Energy Converter — Joules, Calories, kWh, BTU, eV, Ft-lb
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How Energy Unit Conversion Works
An energy converter translates quantities between different energy measurement systems, all of which express the same physical property -- the capacity to do work or transfer heat. The SI (International System of Units) standard unit of energy is the joule (J), defined as the work done by a force of one newton moving an object one meter. According to the National Institute of Standards and Technology (NIST), the joule serves as the base reference for all energy conversions. Different fields use different units for practical reasons: nutritionists use kilocalories, electricians use kilowatt-hours, HVAC engineers use BTUs, and physicists use electronvolts.
This converter handles 8 common energy units with NIST-traceable conversion factors. Enter a value in any unit, select the source and target units, and see the precise conversion. The "All Conversions" panel shows your value expressed in every supported unit simultaneously. For related conversions, see our Temperature Converter and Pressure Converter.
Energy Conversion Formulas
All conversions use the joule as an intermediate base unit. The process is:
Value in Joules = Input Value x (Joules per Source Unit)
Result = Value in Joules / (Joules per Target Unit)
The exact conversion factors used are: 1 kJ = 1,000 J; 1 cal = 4.184 J; 1 kcal = 4,184 J; 1 kWh = 3,600,000 J; 1 BTU = 1,055.06 J; 1 eV = 1.602176634 x 10^-19 J; 1 ft-lb = 1.35582 J.
Worked example: Convert 2,500 kilocalories (a typical daily food intake) to kilowatt-hours. Step 1: 2,500 kcal x 4,184 J/kcal = 10,460,000 J. Step 2: 10,460,000 J / 3,600,000 J/kWh = 2.906 kWh. This means the energy in a day's food could theoretically power a 100-watt light bulb for about 29 hours.
Key Terms You Should Know
- Joule (J): The SI unit of energy. One joule is the energy transferred when a force of one newton moves an object one meter. Named after English physicist James Prescott Joule.
- Kilocalorie (kcal / Cal): The "food calorie" seen on nutrition labels. One kilocalorie equals 1,000 small calories or 4,184 joules. The average adult requires 2,000-2,500 kcal per day.
- Kilowatt-hour (kWh): The standard billing unit for electricity. One kWh equals the energy consumed by a 1,000-watt device running for one hour (3.6 million joules). The average U.S. household uses about 886 kWh per month according to the U.S. Energy Information Administration.
- British Thermal Unit (BTU): The energy needed to raise the temperature of one pound of water by one degree Fahrenheit. Widely used in HVAC, natural gas billing, and heating system ratings. One therm of natural gas equals 100,000 BTU.
- Electronvolt (eV): The energy gained by an electron accelerating through a potential difference of one volt. Used in atomic physics, particle physics, and semiconductor engineering. Extremely small: 1 eV = 1.602 x 10^-19 joules.
- Foot-pound (ft-lb): The energy transferred by a force of one pound-force acting through a distance of one foot. Used in mechanical engineering, ballistics, and torque specifications in the U.S. customary system.
Energy Unit Comparison Table
The following table shows how 1 unit of each energy measure converts to every other unit, useful as a quick reference for common conversions.
| Unit | Equals in Joules | Equals in kWh | Equals in BTU | Common Use |
|---|---|---|---|---|
| 1 Joule | 1 | 2.778 x 10^-7 | 9.478 x 10^-4 | Physics, SI base |
| 1 Kilocalorie | 4,184 | 0.001162 | 3.968 | Food energy, nutrition |
| 1 kWh | 3,600,000 | 1 | 3,412 | Electricity billing |
| 1 BTU | 1,055.06 | 2.931 x 10^-4 | 1 | HVAC, heating/cooling |
| 1 Therm | 105,506,000 | 29.31 | 100,000 | Natural gas billing |
| 1 eV | 1.602 x 10^-19 | 4.45 x 10^-26 | 1.519 x 10^-22 | Atomic/particle physics |
Practical Energy Conversion Examples
Example 1: Electricity bill to BTUs. A home using 900 kWh of electricity per month. In BTUs: 900 x 3,412 = 3,070,800 BTU. This is equivalent to about 30.7 therms of natural gas. Use our Electricity Cost Calculator to see how this translates to dollars.
Example 2: Food energy to electrical energy. A 2,000 kcal daily diet contains 2,000 x 4,184 = 8,368,000 joules = 2.32 kWh of energy. At $0.14/kWh, this amount of electrical energy costs only $0.33. The human body is roughly 25% efficient at converting food energy to mechanical work.
Example 3: Natural gas furnace output. A furnace rated at 80,000 BTU/hour. In kW: 80,000 x 2.931 x 10^-4 = 23.4 kW. Running for 8 hours produces 80,000 x 8 = 640,000 BTU = 187.7 kWh of heat energy. With natural gas at $1.20/therm, this costs about $7.68 per day (640,000 / 100,000 x $1.20).
Tips for Working with Energy Units
- Always check calorie vs. kilocalorie. In nutrition, "Calories" (capital C) always means kilocalories. A food label showing "200 Calories" means 200 kcal or 200,000 small calories. This is the most common source of confusion in energy conversions.
- Use kWh for comparing energy costs. Converting gas (therms or BTU) and electricity (kWh) to the same unit lets you compare heating costs fairly. At $1.20/therm, gas costs $0.041/kWh. At $0.14/kWh, electricity costs 3.4x more per unit of energy, but heat pumps deliver 2-4x more heat per kWh than direct resistance heating.
- Remember that power and energy are different. A watt is power (energy per second); a watt-hour is energy. A 60W light bulb running for 10 hours uses 600 Wh = 0.6 kWh. Use our Electricity Usage Calculator to estimate appliance energy consumption.
- Use scientific notation for extreme scales. Energy spans more than 40 orders of magnitude from electronvolts to kilowatt-hours. This converter automatically switches to scientific notation for very large or very small results to maintain precision.
Frequently Asked Questions
What is the difference between a calorie and a kilocalorie?
A small calorie (cal) is the energy needed to raise the temperature of 1 gram of water by 1 degree Celsius, equal to exactly 4.184 joules. A kilocalorie (kcal), also written as Calorie with a capital C, equals 1,000 small calories or 4,184 joules. Food nutrition labels use kilocalories -- when a label says "200 Calories," it means 200 kcal. This naming convention causes widespread confusion because most people say "calorie" when they mean kilocalorie. In many countries outside the U.S., food labels use kilojoules (kJ) instead, where 1 kcal = 4.184 kJ.
How many joules are in a kilowatt-hour?
One kilowatt-hour (kWh) equals exactly 3,600,000 joules (3.6 megajoules). This comes from the definition: 1 kWh = 1,000 watts x 3,600 seconds = 3,600,000 watt-seconds = 3,600,000 joules. The kilowatt-hour is the standard billing unit for electricity worldwide. The average U.S. household uses approximately 886 kWh per month (about 30 kWh per day), which equals about 3.19 billion joules or 3.19 gigajoules per month. At $0.14/kWh, that energy costs about $124 per month.
What is a BTU and where is it used?
A British Thermal Unit (BTU) is the amount of energy needed to raise the temperature of one pound of water by one degree Fahrenheit at sea level. One BTU equals approximately 1,055.06 joules. BTUs are the primary energy unit in the American HVAC industry: air conditioners are rated in BTU/hour (a typical window unit is 8,000-12,000 BTU/h), furnaces in BTU/hour output (60,000-100,000 for residential), and natural gas is billed in therms (1 therm = 100,000 BTU). Water heaters, boilers, and fireplaces also use BTU ratings to indicate heating capacity.
How do electronvolts relate to joules?
One electronvolt (eV) equals exactly 1.602176634 x 10^-19 joules -- an extraordinarily small amount of energy. It represents the kinetic energy gained by a single electron accelerating through an electric potential difference of one volt. Despite its tiny size, the electronvolt is the preferred unit in atomic physics, nuclear physics, and semiconductor engineering because it produces manageable numbers at atomic scales. For example, visible light photons carry 1.8-3.1 eV of energy, chemical bond energies range from 1-10 eV, and nuclear reactions involve millions of electronvolts (MeV).
How do I convert between electricity and gas for heating cost comparison?
To compare heating costs, convert both to the same unit. Natural gas is billed in therms (100,000 BTU each). One therm equals 29.31 kWh. At $1.20/therm, gas costs $0.041 per kWh of heat. At $0.14/kWh, electric resistance heating costs 3.4x more per unit of energy. However, heat pumps deliver 2-4x more heat energy than they consume in electricity (COP of 2-4), making them competitive with or cheaper than gas in many climates. Use the formula: Gas cost per kWh = price per therm / 29.31.
What is the difference between energy and power?
Energy is the total amount of work that can be done, measured in joules, kWh, BTU, or calories. Power is the rate at which energy is used or produced, measured in watts (joules per second), horsepower, or BTU/hour. A 100-watt light bulb uses 100 joules of energy every second. Running for 10 hours, it consumes 1,000 watt-hours (1 kWh) of energy. The distinction matters for billing: you pay for energy (kWh consumed), not power (watts available). A 2,000W space heater running for 5 hours uses 10 kWh ($1.40 at $0.14/kWh), while a 200W TV running for 5 hours uses only 1 kWh ($0.14).