Energy, power and the joule
The joule is the SI unit of energy — and of heat: the General Conference on Weights and Measures resolved in 1948 that “the unit of quantity of heat is the joule”. Every other energy unit is a fixed number of joules, so converting means multiplying into joules and dividing out again. The trap is mixing energy with power. A watt is a joule per second — a rate — and a kilowatt-hour is the energy of one kilowatt for one hour: exactly 3,600,000 J. India’s Class 10 science textbook puts it the way bills do: “The commercial unit of electric energy is kilowatt hour (kW h), commonly known as ‘unit’. 1 kW h = 1000 watt × 3600 second = 3.6 × 10⁶ watt second = 3.6 × 10⁶ joule”.
| Unit | In joules | Defined by |
|---|---|---|
| 1 kilojoule (kJ) | 1,000 | SI prefix |
| 1 calorie, thermochemical (cal) | 4.184 exactly | NIST SP 811 |
| 1 calorie, International Table (cal_IT) | 4.1868 exactly | NIST SP 811 (1956 steam conference) |
| 1 kilocalorie / food Calorie (kcal) | 4,184 (or 4,186.8 IT) | NIST SP 811 |
| 1 watt-hour (Wh) | 3,600 exactly | NIST SP 811 |
| 1 kilowatt-hour (kWh) | 3,600,000 exactly | NIST SP 811 |
| 1 British thermal unit, IT (BTU) | 1,055.05585262 | from the IT calorie (NIST) |
| 1 therm (US) | 105,480,400 exactly | US Federal Register, 1968 |
| 1 therm (EC) | 105,506,000 exactly | EC Council Directive, 1979 |
| 1 tonne of oil equivalent (toe) | 41,868,000,000 | IEA: 10⁷ kcal (IT) |
| 1 tonne of coal equivalent (tce) | 29,307,600,000 | 0.7 toe |
| 1 electronvolt (eV) | 1.602176634 × 10⁻¹⁹ exactly | SI, since 2019 |
| 1 hartree (Eh) | 4.3597447222060 × 10⁻¹⁸ | CODATA 2022 |
| 1 foot-pound force (ft·lbf) | 1.355818 | NIST SP 811 |
| 1 erg | 10⁻⁷ exactly | NIST SP 811 |
| 1 ton of TNT | 4.184 × 10⁹ (a convention) | NIST SP 811 |
The converter’s “Download the factor table” button saves every unit and its joule value as a CSV file that opens in Excel or Google Sheets.
Which calorie? Which BTU?
The calorie has several definitions, and many converters don’t say which they use. The thermochemical calorie is exactly 4.184 J and is the one chemistry uses; the International Table calorie, fixed by the Fifth International Conference on the Properties of Steam in 1956, is exactly 4.1868 J and underlies engineering tables and energy statistics; NIST also lists a 15 °C calorie of 4.18580 J and a “mean” calorie of 4.19002 J. The BTU follows the same split: the International Table BTU is exactly 1,055.05585262 J because it is built from the IT calorie, the thermochemical BTU is about 1,054.350 J, and the IEA rounds it to 1,055.06 J. The two therms are legal definitions — the US therm (105,480,400 J) is the unit of the US gas industry; the EC therm is 105,506,000 J — and the US Energy Information Administration simply counts a therm as 100,000 BTU.
The choice matters at the fourth figure. The IEA defines a tonne of oil equivalent as 10⁷ kilocalories on the IT calorie — 41.868 GJ — so a calculator that uses the thermochemical calorie turns 1 toe into 10.0067 Gcal instead of 10. This converter labels both calories and both BTUs, and says under each result which one it used.
Food energy: kcal, Calories and kilojoules
A food “Calorie” is a kilocalorie — NIST calls “large calorie” an obsolete term for the kilocalorie used for food. To turn kcal into kJ, multiply by 4.184: a 2,000 kcal day is 8,368 kJ. But do not expect a label’s two numbers to divide to exactly 4.184. The EU’s labelling regulation gives separate, rounded factors for each nutrient, and Australia and New Zealand divide kilojoules by 4.18:
| Per gram of | kJ | kcal |
|---|---|---|
| Carbohydrate (not polyols) | 17 | 4 |
| Protein | 17 | 4 |
| Fat | 37 | 9 |
| Alcohol (ethanol) | 29 | 7 |
| Organic acid | 13 | 3 |
| Polyols | 10 | 2.4 |
| Fibre | 8 | 2 |
| Erythritol | 0 | 0 |
Those are the EU’s Annex XIV factors: 17 kJ against 4 kcal is a ratio of 4.25, and 37 against 9 is 4.11. US labels use 4, 4 and 9 Calories per gram for protein, carbohydrate and fat, round Calories to the nearest 5 or 10, and may add kilojoules in brackets. Rules differ in the details too: the EU counts erythritol as 0 kJ/g, Australia and New Zealand as 1.
That is the answer to a question left unanswered on r/nutrition — why a label read 1,586 kJ but 374 kcal, a ratio of 4.24: a carbohydrate-heavy food comes out near 4.25, a fatty one near 4.1. The commoner slip runs the other way. On r/loseit a user puzzled by an app suggesting “6360 calories a day” found the figure was in kilojoules — about 1,520 kcal. Dividing kJ by 4 is a quick check, 4.6% out; and a test-prep book quoted on Chemistry Stack Exchange gave a kilocalorie as 4.18 × 10⁸ J, wrong by a factor of 100,000.
Converting energy units step by step
Write the conversion factor as a fraction that cancels the unit you start with, then keep as many significant figures as the number you were given. The converter’s “Step by step” box does this for any pair, and reads scientific notation such as 7.30×10^6 or 7.30e6.
- 327 kJ × (1,000 J ÷ 1 kJ) = 327,000 J = 3.27 × 10⁵ J.
- 231 cal × (4.184 J ÷ 1 cal) × (1 kJ ÷ 1,000 J) = 0.967 kJ.
- 2,230 kcal × (4.184 kJ ÷ 1 kcal) = 9,330 kJ = 9.33 × 10³ kJ.
- 534 kWh × (3.6 × 10⁶ J ÷ 1 kWh) = 1.92 × 10⁹ J.
- 7.30 × 10⁶ J × (1 kcal ÷ 4,184 J) = 1.74 × 10³ kcal.
- 672 cal × (4.184 J ÷ 1 cal) = 2.81 × 10³ J.
- 50 ft·lbf × (1.355818 J ÷ 1 ft·lbf) × (1 BTU ÷ 1,055.056 J) = 0.0643 BTU.
Two answers change with the definitions: on the IT calorie, 231 cal is 0.96715 kJ and 7.30 × 10⁶ J is 1,743.6 kcal — the same to three significant figures, which is why homework answers rarely notice.
Power × time: kilowatt-hours, bills and running costs
The appliance method published by the US Department of Energy (reproduced by Virginia Cooperative Extension) is the one to use: wattage × hours used per day ÷ 1,000 = kilowatt-hours a day. A 2 kW heater for three hours is 6 kWh — six “units”. A rating is a maximum, though; a thermostat or a compressor that cycles uses less, which is why the same guidance divides a refrigerator’s plugged-in time by three. For a sense of scale, Ofgem’s typical domestic consumption figures from July 2026 are 2,500 kWh of electricity and 9,500 kWh of gas a year; the average US residential customer bought 10,791 kWh in 2022, according to the EIA; and India’s electricity consumption reached 1,460 kWh per person in 2024–25.
“Why is daily power usage measured in kWh and not just kW?” has been viewed nearly 8,000 times on Home Improvement Stack Exchange; the answer that stuck compares kW to miles per hour and kWh to miles. The slips that follow from mixing them up turn up constantly in forums — “amps per hour”, a “7 kWh charger”, a heater using “1000 kW/h”. Two related conversions trip people up just as often. A battery’s energy is mAh × voltage ÷ 1,000 in Wh, at the cell’s voltage: a 6,000 mAh power bank at 3.7 V holds 22.2 Wh, which is why its box doesn’t match 6,000 mAh at USB’s 5 V (“How to compare mAh and Wh” has over 180,000 views on Electrical Engineering Stack Exchange). And an air conditioner’s “BTU” rating is BTU per hour, a power: 12,000 BTU/h — one ton of cooling — is 3.5 kW of heat moved, and dividing by the unit’s coefficient of performance (a plain ratio, not BTU per watt) gives the electricity it draws.
UK gas bills convert the meter’s cubic metres into kilowatt-hours with a formula set by the Gas (Calculation of Thermal Energy) Regulations: volume × calorific value (around 39.5 MJ/m³, kept between 38 and 41) × 1.02264 for temperature and pressure ÷ 3.6. So 100 m³ of gas is about 1,122 kWh. An older meter that reads hundreds of cubic feet needs × 2.83 first — and applying that step to a metric meter by mistake nearly triples the bill: a UK reader’s 48.7 m³ should have been about 555 kWh, and was billed at 1,569. The calorific value also changes from bill to bill, so 11.2 kWh per cubic metre is only a rule of thumb. In the US, the EIA counts 1 kWh as 3,412 BTU and natural gas at about 1,036 BTU per cubic foot.
Energy statistics: toe, Mtoe, TJ and quads
International energy statistics use the tonne of oil equivalent, which the IEA defines as 10⁷ kilocalories, 41.868 GJ — “within a few per cent, equal to the net heat content of 1 tonne of crude oil”. A million of them is a Mtoe (41.868 PJ); the US uses the quad, 10¹⁵ BTU. Electricity from nuclear, hydro, wind and solar has no fuel to measure, so statistics need a convention: under the physical energy content method used by the IEA, hydro and solar PV electricity counts at 100% and nuclear at an assumed 33% efficiency.
On that basis the Energy Institute’s 2026 Statistical Review puts the world’s total energy supply at 600.31 exajoules in 2025, up 1.7% on 2024, with fossil fuels 86% of it — about 14,300 Mtoe or 167,000 TWh. Electricity generation reached 32,202 TWh, and Ember’s Global Electricity Review 2026 found renewables (33.8% of generation) overtaking coal (33.0%) in 2025.
Chemistry and physics: kJ/mol, eV, kT and hartrees
Molecular energies are quoted per mole or per particle, and the two are linked by the Avogadro constant, which has been exact since 2019 — as have the elementary charge and the Boltzmann constant. So 1 eV per particle is 96.4853 kJ/mol or 23.0605 kcal/mol, and 1 hartree is 27.2114 eV, 2,625.50 kJ/mol or 627.509 kcal/mol. Thermal energy is k_BT: at 298.15 K (25 °C) it is 2.4790 kJ/mol, 0.59248 kcal/mol or 25.693 meV, which is why a barrier of 10 kJ/mol is “about 4 kT” at room temperature. The “kJ/mol & kT” tab converts between all of them at any temperature; its kelvin figure is also E_a/R for an activation energy.
Two questions keep coming up on Chemistry and Physics Stack Exchange. “Joules to kJ/mol” (over 94,000 views) is nearly always a missing Avogadro constant: multiply the energy per molecule by 6.02214076 × 10²³ and divide by 1,000. “Moles of what?”, asked about activation energies and left unanswered, has a short answer: per mole of the reaction as written — a mole of molecular events. And “1 eV is about 11,600 K” is a conversion through the Boltzmann constant, not a statement that one is the other.
Mass and energy: E = mc²
With the speed of light exact, 1 kg of mass is exactly 8.987551787… × 10¹⁶ J — about 25 TWh, or 21.5 megatons of TNT on the convention that a ton of TNT is 4.184 × 10⁹ J. One atomic mass unit is 931.494 MeV and an electron 0.511 MeV. The Hiroshima bomb’s yield, revised to 16 kilotons in the 2002 dosimetry system, is about 67 TJ — under a gram of mass, by the same equation. The ton of TNT is a defined unit; real TNT releases a little more or less per kilogram depending on how it is measured, which is why NIST calls the 4.184 GJ figure “defined (not measured)”. Slipping a prefix is easy at these scales: an accepted answer on Physics Stack Exchange puts the Hiroshima yield at “63GJ”, a thousand times too small.
Exercise: METs and oxygen
Exercise physiologists measure energy in METs. The 2024 Adult Compendium of Physical Activities defines 1 MET as 3.5 mL of oxygen per kilogram per minute, “approximately 1.0 kcal/kg/h”, and classes 1.0–1.5 METs as sedentary, 1.6–2.9 as light, 3.0–5.9 as moderate and 6.0 or more as vigorous. Laboratories turn oxygen into energy with the Weir equation: each litre of oxygen releases about 4.7 kcal when the body burns mainly fat and about 5.05 kcal on carbohydrate. Fitness sites often write the MET rule as kcal per minute = MET × 3.5 × kg ÷ 200 — the same thing, using 5 kcal per litre of oxygen. The Exercise tab does both; both are estimates for an individual, and fitness trackers’ calorie counts vary more still.
Units that are not physical
Game and mod energy units have no joule equivalent. In Minecraft mods, Forge Energy (FE) is an integer counter in the mod API — NeoForge’s code describes it as “derived from the Redstone Flux power system” — so FE, RF and similar units convert only by each mod’s own rules, not by physics.