Conversion from 20 Joules to Watt-hours

Information about the Joule (J)

The joule is the SI unit of energy, work and heat. Its symbol is J. One joule is the work done when a force of one newton moves its point of application through one metre, and equally the energy dissipated when one watt of power flows for one second.

That equivalence is the reason the unit exists. Before the nineteenth century, heat and mechanical work were treated as different things measured in different units, heat in calories and work in foot-pounds. James Prescott Joule spent years demonstrating that a fixed amount of mechanical work always produces the same amount of heat, most famously by stirring water with a paddle wheel driven by falling weights and measuring the temperature rise. Establishing that exchange rate, the mechanical equivalent of heat, unified mechanics and thermodynamics into one subject.

Because it is defined through the base units, the joule connects everything. It is a newton metre, a watt second, a coulomb volt and a kilogram metre squared per second squared, and every one of those forms appears in ordinary use depending on which branch of physics is speaking. Electrical, mechanical, thermal and chemical energy are all counted in the same unit, which is what makes energy accounting across a system possible at all.

The scale is human-sized in a useful way. Lifting an apple one metre takes about one joule. A heartbeat uses roughly one joule. Dropping a textbook from a desk releases about ten. Below that, joules become clumsy and the prefixed units take over; above it, kilojoules and megajoules do the same.

Food energy is properly measured in joules, and labels in Australia, New Zealand and the European Union give kilojoules alongside or instead of calories. The calorie survives in general use mainly through habit, and the conversion, one calorie equal to 4.184 joules, is fixed by definition rather than measured.

Nutrition, ballistics, battery capacity, laser output, explosive yield and the energy released by an earthquake are all quoted in joules or its multiples, which allows quantities from completely different domains to be compared directly.

One joule equals one newton metre, one watt second, about 0.239 calories, or about 0.000278 watt-hours.

Information about the Watt-hour (Wh)

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.