| Watt-hours (Wh) | Microjoules (µJ) |
|---|---|
| 1 Watt-hour | 3600000000 µJ |
| 2 Watt-hours | 7200000000 µJ |
| 3 Watt-hours | 10800000000 µJ |
| 4 Watt-hours | 14400000000 µJ |
| 5 Watt-hours | 18000000000 µJ |
| 10 Watt-hours | 36000000000 µJ |
| 20 Watt-hours | 72000000000 µJ |
| 25 Watt-hours | 90000000000 µJ |
| 50 Watt-hours | 180000000000 µJ |
| 100 Watt-hours | 360000000000 µJ |
| Reference | Watt-hours (Wh) | Microjoules (µJ) |
|---|---|---|
| One food calorie (kcal) | 1.16222 Wh | 4.184 × 109 µJ |
| An AA alkaline battery | 2.77778 Wh | 1 × 1010 µJ |
| Daily adult food intake | 2324.44 Wh | 8.368 × 1012 µJ |
| One unit on an electricity bill | 1000 Wh | 3.6 × 1012 µJ |
| A lightning strike | 277778 Wh | 1 × 1015 µJ |
The watt-hour is a unit of energy equal to the energy delivered by one watt of power flowing for one hour, or exactly 3600 joules. Its symbol is Wh. It is the small change of the kilowatt-hour, used wherever quantities of energy are too modest to state in thousands.
Batteries are its main territory. The capacity of a laptop, phone, power tool or portable speaker is quoted in watt-hours, and this is the figure that matters when comparing devices, because it combines the two numbers usually printed on a cell. A battery marked 3000 milliampere-hours at 3.7 volts stores about 11 watt-hours, and the ampere-hour figure alone is meaningless without the voltage.
Aviation regulation has made the unit unexpectedly public. Lithium batteries above 100 watt-hours may not be carried in aircraft cabin baggage without airline approval, and above 160 watt-hours they are banned from passenger aircraft entirely. This is why laptop and camera batteries carry the figure printed on them, and why portable power banks are designed to sit just under the threshold.
Small-scale energy generation uses it as well. A solar panel on a garden light, an energy-harvesting sensor or a bicycle dynamo produces watt-hours per day rather than kilowatt-hours, and low-power electronics designed to run for years on a single cell are budgeted in milliwatt-hours.
The unit shares the criticism levelled at the kilowatt-hour: it combines a coherent SI unit of power with a non-SI unit of time. In strictly SI terms the correct expression is 3600 joules, or 3.6 kilojoules, and scientific writing uses joules. Everywhere else the practical link to a device's power rating wins.
Energy storage systems, from a home battery to a grid installation, scale upward through kilowatt-hours and megawatt-hours from the same starting point, so the whole family shares one arithmetic.
A common confusion is worth clearing up here. Battery cells are usually labelled in ampere-hours or milliampere-hours, which measure charge and not energy, and two cells with the same ampere-hour rating store quite different amounts if their voltages differ. Multiplying ampere-hours by the nominal voltage gives watt-hours: a 3000-milliampere-hour phone cell at 3.85 volts holds about 11.6 watt-hours. That is why capacity comparisons between devices are only meaningful in watt-hours, why airlines set their limits in watt-hours, and why a power bank advertised in milliampere-hours may deliver less than its number suggests once its own conversion losses are counted.
One watt-hour equals 3600 joules, 0.001 kilowatt-hours, or about 0.86 kilocalories.
The microjoule is a unit of energy equal to one millionth of a joule, or 0.000001 joules. Its symbol is µJ. It is the scale of small living things, of short laser pulses and of the electricity a sensor spends waking up, and it is the smallest energy unit that still describes events an unaided person can notice happening.
Insects live here. A flea of half a milligram leaping twenty centimetres spends about one microjoule, and a mosquito in level flight carries roughly a quarter of one. Lifting a gram by a tenth of a millimetre costs the same. These are the quantities that make the unit intuitive: not invisible in principle, merely too small to matter unless something repeats them millions of times a second.
Ignition safety is written in this range, and the numbers decide how equipment may be built. The minimum energy that will ignite a hydrogen and air mixture is about 17 microjoules; for most hydrocarbon vapours it is a few hundred. Intrinsically safe apparatus for refineries, grain stores and mines is certified by proving that no fault can release more than the mixture requires, which is why circuits destined for hazardous areas are audited in microjoules rather than in volts.
Pulsed light instruments are specified in microjoules almost universally. A vehicle lidar fires pulses of a few microjoules many thousand times a second, laser marking systems use tens to hundreds, and femtosecond amplifiers destined for micromachining sit at the top of the range. The energy per pulse sets what the beam can cut, image or safely illuminate, and the average power alone does not answer that question.
Low-power electronics budgets in the same terms. A passive radio-frequency identification tag harvests a few microjoules from the reader's field and must complete its whole exchange inside that. A short-range radio advertisement costs tens of microjoules, a quartz watch movement about one per second, and a temperature sensor that wakes, measures and sleeps again may spend under ten. Battery life on such devices is arithmetic performed in microjoules.
Above it the millijoule takes over and the effects become mechanical: a spark you feel, a click you hear, a small object dropped. Below it the nanojoule takes over and the effects become optical and electronic. The microjoule occupies the narrow band between, which is why so many disciplines that otherwise share nothing converge on the same prefix.
One microjoule equals 0.000001 joules, about 6.24 × 10¹² electronvolts, or about 2.78 × 10⁻¹⁰ watt-hours.