WATT-HOUR

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.

Contents

Definition

Pricing for kilowatt-hours

Confusions in the use of watt-hours

Other expressions of the watt-hour

Multiples

Conversions

See also

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.” 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. 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 x 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 x 10 h x $0.10/kW·h x 7 days in a week) (see unit juggling for more information).

Confusions in the use of watt-hours

Some sources mistakenly refer to watt-hours as "power." A similar confusion can arise when describing daily energy use. For example, a solar cell array might have a peak power output of 100 watts, but in order to give an indication of its usable output as a function of time-varying conditions (such as the apparent daily solar motion, or dust collection on the surface), its typical output might be described as "1200 watt-hours per day."

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

★ Orders of magnitude (energy)