Conversion from Kilowatt-hours to Microjoules

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.

Information about the Microjoule (µJ)

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.