Energy Conversions

Your electricity bill charges in kilowatt-hours. The nutrition label on a granola bar lists kilocalories. Your car's engine output is rated in horsepower, which is derived from foot-pounds per second. A physics textbook measures everything in joules. These are all units of energy, but they come from such different traditions that converting between them requires knowing the history.

James Prescott Joule, a Manchester brewer's son, spent the 1840s methodically measuring how mechanical work converts to heat. His paddle-wheel experiment, in which falling weights stirred water in an insulated container, established the mechanical equivalent of heat: 4.184 joules raise the temperature of one gram of water by one degree Celsius (the definition of the small calorie). The SI system honored him by naming its energy unit the joule. One joule is one newton applied over one meter, or one watt delivered for one second. The kilowatt-hour used on electric bills is simply 3,600,000 joules, since 1 kW x 3,600 seconds = 3,600 kJ.

The calorie has a confusing dual identity. The "small calorie" (cal) is the energy needed to warm 1 gram of water by 1 degree C. The "food Calorie" (Cal or kcal) is 1,000 small calories, the energy needed to warm 1 kilogram of water by 1 degree C. When a nutrition label says a serving contains 250 Calories, it means 250,000 small calories, or 1,046,000 joules. This 1,000x factor catches people off guard. The food calorie is technically a kilocalorie.

The British thermal unit (BTU) fills a similar role in HVAC, natural gas pricing, and heating system specifications. One BTU is the energy needed to raise the temperature of one pound of water by one degree Fahrenheit, which works out to 1,055.05585 joules. US natural gas is priced per therm (100,000 BTU). Air conditioner capacity is rated in BTU/hour. The electron volt (1.602 x 10^-19 joules), by contrast, operates at the atomic scale and is used in particle physics and semiconductor specifications.

Comparing energy across fuels requires conversion as well. One gallon of gasoline contains about 120,000 BTU, or roughly 33.7 kWh. One cubic foot of natural gas contains about 1,032 BTU. A cord of firewood provides roughly 20 million BTU, varying by species. These comparisons help homeowners evaluate heating options: if electricity costs $0.15 per kWh and natural gas costs $1.20 per therm (100,000 BTU), you can convert both to a cost per joule or cost per BTU to make a direct comparison. Without energy unit conversion, this kind of apples-to-apples analysis is impossible.

Renewable energy capacity is typically rated in watts (power), but energy production is measured in watt-hours. A 400-watt solar panel that receives 5 hours of peak sunlight produces 2 kWh per day. Multiplied by 365 days, that is 730 kWh per year, equivalent to roughly 2.628 billion joules or about 2.49 million BTU. Scaling these figures for entire installations requires comfortable conversion between all major energy units.

Calcflux covers 9 energy units: joule (SI base), kilojoule, megajoule, calorie, kilocalorie, watt-hour, kilowatt-hour, BTU, and electron volt. Key exact factors: 1 calorie = exactly 4.184 J (thermochemical calorie), 1 kWh = 3,600,000 J, 1 BTU = 1,055.05585 J (ISO 31-4). All values reference NIST SP 330 and CODATA 2018 for the electron volt.