Kilowatt-hour

"KWH" redirects here. For other uses, see KWH (disambiguation).

The watt-hour (symbol W·h or W h) is a unit of energy. It is most commonly used on household electricity meters in the form of the kilowatt-hour (kW·h, 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 J/s x 3600 s), the joule being the official SI unit of energy. Thus a kilowatt-hour is 3,600,000 joules or 3.6 megajoules, and a kilowatt refers to the specific rate at which the amount of joules is used in a second (also known as power). As such, a kilowatt equals the production or usage of 1,000 joules of energy per second (that is a definitive rate), and a kilowatt-hour equals the specific amount of energy produced, transmitted & distributed, and/or consumed in a 3,600 second time period, which is 3,600,000 joules as mentioned above.

Definition

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

Americans, typically laymen and utilities tend to use watt-hours to measure energy rather than scientists and Europeans who use 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 the use of one 100 W light bulb (0.1 kW) used 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 $0.10 a day and $0.70 a week to operate (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

SI multiples of watt-hour (W·h)

Submultiples			Multiples
Value	SI symbol	Name	Value	SI symbol	Name
10−1 W·h	dW·h	deciwatt-hour	101 W·h	daW·h	decawatt-hour
10−2 W·h	cW·h	centiwatt-hour	102 W·h	hW·h	hectowatt-hour
10−3 W·h	mW·h	milliwatt-hour	103 W·h	kW·h	kilowatt-hour
10−6 W·h	μW·h	microwatt-hour	106 W·h	MW·h	megawatt-hour
10−9 W·h	nW·h	nanowatt-hour	109 W·h	GW·h	gigawatt-hour
10−12 W·h	pW·h	picowatt-hour	1012 W·h	TW·h	terawatt-hour
10−15 W·h	fW·h	femtowatt-hour	1015 W·h	PW·h	petawatt-hour
10−18 W·h	aW·h	attowatt-hour	1018 W·h	EW·h	exawatt-hour
10−21 W·h	zW·h	zeptowatt-hour	1021 W·h	ZW·h	zettawatt-hour
10−24 W·h	yW·h	yoctowatt-hour	1024 W·h	YW·h	yottawatt-hour
10−27 W·h	rW·h	rontowatt-hour	1027 W·h	RW·h	ronnawatt-hour
10−30 W·h	qW·h	quectowatt-hour	1030 W·h	QW·h	quettawatt-hour
Common multiples are in bold face

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.