This is the front panel of an induction meter of the kind still found in many stairwells. On the left an aluminium disc turns, and the red mark on it passes the little window again and again — six hundred revolutions add up to one kilowatt-hour. Below the disc two blue lines pulse: that is the load current that drives the disc. To the right sits the digit register, whose last window is red, as on any meter that counts tenths, and the digit in it rolls over to the next. Under the register lies a strip: a red fill runs along it from left to right up to the 1.00 mark — as much as builds up in an hour if the load is exactly one kilowatt. The large lettering on the right is the symbol, the same in every language, and beneath it is written what a kilowatt-hour equals in SI units.
Energy · household, tariffs and power engineering
Kilowatt-hour
Non-SI compound unit · quantity: energy · 1 kWh is exactly 3.6 MJ
The joule is known from textbooks and the kilowatt-hour from the electricity bill, which makes it the best-known unit that is not part of the International System. It is built as plainly as can be: take the power in kilowatts, multiply by the time in hours — that is all the arithmetic there is. That very plainness made it the everyday language of energy: the seller of electricity needed to sell not abstract energy but the work of appliances over time, and so took a unit in which both parts are visible to the naked eye.
From the point of view of metrology it is a curiosity: a compound unit glued together from an SI prefix, the SI watt and the non-SI hour, which the International Committee for Weights and Measures tolerates but does not admit into the SI. The conversion, however, is exact to the last digit, since an hour is exactly three thousand six hundred seconds, and so a kilowatt-hour is exactly three point six megajoules, with no rounding at all.
The unit does not live on bills alone. Traction battery capacity is counted in kilowatt-hours, power station output in megawatt-hours and terawatt-hours, a whole country’s consumption in petawatt-hours, and on every one of these scales the same convenience holds: the number tells you at once for how long and at what power you can run. The main household confusion arises where a fraction is written instead of a product: “kW/h” in an advert for a heater means neither energy nor power, but nothing at all.
The symbol is kWh: lowercase prefix “k”, capital “W”, lowercase “h”. The multiplication dot of the full form kW·h may be left out in English practice, but a slash never replaces it — the dot marks a product, the slash a quotient. “h” takes no full stop, since it is a unit symbol and not an abbreviation of a word. The spelled-out name is kilowatt-hour, plural kilowatt-hours, with a hyphen.
A kilowatt-hour is energy, a kilowatt is power, and one cannot stand in for the other: a heater has a power of two kilowatts and uses eight kilowatt-hours over an evening. There is no such thing as “kW/h”: dividing power by time would give a rate of change of power, a quantity that makes no sense in the household. And the ampere-hour is something else again: it counts charge rather than energy, and turns into watt-hours only once multiplied by a voltage.
01 · Definition
power multiplied by timeThe kilowatt-hour is the energy delivered or consumed by a source with a power of one kilowatt over one hour of continuous operation. Since an hour has three thousand six hundred seconds and a watt is a joule per second, a kilowatt-hour equals three point six megajoules — an exact equality, not an approximation.
What matters is that a product of power and time can be made up in endless ways, and all of them give the same energy. A two-kilowatt kettle for half an hour, a half-kilowatt washing machine for two hours and a forty-watt fridge for a day all use the same kilowatt-hour, though they feel completely different: the first roars and boils, the third hums quietly and nobody notices it. The meter does not care about these impressions — it adds up products.
Hence the unit’s main practical value: it answers two questions at once. Knowing energy and power, you get the running time — a sixty-kilowatt-hour battery drawn at fifteen kilowatts lasts four hours; knowing energy and time, you get the power — two hundred and fifty kilowatt-hours a month mean an average of a little over three hundred and forty watts around the clock.
Strictly speaking, a meter measures not a product but an integral: the power in a flat changes every minute, and the instrument keeps adding up its increments. An induction meter does this mechanically — the disc turns the faster, the higher the power, and the number of revolutions is the accumulated energy — while an electronic one counts pulses. Both, however, give the same number, which is then multiplied by the tariff.
A kettle and a fridge in one cell
The scene is drawn the way the unit is built: time runs horizontally, power vertically, and the red rectangle between them is the energy. The grey grid is ruled in cells of exactly one kilowatt-hour each, so the energy can simply be counted by eye: as many cells as the rectangle covers, that many kilowatt-hours have built up. Moving the sliders, it is easy to get the same area from completely different shapes — tall and narrow like a kettle, or low and long like a fridge — and the meter cannot tell them apart. The dashed line marks the one-kilowatt-hour level, and the four buttons set the rectangles of real appliances, so there is something to compare.
02 · Conversion
energy units · bill · power and timeFrom the bill to joules and back
All conversions here are exact: an hour is exactly three thousand six hundred seconds and the prefix “kilo” exactly a thousand, so there is no rounding anywhere in the chain. Only those units come out approximate that are themselves defined through the heat of combustion of a standard fuel.
The second tab works out the electricity bill and the average power; the third untangles the eternal confusion between the kilowatt and the kilowatt-hour.
The tonne of coal equivalent and the tonne of oil equivalent are conventional units: they are set at seven and ten thousand kilocalories per kilogram respectively, while real coal or oil gives now more, now less. Conversions through them therefore suit reporting and planning, but not the calculation of a particular furnace.
| Quantity | Value | Note |
|---|---|---|
| {k} | {v} | {note} |
{text}
04 · Measuring instruments
disc · pulses · clamp · verificationHow products are added up
Meter with an aluminium disc
Two coils — a current coil and a voltage coil — induce eddy currents in an aluminium disc, and the disc turns at a speed proportional to the power; a permanent magnet next to it acts as a brake, which makes the speed exactly proportional rather than haphazard. From there on it is pure mechanics: the revolutions are summed by a counting train, and the nameplate states how many revolutions make one kilowatt-hour. The instrument takes the integral of power over time without a single computing element inside, and that is what makes it beautiful.
Electronic meter with a pulse output
A modern instrument multiplies the instantaneous values of voltage and current a thousand times a second and accumulates the result, and outputs pulses: usually a thousand pulses per kilowatt-hour, a number also printed on the case. Such an output is handy both for verification and for home automation — counting the pulses over a minute is enough to know the instantaneous power. The meter can also do what the disc could not: split energy by time-of-day zones, remember load profiles and send readings over the line.
Current clamp, wattmeter and stopwatch
When you need the consumption of one appliance rather than the whole flat, you go by the definition: measure the power and multiply by the time. The clamp picks up the current without breaking the wire, the wattmeter takes the power factor into account — without it a pump or an LED lamp would give an inflated result — and after that only a stopwatch is needed. The method suits appliances with a steady load and is poor for those that switch on in cycles: a fridge would have to be watched for a day, and then it is simpler to put a plug-in household meter in the socket.
Test bench with a reference meter
A household meter is verified by comparison: the same energy is passed through it and through a reference instrument at different currents — from a few per cent of rated current up to full load — and the discrepancy is read at each step. It must stay within the tolerance of the accuracy class, usually one or two per cent, and curiously the instrument finds the smallest currents hardest, where the torque on the disc is small but friction is still there. That is why old meters more often under-register standby consumption than overstate readings.
05 · Writing rules
multiplication dot, prefix, letter caseA dot, not a fraction
The unit is compound, and so its whole notation rests on the multiplication between the parts. The prefix attaches only to the watt, the hour takes no prefix, and letter case is the usual one: the prefix “k” lowercase, the watt capital, the hour lowercase.
The first mistake is the most common: the fraction bar turns a product into a quotient, and the notation stops meaning anything. The second and fifth confuse energy with power in both directions — a heater’s power is in kilowatts, a battery’s store in kilowatt-hours. The third drops the hours altogether, and then instead of consumption you get a power, and an implausible one: two hundred and fifty kilowatts is the supply of a small factory. The fourth breaks letter case: a capital “K” would mean kelvin, and a capital “H” means henry.
06 · Neighbouring units
joule · watt · ampere-hourThe kilowatt-hour has three close relatives, and these are exactly what it gets confused with: the joule is the same quantity in SI units, the watt is a factor, and the ampere-hour is a compound unit that looks alike but measures charge.
The unit of energy of the International System. One kilowatt-hour contains exactly three point six megajoules, so moving between them is a simple multiplication with no loss of accuracy.
The factor most often confused with the product. The watt answers “how fast”, the kilowatt-hour “how much in all”; the first is printed on the appliance’s nameplate, the second arrives on the bill.
Built on the same pattern and therefore deceptive: it counts charge rather than energy, and turns into watt-hours only after being multiplied by a voltage. Hence the pointlessness of comparing two batteries in ampere-hours if their voltages differ.
Among the Simetrium sheets, the joule, the watt, the ampere-hour and the tonne of coal equivalent stand alongside — all the arithmetic of an energy bill is assembled from them.
07 · Historical section
archive · 1882 → 1889 → 1960 → todayHow the electricity seller came up with a unit
{title}
{text}
The red shape is a two-kilowatt kettle that ran for thirty-six minutes; the blue one a four-hundred-and-fifty-watt pump that ran for two hours forty minutes. The areas are equal, and in both cases the meter will show the same increase of one point two kilowatt-hours. The grid cells are ruled in tenths of a kilowatt-hour, so the energy can be seen right in the cells rather than in a caption, and it is exactly this clarity that has kept the unit in household use for a century and a half.
Why the joule never replaced it
The International Committee for Weights and Measures lists the kilowatt-hour among the units that are outside the system but accepted for use, and explains this exactly as it is: the unit has taken root too firmly in economic life to be abolished. Over a century and a half, tariffs, contracts, national statistics and technical documentation have come to rest on it, and replacing it would cost more than any metrological tidiness, while giving nobody anything.
Nor is it only inertia. The kilowatt-hour is convenient precisely because both factors are visible in it: reading that a battery holds sixty kilowatt-hours, a driver immediately works out that at a draw of fifteen kilowatts it will last four hours of driving, whereas two hundred and sixteen megajoules tell him nothing. A unit that keeps the structure of the calculation inside itself serves people better than a formally tidier one.
There is a benefit for metrology too. Since the hour is defined exactly, conversion introduces no error, and so mixed calculations — a meter in kilowatt-hours, heat engineering in megajoules — balance without remainder. So it came about that the best-known compound unit, assembled from an SI prefix, the SI watt and the non-SI hour, lives at peace: it does not argue with the system, it is simply handier in talking to the consumer.
Catalogue · units of measurement
A data sheet for every quantity
Seven SI base units, twenty-two derived ones with names of their own, and the non-SI quantities that neither science nor daily life does without. Each gets its own sheet: definition, conversion, instruments, writing rules, history. In 36 languages.
Energy, power and the bill
the open data sheet is highlightedSI base units
highlighted are those the kilowatt-hour is built fromAppliances in a flat
energy, money and megajoules computed by the sheet| Instrument | power | time | per use | per month | MJ per month | at the tariff | Remark |
|---|---|---|---|---|---|---|---|
| {name} | {p} | {t} | {once} | {month} | {mj} | {cost} | {note} |
All columns except the first three are computed from power and time, and the table clearly shows something that usually surprises: the kettle, with its two-plus kilowatts, uses less in a month than a forty-five-watt fridge, because the first runs for minutes and the second for all seven hundred and thirty hours. That is exactly what the unit says: what matters is not how powerful an appliance is, but how much area it covers on the power–time plane.