Wh\text{Wh}

watt-hour

Energyexact by definition

The watt-hour is one watt sustained for one hour, which is exactly 3600 joules since the hour is exactly 3600 seconds. The relation is exact. It is the natural unit for batteries and small energy stores, where a capacity in amp-hours multiplied by a voltage gives watt-hours directly.

Watch out: Battery capacity quoted in milliamp-hours is not an energy and cannot be compared across different voltages. A 3000 mAh cell at 3.7 V holds 11.1 Wh, while a 3000 mAh pack at 11.1 V holds 33.3 Wh. Only the watt-hour figure is comparable.

1 Wh\text{Wh} 3,600 J\text{J}

About the watt-hour

The watt-hour is the battery unit, and the reason it is printed on every power bank is an aviation rule. Lithium batteries up to 100 Wh fly freely in carry-on baggage; from 100 to 160 Wh they need airline approval; above 160 Wh they are banned from passenger aircraft outright. Manufacturers design to that line: several flagship laptops ship with batteries of 99 to 100 Wh, as large as a battery can be and still board without paperwork, and the Wh figure on the casing exists mostly so security staff can check it against the limit.

The scale is worth internalising. A phone battery holds 12 to 18 Wh, a laptop 50 to 100, a cordless tool pack 100 to 200, an e-bike 400 to 750, and an electric car leaps to tens of thousands, which is why cars are quoted in kilowatt-hours instead. Behind every label sits the multiplication volts times amp-hours: a 3.7 V cell of 5000 mAh is 18.5 Wh, and running that multiplication is the only way to compare batteries of different voltages, as the caution spells out.

One watt-hour is exactly 3600 joules, so a 15 Wh phone battery stores 54 kJ, about the food energy in three grams of sugar. A day of heavy phone use runs on less chemical energy than a bite of a biscuit, an honest measure of how frugal electronics are next to bodies and vehicles.

One watt-hour in every energy unit

2.24694e+22electron volt (eV)
8.25736e+20hartree (Eh)
2.24694e+19kiloelectron volt (keV)
2.24694e+16megaelectron volt (MeV)
22,469,400,000,000gigaelectron volt (GeV)
3,600,000,000,000nanojoule (nJ)
36,000,000,000erg (erg)
22,469,400,000teraelectron volt (TeV)
3,600,000,000microjoule (µJ)
3,600,000millijoule (mJ)
31,862.7inch-pound (in·lb)
3,600joule (J)
2,655.22foot-pound (ft⋅lb)
860.421calorie (cal)
859.845calorie (International Table) (cal IT)
3.6kilojoule (kJ)
3.41443BTU (thermochemical) (BTU th)
3.41214British thermal unit (BTU)
1watt-hour (Wh)this unit
0.860421kilocalorie (kcal)
0.0036megajoule (MJ)
0.00134102horsepower-hour (hp·h)
0.001kilowatt-hour (kWh)
0.0000341214therm (therm)
0.0000036gigajoule (GJ)
0.00000341214million BTU (MMBTU)
0.000001megawatt-hour (MWh)
8.60421e-07ton of TNT (t TNT)
8.59845e-08tonne of oil equivalent (toe)
3.60000e-09terajoule (TJ)
1.00000e-09gigawatt-hour (GWh)
8.60421e-10kiloton of TNT (kt TNT)
3.60000e-12petajoule (PJ)
1.00000e-12terawatt-hour (TWh)
8.60421e-13megaton of TNT (Mt TNT)
3.41214e-15quad (quad)