# Watt hour

Physical unit
Unit name Watt hour
Unit symbol ${\ displaystyle \ mathrm {Wh}}$
Physical quantity (s) Energy , work , internal energy , warmth
Formula symbol ${\ displaystyle W, \, E \,}$
dimension ${\ displaystyle {\ mathsf {M \; L ^ {2} \; T ^ {- 2}}}}$
system Approved for use with the SI
In SI units ${\ displaystyle \ mathrm {1 \, Wh = 3 {,} 6 \; kWs = 3 {,} 6 \; kJ}}$
Derived from Joules
AC electricity meter from 1913, which gives its result in kilowatt hours.

The watt-hour (unit symbol Wh ) is a unit of measurement for work or energy . Although it does not belong to the International System of Units (SI), it is approved for use with the SI. This makes it a legal unit of measurement . One watt hour corresponds to the energy that a system (e.g. machine , person , incandescent lamp ) with an output of one watt absorbs or emits in one hour . A 50 watt incandescent lamp that lights up for one hour converts 50 Wh.

The kilowatt hour ( kWh ), a thousand times the watt hour , is common and widespread in everyday life . In this unit, electricity costs in particular, but also heating costs are billed and recorded with measuring devices such as the electricity meter or heat meter .

In contrast to the unit kilometers per hour , which is written km / h because it is divided by the hour, there is no “/” to be written for the kilowatt hour kWh because it is multiplied by the hour. The spelling “kW / h” is therefore wrong.

When specifying the electricity production of power plants or the demand for electrical energy of entire countries, the prefixes Mega (M) (for one million ), Giga (G) (for one billion ) or Tera (T) (for one trillion ) of the corresponding unit used to get more manageable numerical values. Examples:

• 1000 kilowatt hours = 1 megawatt hour (MWh)
• 1000 megawatt hours = 1 gigawatt hour (GWh)
• 1000 gigawatt hours = 1 terawatt hour (TWh)

## Connection with other units of energy

The watt hour is derived from the SI unit joule :

• 1 Wh = 3600 Ws (watt second) = 3600 joules = 3.6 kilojoules (kJ).

The unit watt hour is mostly used with the decimal SI prefix kilo (e.g. for electricity billing).

• 1 kilowatt hour (kWh) = 1  kWh = 1000 watt 1  h = 1000 Wh = 1000 W 3600  s = 3.6 10 6  J = 3.6 megajoules (MJ)

For example, if a solar system with an output of one kilowatt converts sunlight into electrical energy for one hour, it delivers one kilowatt hour.

## Examples

With the energy 1 kWh you can for example:

• Connect a household to the Internet for 111 hours with a WiFi router (with an output of 9 watts)
• 50 hours of work on a laptop (with an output of 20 watts)
• Work on the desktop computer for five hours (at an output of 200 watts; at full output, this usually fluctuates a lot)
• Watch TV for around 15 hours with a device with a liquid crystal display (with a power requirement of around 65 watts)
• Vacuuming for around 67 minutes (with an output of 900 watts)
• Dry hair for three quarters of an hour (at an output of 1400 watts)
• Cook for 40 minutes on a hotplate at maximum level (with an output of 1500 watts)
• Cover its average primary energy requirement for around eleven minutes (power consumption in Germany around 5.5 kW on average)
• Heat a pail full of water (10.75  liters ) under normal pressure from 20 ° C to 100 ° C
• Drive around 1.7 km in a car with a combustion engine (with a typical energy requirement of 6 liters of petrol or 60 kWh per 100 km)
• Drive around 6.7 km with an electric car (with a typical energy requirement of 15 kWh per 100 km)
• Cycle around 130 km with a pedelec with moderate pedaling (with a range of around 40 to 45 km from a battery charge of 330 Wh)

For comparison, the following rule of thumb for the energy content of primary energy sources is worth mentioning:

10 kWh ≈ 1 m³ natural gas ≈ 1 l oil ≈ 1 l gasoline ≈ 1 kg coal ≈ 2 kg wood ≈ 10 h of direct sunlight on 1 m² on earth

depending on the efficiency of the power plant and power line, only around 40% reach the consumer.

Although the unit kWh is mainly used for electrical consumers or heating, it can also be compared with the energy consumption of a person : a typical daily turnover of 9000 kJ for an adult man (without heavy physical work) would correspond to a value of 2.5 kWh . Thus it has an average consumption of around 100 watts, whereby the converted per capita primary energy requirement in Germany is around 5000 watts, i.e. 50 times as much. With the energy of 1 kWh from the example above, a person weighing approx. 80 kg can walk 10 km.

## Related units

### Megawatt day

A megawatt day (MWd) is the energy that a power plant with an output of 1  megawatt delivers in one day . It is used in energy and reactor technology.

${\ displaystyle 1 \, \ mathrm {MWd} = 10 ^ {6} \ times 24 \, \ mathrm {Wh} = 86 {,} 4 \ times 10 ^ {9} \, \ mathrm {J} = 24 \ , \ mathrm {MWh}}$

### Gigawatt year

A gigawatt year (GWa) is the energy that a power plant with an output of 1 gigawatt delivers in one year (when operated without interruptions). The gigawatt year is not a legal unit in metrology in Germany because the year (unit symbol: a) is not such a unit there.

${\ displaystyle 1 \, \ mathrm {GWa} \ approx 10 ^ {6} \, \ mathrm {kWa} \ cdot 365 \ mathrm {\ frac {d} {a}} \ cdot 24 \ mathrm {\ frac {h } {d}} = 8 {,} 76 \ cdot 10 ^ {9} \, \ mathrm {kWh} = 8 {,} 76 \, \ mathrm {TWh}}$

## Individual evidence

1. The International System of Units (SI) . German translation of the BIPM brochure "Le Système international d'unités / The International System of Units (8e édition, 2006)". In: PTB-Mitteilungen . tape 117 , no. 2 , 2007 ( Online [PDF; 1.4 MB ]).
2. on the basis of EU Directive 80/181 / EEC in the states of the EU or the Federal Law on Metrology in Switzerland
3. Konrad Mertens: Photovoltaics . Carl Hanser, Munich 2011, ISBN 978-3-446-42172-1 .
4. Runner's World Calorie Calculator. Accessed on November 10, 2012 (where 1 kcal = 4.184 kJ = 4184 Ws = 1.162 Wh is to be converted).