How do I convert between joules and calories?

Multiply joules by 0.239006 to get calories, or multiply calories by 4.184 to get joules. The factor 4.184 J/cal is exact for the thermochemical calorie, which is the standard used in food energy labeling and most scientific work. For example, a 2,000 Calorie daily diet provides 2,000 × 1,000 × 4.184 = 8,368,000 J = 8.37 MJ of food energy. The dietary Calorie (capital C) is actually a kilocalorie (1,000 cal), which is the most common source of conversion error. If a food label says 200 Calories, it means 200 kcal = 200,000 cal = 836,800 J. Always check whether calories means small calories (cal) or dietary Calories (kcal).

What is the difference between a BTU and a therm?

A therm equals 100,000 BTU. The BTU (British thermal unit) is the base unit: the energy to raise one pound of water by one degree Fahrenheit. The therm was created as a billing unit for natural gas because residential gas consumption in BTU produces inconveniently large numbers. A typical US home uses 600–1,200 therms annually, which would be 60,000,000–120,000,000 BTU — a six-to-eight-digit number that is harder to read and compare. In joules: 1 therm = 1.055 × 10⁸ J. In kWh: 1 therm = 29.31 kWh. In eV: 1 therm = 6.585 × 10²⁵ eV. The US Energy Information Administration reports national natural gas consumption in quads (10¹⁵ BTU), where 1 quad = 10,000,000 therms.

How many electronvolts are in one joule?

One joule equals exactly 6.241509074 × 10¹⁸ electronvolts. This conversion factor became exact on May 20, 2019, when the International System of Units (SI) redefined the elementary charge as e = 1.602176634 × 10⁻¹⁹ C exactly. Since 1 eV = e × 1 V = 1.602176634 × 10⁻¹⁹ J, the reciprocal gives the exact number of electronvolts per joule. This is a fundamental constant of nature, not a measured value subject to experimental uncertainty. For practical work, 1 J ≈ 6.24 × 10¹⁸ eV is sufficient, but the exact relationship matters in precision metrology, quantum standards, and fundamental physics.

Why does food use different energy units from electricity?

Food energy is measured in Calories (kilocalories) because the calorie was developed by chemists studying heat released during combustion long before electricity became a household energy source. The bomb calorimeter — used to measure food energy by burning a sample and measuring the temperature rise of surrounding water — naturally produces results in calories. The different unit systems evolved in isolation: food scientists in the early 20th century used calories, electric utilities used watt-hours, and heating engineers used BTUs. By the time the SI system attempted to unify them in the 1960s, each industry had decades of embedded standards, regulations, and consumer familiarity. The conversion between them is exact and straightforward, but changing labels, meters, and public education would cost billions.

Which energy unit should I use for a specific application?

Use joules for any scientific or engineering calculation where SI consistency is required, for physics and chemistry problems, and for publications in scientific journals. Use kilowatt-hours for electricity consumption, battery capacity, solar generation, and any context involving the electrical grid. Use BTUs for HVAC equipment sizing, furnace and air conditioner specifications, and natural gas appliance ratings in the United States. Use calories (or Calories) for food energy, nutrition labeling, metabolic rates, and exercise energy expenditure. Use electronvolts for atomic, molecular, nuclear, and particle physics; semiconductor band gaps; and quantum chemistry. Use therms for residential natural gas billing in the US and UK. Use quads for national and global energy statistics and policy analysis. For any conversion between these contexts, the master conversion table provides exact factors. - Electronvolt to Joule Converter - Joule to Electronvolt Converter - Conversion Calculator - Temperature Converter - Weight Converter

Energy Conversion: Six Ways to Measure the Same Physical Quantity

Energy is the most fundamental conserved quantity in physics, yet it is measured in an extraordinary variety of units that reflect different historical traditions and practical contexts. The joule is the SI standard — the work done by a force of one newton over one meter — but a nutrition label lists calories, an electricity bill shows kilowatt-hours, a furnace specification uses British thermal units, and a particle physicist works in electronvolts. The conversion between these units spans 43 orders of magnitude, from the 10⁻¹⁹ J of a single infrared photon to the 10⁴² J annual energy output of the Sun. James Prescott Joule established the mechanical equivalent of heat through his paddle-wheel experiments in 1843, and the SI system eventually named its energy unit after him. [James Prescott Joule, 1843; SI Brochure 9th edition, 2019; 26th CGPM, 2018] {#deck}

The major energy units and where they are used
Master conversion table: all major energy units
The conversion formulas between every unit pair
Worked examples: translating between domains
Why so many units? Historical and practical reasons
Frequently Asked Questions

The major energy units and where they are used

Joule (J) — the SI standard: The joule is the coherent SI unit of energy, defined as the energy transferred when a force of one newton acts through a distance of one meter. Used universally in physics, engineering, and scientific research. All other energy units are defined relative to the joule.

Calorie (cal) — food and chemistry: The calorie was originally defined as the energy needed to raise one gram of water by one degree Celsius. The dietary Calorie (capital C, or kilocalorie, kcal) equals 1,000 cal = 4,184 J. The calorie is used in food energy labeling, chemistry (enthalpy of reaction), and thermodynamics. The 15°C calorie (cal₁₅) and thermochemical calorie (calₜₕ) are variant definitions differing by approximately 0.03%, but the 4.184 J calorie is the standard for food and most scientific work since the 1950 adoption by the International Union of Nutritional Sciences.

Kilowatt-hour (kWh) — electricity billing: The kilowatt-hour is the energy consumed by a 1 kW device operating for one hour: 1 kWh = 3.6 × 10⁶ J. Used by electric utilities worldwide for residential, commercial, and industrial billing. In 2023, global electricity generation was approximately 30,000 TWh (terawatt-hours), or 1.08 × 10²⁰ J.

British thermal unit (BTU) — heating and cooling: The BTU is the energy needed to raise one pound of water by one degree Fahrenheit. Used for HVAC system ratings, natural gas billing (in therms, where 1 therm = 100,000 BTU), and furnace/air conditioner capacity specifications. 1 BTU = 1,055.05585262 J (the International Table BTU, the most common standard).

Electronvolt (eV) — particle and quantum physics: The electronvolt is the kinetic energy gained by a single electron accelerated through a potential difference of one volt. Used for atomic, nuclear, and particle physics; material science (band gaps); and quantum chemistry. 1 eV = 1.602176634 × 10⁻¹⁹ J exactly (after the 2019 SI redefinition).

Therm — natural gas billing: The therm equals 100,000 BTU, used for residential natural gas billing in the US and UK. A typical US home consumes 600–1,200 therms annually.

Quad — national energy statistics: The quad equals one quadrillion BTU (10¹⁵ BTU), used by the US Energy Information Administration for national and global energy accounting. The US consumes approximately 100 quads of primary energy annually.

Master conversion table: all major energy units

Conversion Factors Between Major Energy Units

Unit	Joules	Calories	kWh	BTU	eV	Therms
1 J	1	0.2390	2.778 × 10⁻⁷	9.478 × 10⁻⁴	6.242 × 10¹⁸	9.478 × 10⁻⁹
1 cal	4.184	1	1.162 × 10⁻⁶	3.966 × 10⁻³	2.611 × 10¹⁹	3.966 × 10⁻⁸
1 kWh	3.6 × 10⁶	8.60 × 10⁵	1	3,412	2.247 × 10²⁵	0.03412
1 BTU	1,055	252.0	2.931 × 10⁻⁴	1	6.585 × 10²¹	0.00001
1 eV	1.602 × 10⁻¹⁹	3.827 × 10⁻²⁰	4.450 × 10⁻²⁶	1.519 × 10⁻²²	1	1.519 × 10⁻²⁷
1 therm	1.055 × 10⁸	2.521 × 10⁷	29.31	100,000	6.585 × 10²⁵	1

Typical energy quantities in multiple units:

One apple (100 g) lifted 1 meter: 1 J = 0.239 cal = 2.78 × 10⁻⁷ kWh = 0.000948 BTU = 6.24 × 10¹⁸ eV
One dietary Calorie (food label): 4,184 J = 1,000 cal = 0.001162 kWh = 3.97 BTU = 2.61 × 10²² eV
Average US daily home electricity: 30 kWh = 1.08 × 10⁸ J = 25.8 Mcal = 102,400 BTU = 6.74 × 10²⁶ eV
One gallon of gasoline: 120,000 BTU = 1.27 × 10⁸ J = 35.3 kWh = 30.3 Mcal = 7.90 × 10²⁶ eV
Annual US primary energy: 100 quads = 1.055 × 10²⁰ J = 2.52 × 10¹⁹ cal = 2.93 × 10¹³ kWh = 6.59 × 10³⁸ eV

The conversion formulas between every unit pair

From joules:

Calories = J × 0.239006
kWh = J × 2.77778 × 10⁻⁷
BTU = J × 9.47817 × 10⁻⁴
eV = J × 6.241509 × 10¹⁸
Therms = J × 9.47817 × 10⁻⁹

From calories:

Joules = cal × 4.184
kWh = cal × 1.16222 × 10⁻⁶
BTU = cal × 3.96567 × 10⁻³
eV = cal × 2.61144 × 10¹⁹
Therms = cal × 3.96567 × 10⁻⁸

From kilowatt-hours:

Joules = kWh × 3.6 × 10⁶
Calories = kWh × 8.60421 × 10⁵
BTU = kWh × 3,412.14
eV = kWh × 2.24694 × 10²⁵
Therms = kWh × 0.0341214

From BTUs:

Joules = BTU × 1,055.06
Calories = BTU × 252.164
kWh = BTU × 2.93071 × 10⁻⁴
eV = BTU × 6.58514 × 10²¹
Therms = BTU × 0.00001

From electronvolts:

Joules = eV × 1.60218 × 10⁻¹⁹
Calories = eV × 3.82673 × 10⁻²⁰
kWh = eV × 4.45049 × 10⁻²⁶
BTU = eV × 1.51857 × 10⁻²²
Therms = eV × 1.51857 × 10⁻²⁷

From therms:

Joules = therms × 1.05506 × 10⁸
Calories = therms × 2.52164 × 10⁷
kWh = therms × 29.3071
BTU = therms × 100,000
eV = therms × 6.58514 × 10²⁵

Rounding and precision: The conversion factors above are given to 5–6 significant figures, sufficient for all practical engineering and scientific calculations. For exact conversion where the definition is exact (e.g., 1 cal = 4.184 J, 1 kWh = 3.6 × 10⁶ J), use the exact definition rather than the rounded value. For conversions involving the 2019 SI-defined constants (e, h, k, N_A), the values are exact.

Worked examples: translating between domains

Worked example 1: How many kWh is one dietary Calorie?

A food label lists 200 Calories (kcal). Express in kWh and joules.

Joules = 200 × 4,184 = 836,800 J = 8.368 × 10⁵ J
kWh = 836,800 / 3.6 × 10⁶ = 0.2324 kWh
In eV: 8.368 × 10⁵ × 6.242 × 10¹⁸ = 5.224 × 10²⁴ eV
Result: 200 Calories = 837 kJ = 0.232 kWh = 5.22 × 10²⁴ eV

Worked example 2: Convert a furnace BTU rating to kW

A furnace is rated at 100,000 BTU/h. Express the hourly energy consumption in kWh and joules.

kWh per hour = 100,000 × 2.931 × 10⁻⁴ = 29.31 kWh
Joules per hour = 100,000 × 1,055 = 1.055 × 10⁸ J
In eV per hour: 1.055 × 10⁸ × 6.242 × 10¹⁸ = 6.585 × 10²⁶ eV
At $0.16/kWh, one hour of full operation costs 29.31 × $0.16 = $4.69 in electrical equivalent energy

Worked example 3: Gasoline energy in multiple units

One gallon of gasoline contains approximately 120,000 BTU of chemical energy. Express in all major units.

Joules = 120,000 × 1,055 = 1.266 × 10⁸ J
Calories = 1.266 × 10⁸ × 0.2390 = 3.025 × 10⁷ cal = 30,250 kcal (Calories)
kWh = 1.266 × 10⁸ / 3.6 × 10⁶ = 35.17 kWh
eV = 1.266 × 10⁸ × 6.242 × 10¹⁸ = 7.902 × 10²⁶ eV
Result: one gallon of gasoline = 120,000 BTU = 35.2 kWh = 7.90 × 10²⁶ eV

Worked example 4: Solar energy reaching Earth

The total solar energy reaching Earth's surface per square meter per second (solar constant) is approximately 1,361 W/m², or 1,361 J per square meter per second. Express the daily energy per square meter in all units.

Daily J/m² = 1,361 × 86,400 = 1.176 × 10⁸ J/m²
Daily kWh/m² = 1.176 × 10⁸ / 3.6 × 10⁶ = 32.67 kWh/m²
Daily BTU/m² = 32.67 × 3,412 = 111,500 BTU/m²
Daily eV/m² = 1.176 × 10⁸ × 6.242 × 10¹⁸ = 7.34 × 10²⁶ eV/m²
Result: each square meter of Earth's surface receives 32.7 kWh of solar energy daily — enough to power an average US home for one day from roughly 30 m² of solar panels at 20% efficiency

Worked example 5: Annual US energy in all units

The US consumed approximately 100 quads of primary energy in 2023. Express in every major unit.

Joules = 100 × 10¹⁵ × 1,055 = 1.055 × 10²⁰ J
Calories = 1.055 × 10²⁰ × 0.2390 = 2.521 × 10¹⁹ cal
kWh = 1.055 × 10²⁰ / 3.6 × 10⁶ = 2.931 × 10¹³ kWh
BTU = 100 × 10¹⁵ = 10¹⁷ BTU
eV = 1.055 × 10²⁰ × 6.242 × 10¹⁸ = 6.585 × 10³⁸ eV
In therms: 100 × 10¹⁵ / 100,000 = 10¹² therms

Why so many units? Historical and practical reasons

The proliferation of energy units reflects the historical independence of scientific and engineering disciplines before the SI system achieved global adoption.

The joule (1843): James Prescott Joule's paddle-wheel experiments established that mechanical work and heat are interconvertible forms of energy, with a fixed ratio of 4.1868 J per calorie. The unit was named in his honor at the 1889 British Association meeting. The SI system formalized the joule as the coherent energy unit in 1960.

The calorie (1824): Nicolas Clément defined the calorie during lectures on steam engine efficiency. The calorie predates the joule by nearly two decades and became entrenched in chemistry, nutrition, and thermodynamics before the SI system existed. Its persistence in food labeling is a textbook example of unit inertia — changing every food label worldwide would cost billions.

The kilowatt-hour (1880s): As electricity became a commercial commodity, utilities needed a billing unit that related directly to meter readings. The kilowatt-hour — power in kilowatts multiplied by time in hours — mapped naturally onto the electromechanical meter's rotating disk. The joule would have produced inconveniently large numbers (a typical monthly bill of 900 kWh = 3.24 × 10⁹ J).

The BTU (1830s): British thermal unit was defined during the early development of steam engine thermodynamics. It was designed for water-based heating systems: one BTU raises one pound of water by one degree Fahrenheit, making it intuitive for boiler and radiator engineering. The unit persists in HVAC because the installed base of equipment, standards, and training materials all use BTU.

The electronvolt (1905–1910s): The electronvolt emerged from early particle physics experiments as a natural unit: the energy gained by a single electron (with elementary charge e) crossing a one-volt potential difference. It became indispensable in nuclear and particle physics because the energies involved are on the order of MeV to TeV — far more convenient than 10⁻¹³ to 10⁻⁷ J.

The therm (1940s): The British gas industry standardized the therm (100,000 BTU) for residential billing through the Gas Act of 1948. The therm produces manageable two-to-four-digit numbers for household consumption (100–300 therms per heating season) while staying within the BTU family used by furnace engineers.

The quad (1970s): Following the 1973 oil embargo, the US Department of Energy needed a single number to describe the nation's entire energy supply. The quad (10¹⁵ BTU) was created to reduce national energy statistics to two-digit figures (about 100 quads for the US).