)
1 megawatt hour = 1000kWh
1 gigawatt hour = 1000MWh
1 terawatt hour = 1000GWh
1 kilojoule = 1000 Joules
1 megajoule = 1000kJ
1 gigajoule = 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 kJ= 0.278 Wh
1 MJ= 0.278 kWh
1 GJ= 278 kWh
1 TJ= 278 MWh
1 PJ= 278 GWh
1 kWh= 3.60 MJ
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'). (So it requires 1000 × 80 = 80 000 calories to heat one litre of water from 20° to boiling point, and 80 000c = 335.2kJ or 93.2Wh.)

## Energy Density

The term energy density is used for the amount of energy that can be 'got out of' a fuel or power source. It is somewhat subjective: for example the effective energy density of petroleum within the atmosphere is very different to what it is in space, because in the former an oxidiser is available from the atmosphere while in the latter the oxidiser must be carried. In this section I have, of course, considered only the mass of the fuel, not the oxidiser.

### 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.

FuelWh/kgMWh/tonneMJ/LMJ/kgSource
Ammonia6 25522.5Wikipedia
Propane13 80013.8 25.449.6ABARE and Xtronics
Petrol (automotive gasoline)12 900 12.934.246.4 ABARE and Xtronics
Kerosene12 80012.8 3746.1ABARE
Heating oil12 80012.8 37.346.2ABARE
Ethanol8 2008.2 23.429.6ABARE and Xtronics
Methanol5 5005.5 15.619.7ABARE
Coal2 800
to 8 300
2.8
to 8.3
- 10
to 30
ABARE and others
Energy in air-seasoned firewood4 400 4.4- approx. 16.0ABARE and others
Hydrogen39 00039    -142   Several, including Hypertextbook
Bagasse2 7002.7 -9.6ABARE
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.

### Energy density of some batteries

Battery typeEnergy density Cycles
Wh/kgkJ/kgMJ/kg Cycle life is to 80% initial capacity
NiMH60-120220-4300.22-0.43 300 to 500
Lithium-ion110-160400-5800.40-0.58 300 to 500
Lithium-ion-polymer100-130360-4700.36-0.47 300 to 500
Reusable alkaline80290 (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 sourceEnergy density
Wh/kgkJ/kgMJ/kg
Compressed air341220.12
Flywheel1204320.43

### 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 1 kg 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 a megalitre of water falling 100m 270kWh Energy from 100ML of water falling 100m 27MWh Energy from 1GL of water falling 100m 270MWh 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 10kL of water per second falling 10m 980kW Power from a 100kL of water per second falling 10m 9.8MW Power from a 100kL of water per second falling 100m 98MW

### 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.

So when an evaporative air cooler evaporates one litre of water it cools a room by about the same amount as running a simple 1kW heater would warm the room in three quarters of an hour.

### 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:

1. The weight of the fuel tank containing the fuel (particularly important in the case of hydrogen);
2. 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.

## CO2 released per kWh

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

#### 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.

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

#### Burning 1 kg 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 3.7 kg = 3.1 kg of CO2. A litre of petrol weighs roughly 800 grams, so burning a litre would release about 2.5 kg of CO2

#### Burning 1 kg of natural gas

Natural gas is mostly methane. A molecule of methane is composed of one atom of carbon and 4 atoms of hydrogen. In atomic weights, 12 for the carbon, 4 x 1 = 4 for the hydrogen; so the molecular weight of methane is about 16, 75% of which is carbon.

So burning one kilogram of methane (natural gas) would release 75% of 3.7 kg = 2.8  kg 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

10nPrefixSymbolDecimal EquivalentLanguage
1018ExaE 1 000 000 000 000 000 000Billion billion
1015PetaP 1 000 000 000 000 000Million billion
1012TeraT1 000 000 000 000 Trillion
109GigaG1 000 000 000 Billion
106MegaM1 000 000Million
103kilok1000Thousand
10-3millim0.001Thousandth
10-6microµ0.000001Millionth