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The watt-hour (symbol W·h or Wh) is a unit of energy. It is most commonly used on household electricity meters in the form of the kilowatt-hour (kW·h or kWh), which is 1,000 watt-hours.

It is not used in the International System of Units (SI), despite being based on the watt, as the hour is not an SI unit. The SI unit of energy is the joule (J), equal to one watt-second. It is, however, a commonly used unit, especially for measuring electric energy.

1 watt-hour is equivalent to 3,600 joules (1 W x 3600 s), the joule being the canonical SI unit of energy. Thus a kilowatt-hour is 3,600,000 joules or 3.6 megajoules.

Definition

One watt-hour is the amount of (usually electrical) energy expended by a one-watt load (e.g., light bulb) drawing power for one hour.

Laymen and utilities tend to use watt-hours to measure energy rather than joules (J), for reasons of convenience and intuition. For example, a light bulb draws power (units of watts) over a certain amount of time, resulting in a net amount of used energy; a watt has units of energy-per-time, and an hour is a convenient unit for measuring time, so when multiplied together they produce a unit of energy called the watt-hour. The watt-hour is derived from the multiplication of the SI unit of power (watt) and a non-SI unit of time (hour). In simple terms, it means the amount of power (watts) used for any given number of hours. A lightbulb that needs 50 J of energy per second to light up (50 watts) will consume 500 watt-hours of energy if left on for 10 hours.

The kilowatt-hour is commonly used for electrical and natural gas energy. Many electric utility companies use the kilowatt-hour for billing. This is a convenient unit because the energy usage of a typical home in one month is several hundred kilowatt-hours. In addition, the typical consumer can readily conceptualize the notion of "using a kilowatt for one hour”; common appliances that consume approximately 1 kW include hairdryers, microwave ovens, and vacuum cleaners. Megawatt-hours are used for metering of larger amounts of electrical energy. For example, a power plant's daily output is likely to be measured in megawatt-hours.

Pricing for kilowatt-hours

Power companies sell energy in units of kilowatt-hours. In general, energy (E) is equivalent to power (P) multiplied by time (t). To determine E in kilowatt-hours, P must be expressed in kilowatts and t must be expressed in hours. Suppose a 1.5-kW electric heater runs for 3 h. Then P = 1.5 kW and t = 3 h, so the energy E in kilowatt-hours is: E = Pt = 1.5 kW × 3 h = 4.5 kW·h. If P and t are not specified in kilowatts and hours respectively, then they must be converted to those units before determining E in kilowatt-hours. Consider a set-up with one 100 W light bulb (0.1 kW) left on for 10 hours per day. This will consume 1 kilowatt-hour per day (0.1 kW × 10 h). If a power company charges $0.10/kW·h, then this light bulb will cost $0.70 to operate over the course of a week (0.1 kW × 10 h × $0.10/kW·h × 7 d/week) (see Units of measurement#Expressing a physical value in terms of another unit for more information).

Other expressions of the watt-hour

Another derived unit that is sometimes used for household purposes is the kWh/yr., usually considered in annual energy consumption calculations, but with the dimensions of power, with 1 kWh/yr. = 0.114 W. Note that this unit uses three units of time in one unit, namely second, hour and year, of which only the first is an SI unit.

The Board of Trade Unit or B.O.T.U. is an obsolete UK synonym for kilowatt-hour. The term derives from the name of the Board of Trade that regulated the electricity industry. The B.O.T.U. should not be confused with the British thermal unit or BTU, which is a much smaller quantity of thermal energy.

Burnup of nuclear fuel is normally quoted in megawatt days per ton (MWd/MTU), where ton refers to a metric ton of uranium metal or its equivalent, and megawatt refers to the entire thermal output, not the fraction which is recovered as electricity.

Multiples

Kilo-, mega-, giga-, and tera- are the most-used prefixes.

Multiple	Name	Symbol		Multiple	Name	Symbol
100	watt-hour	W·h
103	kilowatt-hour	kW·h		10–3	milliwatt-hour	mW·h
106	megawatt-hour	MW·h		10–6	microwatt-hour	µW·h
109	gigawatt-hour	GW·h		10–9	nanowatt-hour	nW·h
1012	terawatt-hour	TW·h		10–12	picowatt-hour	pW·h
1015	petawatt-hour	PW·h		10–15	femtowatt-hour	fW·h
1018	exawatt-hour	EW·h		10–18	attowatt-hour	aW·h
1021	zettawatt-hour	ZW·h		10–21	zeptowatt-hour	zW·h
1024	yottawatt-hour	YW·h		10–24	yoctowatt-hour	yW·h

Conversions

from / to	Joule	Watt-hour	Electronvolt	Calorie
1 J = 1 kg m2 s-2 =	1	0.278 × 10−3	6.241 × 1018	0.239
1 W·h =	3600	1	2.247 × 1022	859.8
1 eV =	1.602 × 10−19	4.45 × 10−23	1	3.827 × 10−20
1 cal =	4.1868	1.163 × 10−3	2.613 × 1019	1

See also

• Ampere-hour
• Orders of magnitude (energy)

External links

• Power and Energy in the Home - The Trustworthy Cyber Infrastructure for the Power Grid (TCIP) group at the University of Illinois at Urbana-Champaign has developed an applet which illustrates the consumption and cost of energy in the home, and allows the user to see the effects of manipulating the flow of electricity to various household appliances.

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