Energy Converter
Convert energy between joules, calories, kilowatt-hours, BTU, and electronvolts. Includes real-world reference points for electricity, food, and physics.
Energy Converter
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Formula: 1 cal = 4.184 J | 1 kWh = 3,600,000 J | 1 BTU = 1055.06 J | 1 eV = 1.602e-19 J
Worked example — 1 kWh = 3,600,000 J = 860,421 cal = 3,412.14 BTU
Formula
1 cal = 4.184 J | 1 kWh = 3,600,000 J | 1 BTU = 1055.06 J | 1 eV = 1.602e-19 J
The joule (J) is the SI unit of energy, defined as the work done when a force of one newton moves an object one meter. All other energy units convert to joules through a fixed, internationally agreed factor: calories via the mechanical equivalent of heat, kilowatt-hours via power multiplied by time, BTU via the heat needed to warm one pound of water by one degree Fahrenheit, and electronvolts via the charge of a single electron.
Worked Examples
Example 1: Electricity Bill Energy Use
Problem:A household appliance uses 1 kWh of electricity. Express this in joules, calories, and BTU.
Solution:Joules = 1 kWh x 3,600,000 J/kWh = 3,600,000 J Calories = 3,600,000 / 4.184 = 860,421 cal BTU = 3,600,000 / 1055.06 = 3,412.14 BTU
Result:1 kWh = 3,600,000 J = 860,421 cal = 3,412.14 BTU
Example 2: Food Energy to Joules
Problem:A snack bar contains 180 food Calories (kcal). Convert this to joules and kilojoules.
Solution:Joules = 180 kcal x 4184 J/kcal = 753,120 J Kilojoules = 753,120 / 1000 = 753.12 kJ
Result:180 Calories = 753,120 J = 753.12 kJ
Example 3: Particle Physics Energy Scale
Problem:A particle accelerator imparts 2.5 MeV of kinetic energy to an electron. Convert this to joules.
Solution:1 MeV = 1,000,000 eV x 1.602e-19 J/eV = 1.602e-13 J 2.5 MeV = 2.5 x 1.602e-13 = 4.005e-13 J
Result:2.5 MeV = 4.005 x 10^-13 joules
Frequently Asked Questions
What is a joule?
A joule is the energy transferred when a force of 1 newton acts over 1 meter. It equals 1 watt-second. It is the SI base unit of energy, named after 19th-century physicist James Prescott Joule, whose experiments established the mechanical equivalent of heat. Because a single joule is small in everyday terms (lifting a small apple one meter takes about 1 joule), most household and industrial energy figures are expressed in kilojoules, kilowatt-hours, or BTUs instead of raw joules.
How do I convert joules to calories?
Divide joules by 4.184 to get thermochemical calories, or by 4.1868 for International Table calories. For food Calories (kcal), divide by 4184. For example, 1000 J equals about 239 small calories or 0.239 food Calories. The two calorie definitions differ by less than 0.07 percent and are used interchangeably for almost all practical purposes.
What is the difference between a calorie and a kilocalorie?
A kilocalorie (kcal) equals 1000 small calories. Food labels use kilocalories but call them 'Calories' (capital C). One food Calorie equals 4184 joules. This distinction matters when converting energy in nutritional or scientific contexts. A food label stating '200 Calories' per serving is stating 200 kilocalories, or 836,800 joules — a common point of confusion for anyone reading labels from countries that list kilojoules explicitly.
How are joules related to kilowatt-hours?
One kilowatt-hour (kWh), the unit on electricity bills, equals 3,600,000 joules. This comes from 1000 watts multiplied by 3600 seconds in an hour. A 100-watt bulb running for 10 hours consumes 1 kWh or 3.6 million joules of energy. Utility companies bill in kWh rather than joules purely for convenience — a typical US household uses around 30 kWh (108 million joules) per day, a figure that would look unwieldy expressed only in joules.
What is a BTU and where is it commonly used?
A British Thermal Unit (BTU) is defined as the energy needed to raise the temperature of one pound of water by one degree Fahrenheit, equal to approximately 1,055.06 joules. It remains the standard unit for rating furnaces, air conditioners, and water heaters in the United States. A central air conditioner might be rated at 36,000 BTU/hour (a '3-ton' unit, since one ton of cooling equals 12,000 BTU/hour), while a home furnace might be rated at 80,000 to 120,000 BTU/hour of heat output.
What is an electronvolt and why is it used in physics?
An electronvolt (eV) equals approximately 1.602 x 10^-19 joules and represents the kinetic energy gained by a single electron accelerated through one volt of electric potential. Because joules are an enormous unit at the scale of individual atoms, physicists use electronvolts (and multiples like keV, MeV, GeV) to describe photon energies, particle collision energies, and electron binding energies without writing extremely small decimals. The Large Hadron Collider accelerates protons to energies measured in TeV (trillion electronvolts).
How much energy is in common everyday activities and foods?
Concrete reference points make energy units easier to grasp: a slice of bread contains roughly 65 food Calories (272,000 joules); climbing a flight of stairs uses about 5,000 joules; a smartphone battery stores roughly 40,000 joules (11 Wh); a car battery stores about 1.8 million joules (0.5 kWh); and boiling a kettle of water uses approximately 400,000-500,000 joules. Comparing an unfamiliar energy quantity to one of these references is often faster than relying on unit conversion alone.
What is the difference between energy and power in these units?
Energy is a quantity, power is the rate at which it is delivered. The joule is energy; the watt is power and equals one joule per second. That is why a kilowatt-hour is an energy unit, not a power unit: it is 1,000 watts sustained for 3,600 seconds, giving 3,600,000 joules. A 2 kW heater running for three hours consumes 6 kWh, which is 21.6 megajoules. Mixing the two, for example quoting a battery in kilowatts rather than kilowatt-hours, is one of the most common energy-unit mistakes.
Why do food labels in some countries show kilojoules instead of Calories?
Kilojoules are the SI expression of food energy, so many countries require or prefer them on nutrition panels, while US labels use the food Calorie, which is really a kilocalorie. The conversion is fixed: one kilocalorie equals 4.184 kilojoules. A 2,000 Calorie daily reference intake is therefore about 8,368 kilojoules. Labels showing both figures are not listing two different energy amounts, only the same energy in two units, so compare like with like before concluding one product is higher in energy.
What is a therm and how does it relate to BTU and joules?
A therm is defined as exactly 100,000 BTU and is the billing unit on many US natural gas bills. Using 1,055.06 joules per BTU, one therm equals about 105.5 megajoules, which is roughly 29.3 kilowatt-hours. That equivalence is what makes it possible to compare a gas bill quoted in therms against an electricity bill quoted in kWh: convert both to the same unit first, then compare cost per unit of delivered energy, allowing for the efficiency of the appliance that burns the gas.
References
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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