Conversion from Watt-hours to Gigajoules

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.

Information about the Gigajoule (GJ)

The gigajoule is a unit of energy equal to a billion joules, or 1000 megajoules. Its symbol is GJ. Unlike the smaller prefixed joules it is a working commercial unit: gas and heat are bought and sold in gigajoules, and a household's annual energy use is a number of gigajoules that fits comfortably on one line of a bill.

Heating is where most people meet it. District heating in Denmark and the Netherlands is metered and invoiced in gigajoules, and Canadian natural gas bills are denominated in them. One gigajoule is roughly the heat in 26 cubic metres of natural gas, or in 29 litres of petrol, and a well-insulated house in a cold climate consumes something between 40 and 100 gigajoules a year for space heating and hot water.

The unit also measures what materials cost to make. Producing a tonne of structural steel takes roughly 20 to 25 gigajoules of primary energy, a tonne of cement about 4, and a tonne of primary aluminium close to 200. Those figures are why aluminium is described as stored electricity, and why embodied-energy tables in construction are published in gigajoules per tonne rather than in any smaller unit.

For destructive energy it is the natural scale between the domestic and the catastrophic. A tonne of TNT releases 4.184 gigajoules by definition, and a lightning strike delivers on the order of one to five, though almost all of that goes into heating and shattering the air rather than into whatever it hits. A tonne of hard coal holds about 29 gigajoules of chemical energy.

Human beings appear in the same table. An adult eating about ten megajoules a day consumes roughly 3.7 gigajoules of food energy a year, which is less than a single small car burns in a month. Setting the two figures side by side in one unit is one of the clearest ways to show how much of modern energy use happens outside the body.

Above the gigajoule, national statistics move on to terajoules and petajoules; below it, appliances and vehicles are described in megajoules and kilowatt-hours. The gigajoule sits at the join, which is why energy regulators and utilities converge on it: it is large enough for a building and small enough for a bill.

One gigajoule equals 1,000,000,000 joules, about 277.8 kilowatt-hours, or about 239,000 kilocalories.