Conversion from Decajoules to Kilowatt-hours

Information about the Decajoule (daJ)

The decajoule is a unit of energy equal to ten joules. Its symbol is daJ, and the spelling dekajoule with a k is also accepted. It is the least written of all the joule multiples, not because the quantity is obscure but because deca is the least used prefix in the entire metric system, and understanding that is more useful than memorising the unit itself.

The quantity is one of the easiest in physics to picture. Lifting a one-kilogram bag of sugar by one metre takes 9.81 joules, so almost exactly one decajoule. A heart beats about a joule per stroke, so ten beats. A rifle pellet from an unlicensed air rifle in Britain carries up to 16 joules, or a little over 1.6 decajoules. These are quantities the body understands directly as effort.

Deca survives in ordinary life in only a handful of places, and almost all of them involve mass. In Austria, Poland, Hungary and the Czech lands, delicatessen counters still sell by the dekagram, so a customer asks for twenty deka of ham rather than two hundred grams. The decanewton is used for rope and cable ratings and, in France, for towing capacities, because it happens to be close to the weight of a kilogram.

Elsewhere the prefix simply lost. Engineering standardised on steps of a thousand, which places kilo directly above the base unit and leaves nothing for deca to do that a two-digit number does not already do better. Writing 40 joules is shorter than writing 4 decajoules, and it sorts correctly in a table alongside 400 joules and 4 kilojoules without any mental arithmetic.

The scale itself is worth knowing even under another name, because it is the scale of single human actions. Throwing a ball, closing a heavy door, lifting a full kettle onto a hob, drawing a bow: each of these costs a few tens of joules. Impact tests on packaging and protective equipment are specified here too, and so are the energy limits written into rules for airguns and industrial fastening tools.

When a decajoule appears in a document, converting it takes one step in either direction. Multiply by ten for joules, divide by a hundred for kilojoules. Both forms are exact, and the joule form is the one that will match every other figure in a modern specification.

One decajoule equals 10 joules, about 2.39 calories, or about 0.00278 watt-hours.

Information about the Kilowatt-hour (kWh)

The kilowatt-hour is a unit of energy equal to the energy delivered by one kilowatt of power flowing for one hour, or exactly 3.6 million joules. Its symbol is kWh. It is the unit in which virtually all electricity in the world is bought and sold.

Its form explains its usefulness. Power multiplied by time gives energy, so a device rated in watts and a duration in hours produce a figure that can be read straight off a bill. A two-kilowatt heater running for three hours consumes six kilowatt-hours, and no conversion is needed between the rating on the appliance and the number on the meter.

Domestic consumption sits at a comprehensible scale. A typical European household uses somewhere between 2000 and 5000 kilowatt-hours a year, an American one closer to 10,000. A kettle boiling once costs about 0.1, a load of washing about 0.7, and a modern refrigerator around 200 a year. Those figures make the unit an effective tool for reasoning about where energy actually goes in a home.

Electric vehicles brought it to a new audience. Battery capacity is quoted in kilowatt-hours, typically between 40 and 100 for a passenger car, and efficiency is expressed as kilowatt-hours per hundred kilometres, the electrical analogue of litres per hundred kilometres. Charging power in kilowatts then determines how long a given amount of energy takes to deliver.

The unit is not SI and is sometimes criticised for compounding a prefixed unit with a non-SI time unit. The megajoule is the formally correct alternative, and some countries do bill gas in megajoules or gigajoules, but the kilowatt-hour's direct link to appliance ratings has kept it dominant for electricity everywhere.

Larger multiples run the electricity industry. A megawatt-hour is the unit of wholesale trading, a gigawatt-hour describes the output of a power station over a day, and a terawatt-hour is used for national annual consumption.

Tariffs have turned the unit into a signal as much as a measurement. Time-of-use pricing charges different amounts per kilowatt-hour by hour of the day, wholesale markets settle in half-hourly blocks, and in periods of high wind and low demand the price has gone negative, so that generators pay to keep supplying. Households with a battery or an electric car respond by shifting consumption into the cheap hours, which flattens the load on the network. The kilowatt-hour is also the unit in which the carbon intensity of electricity is reported, in grams of carbon dioxide per kilowatt-hour, which lets a country's generation mix be judged on one number.

One kilowatt-hour equals 3.6 million joules, 3600 kilojoules, or about 860 kilocalories.