Some units belong to no measurement system at all. They are not SI, not Imperial and not US customary. They were created for one field, they fit the quantities that field deals with, and they survived because replacing them would make everyday numbers harder to read rather than easier. The calorie, the watt-hour and the electronvolt are the clearest examples, and all three measure energy.
Energy attracts these units because it spans an extraordinary range. A single chemical bond breaking involves about 10-19 joules. A day's electricity for a household involves about 107. That is twenty-six orders of magnitude between two ordinary quantities. The joule sits awkwardly at both ends, so each field adopted a unit sized to its own work.
A measurement system is more than a collection of units. It has base units, rules for deriving the rest, and usually a set of prefixes. SI has all three. The units on this page have none of them. They are individual definitions, each fixed by a conversion to the joule, with no structural relationship to one another.
The International Bureau of Weights and Measures recognises several such units for use alongside SI. Some, like the litre, the hour and the tonne, are accepted because they are too entrenched to remove. Others, like the electronvolt and the astronomical unit, are accepted because their values are experimentally determined and genuinely useful. The units here fall into both categories, and none of them is deprecated.
The calorie was defined as the energy needed to raise one gram of water by one degree Celsius. That quantity depends slightly on the starting temperature, which is why several calories were defined over the years with marginally different values. The thermochemical calorie, fixed at exactly 4.184 joules, is the one in general use today.
The confusion around this unit is entirely about scale. The calorie printed on food packaging is not the calorie of physics. It is the kilocalorie, one thousand times larger, and it is written with a capital C or as kcal to mark the difference. A chocolate bar listed at 250 calories contains 250 kilocalories, which is 250,000 physics calories, or about 1.05 million joules. Nutrition labels in most countries now print kilojoules alongside, which removes the ambiguity.
The unit persists in nutrition because the numbers land well. Daily energy intake is roughly 2000 to 2500 kilocalories, a range that is easy to hold in mind. In joules the same figures would run to eight or ten million, which conveys nothing to a reader comparing two products in a shop.
The watt-hour is the energy delivered by one watt of power sustained for one hour. Since a watt is one joule per second and an hour is 3600 seconds, a watt-hour is exactly 3600 joules and a kilowatt-hour is exactly 3.6 megajoules.
It is worth being precise about the distinction the unit depends on, because it is the most commonly confused pair in the whole of measurement. Power is a rate, the speed at which energy is used. Energy is the total amount. A 2000-watt heater draws energy at a fixed rate; run for three hours it consumes 6 kilowatt-hours. Electricity is billed on energy, not power, which is why the meter reads in kilowatt-hours.
The unit dominates the energy industry at every scale. Domestic bills are in kilowatt-hours. Electric car batteries are rated in kilowatt-hours, typically 40 to 100. Power station output is measured in megawatt-hours, and national consumption in terawatt-hours. The joule is never used for any of these, despite being the SI unit, because the numbers would be unmanageable: a year of household electricity is about 12 gigajoules, which almost nobody can interpret.
| Quantity | Typical value | In joules |
|---|---|---|
| LED bulb, one hour | 0.01 kWh | 36,000 J |
| Kettle, one boil | 0.1 kWh | 360,000 J |
| Household, one day | 10 kWh | 36,000,000 J |
| Electric car, full charge | 60 kWh | 216,000,000 J |
The electronvolt is the energy an electron gains crossing a potential difference of one volt. Since the 2019 redefinition of SI it is exact: 1.602176634 × 10-19 joules, because the elementary charge is now a defined constant.
It is the working unit of particle and atomic physics. Chemical bonds are a few electronvolts. Visible light photons run from about 1.6 to 3.3 electronvolts. X-rays are thousands, written keV. Nuclear transitions are millions, written MeV. Particle accelerators reach billions and trillions, written GeV and TeV, and the Large Hadron Collider operates at 13 TeV. Using joules at this scale would mean carrying an exponent of minus nineteen through every calculation.
The electronvolt also does a second job. Through mass-energy equivalence, physicists quote particle masses in electronvolts divided by the speed of light squared, and usually drop the divisor as understood. An electron is 511 keV, a proton 938 MeV, and the Higgs boson about 125 GeV. This makes masses and energies directly comparable, which matters when the two are converted into each other routinely.
Energy is not the only quantity with units outside the system. A number of others are formally accepted for use with SI without being part of it, and several appear elsewhere on this site.
Time is the largest exception. The minute, the hour and the day are not SI units, and they are not decimal, yet no serious proposal to replace them has ever succeeded. The second is the SI base unit, and everything above it is inherited from Babylonian sexagesimal counting. Angle works the same way: the degree, the arcminute and the arcsecond divide a circle into 360 rather than a power of ten, while the SI unit is the radian.
Volume and mass each have one accepted outsider. The litre is exactly one cubic decimetre, kept because cubic metres are too large for household quantities and cubic centimetres too small. The tonne is exactly 1000 kilograms, kept for the same reason at the other end of the scale. Land area has the hectare, 10,000 square metres, which persists because the square kilometre is too coarse for a field and the square metre far too fine.
Pressure has two. The bar is exactly 100,000 pascals, and the atmosphere exactly 101,325. Both are convenient because they sit close to ordinary air pressure, so a reading near one is immediately meaningful in a way that 101,325 pascals is not.
| Unit | Quantity | Exact SI value | Convert |
|---|---|---|---|
| Litre | Volume | 0.001 m³ | liters to cubic meters |
| Tonne | Mass | 1000 kg | tonnes to kilograms |
| Hour | Time | 3600 s | hours to seconds |
| Degree | Angle | π/180 rad | degrees to radians |
| Hectare | Area | 10,000 m² | hectares to square meters |
| Bar | Pressure | 100,000 Pa | bars to pascals |
The common thread is legibility. Each unit was chosen so that the quantities of its field come out as numbers between roughly one and a few thousand. That range is where human comparison works best. A unit that forces every figure into scientific notation makes a field harder to think in, whatever its formal merits.
There is also inertia, and it is not merely stubbornness. Decades of published measurements, equipment calibrations, billing systems and regulations are expressed in these units. Changing them would invalidate the readability of the entire existing record for no gain in accuracy, since the conversions are exact.
What has disappeared is ambiguity. Every unit here is now defined as an exact number of joules, so nothing is lost in translating between them. That was not always true. The calorie in particular had several competing definitions well into the twentieth century, and older sources should be read with care.
| Unit | Symbol | Value in joules | Convert |
|---|---|---|---|
| Electronvolt | eV | 1.602176634 × 10-19 | electronvolts to joules |
| Calorie | cal | 4.184 | calories to joules |
| Watt-hour | Wh | 3600 | watt-hours to joules |
| Kilocalorie | kcal | 4184 | kilocalories to joules |
| Kilowatt-hour | kWh | 3,600,000 | kilowatt-hours to joules |
Historical figures in these units need care, because the calorie was defined several times over. The thermochemical calorie of exactly 4.184 joules is standard today, but the International Steam Table calorie is 4.1868 joules, the 15-degree calorie about 4.1855, and the mean calorie about 4.190. The spread is under a quarter of a per cent, which is irrelevant for nutrition and significant in precise thermochemistry. A source published before about 1950 should be checked for which calorie it means.
The electronvolt has the opposite history. Its value depended on measurements of the elementary charge, so it improved steadily and shifted in its final digits with each revision of the fundamental constants. Since 2019 it has been exact and will not change again. Older papers quoting energies to many significant figures may differ slightly from modern values for this reason.
The watt-hour has never been ambiguous, because it derives from the second and the joule by definition rather than by experiment. A kilowatt-hour recorded in 1920 means exactly what it means now.
Because every unit here is defined exactly in joules, converting between any two of them is exact arithmetic. The joule is the natural bridge: convert into it, then out again. A kilowatt-hour is 860.4 kilocalories. A kilocalorie is 1.163 watt-hours. An electronvolt is too small to compare usefully with either, which is precisely why all three units exist.
You can browse every energy unit on this site from the energy unit archive, or see how these relate to the joule and its prefixes in the SI system.