Convert kWh to cal kilowatt hours ↔ calories Free Online Secure
Type a value in kilowatt hours and read it in calories at once. The factor is exact by definition, the arithmetic happens in your browser, and nothing is sent anywhere.
Nothing uploaded
Common values — Convert kWh to cal (kilowatt hours ↔ calories)
| kWh | cal |
|---|---|
| 1 | 860420.650096 |
| 2 | 1720841.30019 |
| 3 | 2581261.95029 |
| 5 | 4302103.25048 |
| 10 | 8604206.50096 |
| 20 | 17208413.0019 |
| 50 | 43021032.5048 |
| 100 | 86042065.0096 |
Where these units come from
Energy collected a unit from every field that discovered it separately. The joule is the SI one and the plainest: a newton acting over a metre. The calorie came from the study of heat and was defined by warming water one degree — which is why there are several of them, depending on which degree you start from; the thermochemical calorie, exactly 4.184 J, is the one used here. The kilowatt hour is not a physicist's unit at all but an accountant's: a kilowatt drawn for an hour, which is how electricity is sold. The BTU is its British cousin, built from the pound and the Fahrenheit degree, and it still runs the heating and cooling trade worldwide.
Where you meet them
Joules belong to physics and to food labels outside the English-speaking world. Kilowatt hours arrive on every electricity bill and describe the capacity of batteries, from a phone to a car. BTUs rate air conditioners, boilers and gas appliances almost everywhere, including in countries that are otherwise entirely metric. Calories — in practice kilocalories — rule nutrition, which is the one place where the unit's name is routinely a thousand times out.
Questions people ask
Why is a kilowatt hour not just a kilowatt?
Because one is a rate and the other is an amount. A kilowatt is how fast energy flows — a kettle draws about two of them. A kilowatt hour is what you get if that flow continues for an hour, and it is what the meter counts and the bill charges for. Running a 2 kW kettle for six minutes uses 0.2 kWh; running a 10 W lamp all day uses about the same.
Is the calorie on a food label the same as the one here?
No, and the difference is a factor of a thousand. The Calorie printed on food is a kilocalorie: a thousand of the calories used on this page. A 500-Calorie meal is 500,000 calories in the physicist's sense, or about 2.1 megajoules. Food labels in most of the world now print kilojoules beside it, which avoids the ambiguity entirely.
Is the answer exact?
Where both units are defined in terms of one another by whole numbers, yes — the page says so above the figure, and the only rounding is in how many digits are shown. Where the ratio has no finite decimal, the page shows twelve significant digits and says the relation is approximate rather than pretending otherwise.
Does anything I type leave my device?
No. The arithmetic runs in your browser; nothing is uploaded and there is no server to upload it to. Load the page once and it keeps working with the network switched off.
Kilowatt-hours to calories: electric heating in the physics laboratory
School and university physics measures heat in calories, because a calorie was defined as the heat that warms one gram of water by one degree. Electric heaters, on the other hand, are paid for in kilowatt-hours. A student who powers an immersion heater and wants to compare the electrical energy used with the heat the water gained must translate between the two. To convert kWh to cal, multiply by 860,421: 1 kWh is 860,421 calories, 0.5 kWh is 430,210 and 0.01 kWh is 8,604. The calculator above multiplies as you type, and the sections below show what the figures mean in calorimetry, in thermodynamics and in a few household checks.
The page gives the rule with worked examples, a profile of each unit, a comparison and a long run of laboratory and practical cases, followed by the usual slips. The calculation runs in your browser and nothing you type is sent anywhere. Experiments with mains electricity should only be done under supervision and with proper equipment.
How to convert kWh to cal: multiply by 860,421
The rule
One thermochemical calorie is exactly 4.184 joules and one kWh is exactly 3,600,000 joules, so a kWh holds 860,420.65 calories. To convert kWh to cal, multiply the kWh by 860,421: 0.1 kWh gives 86,042 calories, 2 kWh give 1,720,841 and 25 kWh give 21,510,516. To go back, divide calories by 860,421.
Calories, kilocalories and Calories
This page uses the small calorie, symbol cal. The kilocalorie is a thousand of them, and the food Calorie with a capital C is a kilocalorie. If you need kilocalories, divide the result by 1,000: 1 kWh is 860.4 kcal and 3 kWh are 2,581 kcal.
Worked examples
A 100-watt lamp that burns for an hour has used 0.1 kWh, which is 86,042 calories. A laboratory immersion heater of 500 W running for 10 minutes supplies 0.0833 kWh, 71,702 calories. A 60 Wh laptop battery stores 51,625 calories.
A quick sanity test
The result in calories is more than 800,000 times the number of kWh. If a “convert kWh to cal” calculation gave a smaller number than you started with, you divided instead of multiplying.
The kilowatt-hour
The unit on the meter
The kilowatt-hour is the energy a load of one kilowatt uses in one hour, exactly 3.6 megajoules. It is how electricity is sold and how battery packs are rated.
Where it appears
Bills, meters, appliance labels and battery capacities.
The calorie
The classroom unit of heat
The thermochemical calorie is defined as 4.184 joules, close to the heat needed to warm one gram of water by one degree Celsius. Older textbooks, chemistry data tables and calorimeter manuals still use it, often alongside the kilocalorie.
Where it appears
Physics and chemistry teaching, calorimetry and older heat tables.
kWh against calories
One kWh equals 860,421 calories, so a number in calories is enormous next to the same energy in kWh. In kilocalories the factor is 860.4. A tenth of a kWh is 86,042 calories and a quarter of a kWh is 215,105. They measure the same energy; only the size of the unit differs.
The conversion is exact. The most common trap is mixing the calorie with the kilocalorie, which changes the result by a factor of a thousand.
Where the conversion shows up
Electrical calorimetry
In the standard school experiment a heater warms a known mass of water while a meter records the electrical energy. A heater of 12 V and 3 A that runs for 300 seconds supplies 10,800 joules, which is 2,581 calories, or 0.003 kWh. If 200 g of water warms by 11 °C, it gains 2,200 calories, so about 85 per cent of the electrical energy reached the water. A “convert kWh to cal” calculation puts the meter reading on the same scale as the thermometer.
Heating a kettle by measurement
A 2.2 kW kettle that takes 3 minutes 45 seconds to heat a litre of water from 20 to 100 °C uses 0.1375 kWh, 118,308 calories. The water gained 80,000 calories, so the kettle is about 68 per cent efficient in that test, and the rest was lost to the body of the kettle and the air.
Specific heat in electrical terms
Heating 1 kg of copper by 100 K takes 9,200 calories, 0.0107 kWh. The same for water takes 100,000 calories, 0.116 kWh, which shows why water stores so much heat compared with metals.
Joule and the mechanical equivalent
In the 1840s James Prescott Joule stirred water with a paddle driven by falling weights and measured the tiny rise in temperature. His results fell between 4.1 and 4.2 joules per calorie. Modern practice fixes the value at 4.184, so a kWh holds 860,421 calories. A “convert kWh to cal” calculation therefore rests on a definition, not on an experiment.
The heat capacity of the human body
A 70 kg adult has a specific heat of about 0.83 cal/g·°C, so raising the body by one degree takes 58,100 calories, 0.0675 kWh. The body does this in a fever by burning fuel, not by drawing power from a socket. The small kWh figure shows how little energy a fever really involves.
Air and the energy to warm it
Air at 1.2 kg/m³ has a specific heat of 0.24 cal/g·°C, so a cubic metre needs 288 calories per degree. A kWh therefore warms nearly 3,000 cubic metres of air by one degree. A typical 60 m³ room warmed by 10 degrees takes only 0.2 kWh in the air itself, and the rest of a heater's work goes into walls and furniture.
Heat storage in building materials
A concrete wall of 10 m² and 20 cm thickness weighs about 4,800 kg and has a specific heat of 0.21 cal/g·°C, so it stores 1,008 kcal per degree. A 5-degree swing stores 5,040 kcal, 5.9 kWh. This is the thermal mass that smooths daily temperature changes.
Melting a metal
To melt 1 kg of aluminium from 20 to 660 °C takes 137,600 calories to heat plus 94,900 to melt, about 232,500 calories, 0.27 kWh, in the ideal case. Real furnaces need two or three times as much because of losses. A “convert kWh to cal” calculation gives the lower bound that no furnace can beat.
The bomb calorimeter
A bomb calorimeter burns a sample in oxygen. One gram of benzoic acid, the standard, releases 6,318 calories, which is 0.00734 kWh. The same sample is burned to calibrate the instrument, and the result is quoted in calories per gram or in joules.
Hydrogen in calories
Hydrogen releases about 120 kJ per gram on its lower heating value, which is 28,700 calories, 0.033 kWh. One kWh of hydrogen therefore weighs 30 g. Chemistry tables give such numbers in calories per gram or kilocalories per mole, and a quick convert kWh to cal converts them to a power-engineering scale.
The Dulong–Petit rule
In 1819 Dulong and Petit noticed that many solid elements need about 6 calories to warm one mole by a degree. Modern theory gives 3R, which is 5.96 cal/mol·K. For copper, 63.5 g at 0.092 gives 5.84. Warming a mole of any such element by 100 K takes about 596 calories, 0.0007 kWh.
Thermal mass of a steel block
One tonne of steel, at 0.107 cal/g·°C, needs 10.7 million calories to warm by 100 degrees. That is 12.4 kWh. A forge or heat-treatment furnace taking it to 800 degrees needs about 97 kWh in the metal alone, before the losses of the furnace walls and exhaust.
Foot-pounds and calories
An engineer may meet energy in foot-pounds-force. One kWh is 2.655 million ft·lbf, and one calorie is 3.086 ft·lbf. Lifting a one-pound weight by 778 feet would take about 252 calories. The classic mechanical equivalent of heat is the same idea expressed in older units.
The mental shortcut
To convert kWh to cal in your head, multiply the kWh by 860 for kilocalories: 3 kWh × 860 = 2,580 kcal, against the exact 2,581. The slip is below 0.05 per cent. For small calories add three zeros to the kilocalorie figure.
Three different calories
The thermochemical calorie is 4.184 J. The International Table calorie is 4.1868 J, and the 15-degree calorie is about 4.1855 J. A kWh holds 860,421 thermochemical calories, 859,845 International Table calories and 860,112 fifteen-degree calories. The difference of 0.07 per cent is invisible in classroom work.
Spreadsheet formulas
In a spreadsheet, keep the kWh in column A and use =A2*860420.65 in column B for calories, or =A2*860.42065 for kilocalories. For the opposite direction use =B2/860420.65. A column that multiplies the kWh by 3.6 gives MJ and offers a quick cross-check.
Rounding in lab reports
An energy meter shows the kWh to three or four figures, and a thermometer shows temperature to a tenth of a degree. Quote calories to the same number of figures. 0.0833 kWh is 71,700 calories, not 71,702 or 71,702.4. Extra digits invite a marker's red pen.
Landmarks to memorise
1 kWh is 860.4 kcal. A tenth of a kWh is 86 kcal. 10 kWh is 8,604 kcal. 100 kWh is 86 Mcal. One MWh is 860 Mcal, 0.86 Gcal. In small calories, add three zeros to each of these. With these landmarks most mental convert kWh to cal work is possible.
Reference ladder
0.005 kWh: 4,302 cal. 0.02 kWh: 17,208 cal. 0.075 kWh: 64,532 cal. 0.4 kWh: 344,168 cal. 1.5 kWh: 1,290,631 cal. 6 kWh: 5,162,524 cal. 12 kWh: 10,325,048 cal. A table like this makes it quick to test any calculator output.
Checking by reversing
To check a “convert kWh to cal” calculation result, divide the answer by 860,421. If 0.4 kWh gave 344,168 cal, then 344,168 / 860,421 = 0.4. A second test concerns size: the calorie figure must have six more digits than the kWh figure.
Link to MJ and BTU
A kWh is 3.6 MJ, 860.4 kcal and 3,412 BTU. One BTU is 252 calories. Therefore 10,000 BTU is 2.52 million calories, 2.93 kWh. All three units describe the same heat, and a “convert kWh to cal” calculation only swaps one label for another.
A worked example
A class heats 400 g of water from 18 to 58 °C with a 150 W heater. The water gains 400 × 40 = 16,000 calories. With no losses a 150 W heater would need 446 seconds to supply that, but the class runs it for 560 seconds. Their electrical input is 0.0233 kWh, 20,076 calories, so the efficiency is 80 per cent.
Two routes to one answer
You can reach calories from kWh directly with 860,421, or via joules: 3.6 million multiplied by 1 / 4.184. For kilocalories take the MJ route with 3.6 × 239.006 = 860.4. If the two routes disagree, a digit was copied wrongly.
Water as a thermal reservoir
A kilowatt-hour warms 860 kg of water by one degree. Ten kWh would warm one cubic metre by 8.6 degrees, and 1.16 kWh would warm it by one degree. A hot-water cylinder of 200 litres warmed by 40 degrees stores 8,000 kcal, 9.3 kWh, which is why such tanks act as a heat battery.
Specific heats of common materials
In calories per gram per degree: water 1.00, ethanol 0.58, ice 0.50, steam 0.48, air 0.24, aluminium 0.215, concrete 0.21, iron 0.107, copper 0.092, mercury 0.033 and lead 0.031. The lower the number, the less electricity it takes to raise a kilogram by a degree. Multiply the figure by the mass and the temperature rise to get calories, then divide by 860,421 for kWh.
Melting and boiling
Melting one gram of ice takes 79.7 calories and boiling one gram of water takes 539 calories. So 1 kg of ice needs 79,700 calories, 0.0926 kWh, to melt, and 1 kg of boiling water needs 539,400 calories, 0.627 kWh, to evaporate. A single kWh melts 10.8 kg of ice or boils away 1.6 kg of water.
The ice calorimeter
In 1782 and 1783 Lavoisier and Laplace measured heat by the amount of ice it melted. If a reaction melts 50 g of ice, it released 3,985 calories, about 0.0046 kWh. The method is slow and has been replaced by electronic sensors, but the idea of measuring heat by its effect on water or ice lives on in every calorimeter.
Mixing hot and cold water
Mix 200 g of water at 80 °C with 300 g at 20 °C and the result settles at 44 °C. The hot water gave up 7,200 calories, 0.0084 kWh, and the cold water took it up. Such exercises teach conservation of energy, and a “convert kWh to cal” calculation links them to electric heaters.
The water equivalent of a calorimeter
A calorimeter vessel also absorbs heat. A brass cup of 100 g at 0.092 cal/g·°C behaves like 9.2 g of water. Students add this to the water mass before they work out the heat. For a 10 K rise it comes to 92 calories, 0.0001 kWh, tiny in kWh but roughly 4 per cent of the result when 200 g of water is used.
Joule heating in a resistor
A resistor of 100 ohms carrying 2 amps dissipates 400 W. In a minute it releases 24,000 joules, 5,736 calories, 0.00667 kWh. Because all of it turns to heat, this is the simplest calorimetric source, and the electrical energy in kWh equals the heat in calories divided by 860,421.
More values for convert kWh to cal
A longer list of conversions
If the value you need is not in the first list, these further conversions may be close enough to read off directly:
- 0.1 kWh = 86,042.1 cal
- 0.5 kWh = 430,210 cal
- 3 kWh = 2,581,262 cal
- 4 kWh = 3,441,683 cal
- 7 kWh = 6,022,945 cal
- 15 kWh = 12,906,310 cal
- 20 kWh = 17,208,413 cal
- 75 kWh = 64,531,549 cal
- 200 kWh = 172,084,130 cal
- 500 kWh = 430,210,325 cal
- 2,000 kWh = 1,720,841,300 cal
- 10,000 kWh = 8,604,206,501 cal
Common slips with a “convert kWh to cal” calculation
Calorie or kilocalorie
The factor 860 applies to kilocalories and 860,421 to small calories. A label saying "2,500 calories" on an air-conditioner almost always means kilocalories per hour.
Power and energy
A heater of 1 kW releases 860 kcal per hour, but a heater that has run for an hour has used 1 kWh. A rate in kcal/h is a power; an amount in kcal is an energy.
Assuming all the energy reaches the sample
An electric heater gives its energy as heat, but the sample only gets a share of it. The kWh figure in the meter is always larger than the calories gained by the water, and the ratio is the efficiency.
Short answers
How do I convert kWh to cal?
Multiply the kWh by 860,421 for calories or by 860.4 for kilocalories.
How many calories are in 1 kWh?
860,421 calories, which is 860.4 kcal.
How many kcal are in 3 kWh?
2,581 kcal.
How many kWh in 1,000 kcal?
1.162 kWh.
Does my number leave my device?
No, the calculation runs in your browser.
More pages and a wrap-up
For other energy conversions see Convert kWh to J, Convert kWh to BTU, Convert J to cal, Convert cal to J, Convert km to mi, Convert mi to km, Convert °C to °F, Convert °F to °C, Convert MPG (US) to MPG (UK). For the opposite direction see Convert cal to kWh.
In short, a “convert kWh to cal” calculation means one multiplication by 860,421 and a unit written next to the result. Your figure is calculated locally, with no account and no upload.