Energy Units Explained: Joules, kWh, Calories and BTU With Worked Examples

Every unit of energy is a fixed number of joules. A kilowatt-hour is 3,600,000 J, a food Calorie is 4,184 J, and a British thermal unit is 1,055.05585262 J. Once those factors are in hand, an electricity bill, a gas bill, a nutrition label and an air-conditioner sticker can all be put on one scale and compared directly. The units only look unrelated because they grew up in different trades: electricity, nutrition, heating and physics each settled on its own.

The Joule and the Watt

The joule is the SI unit of energy. It is the work done when a force of one newton acts through one meter, which in base units is one kilogram times one meter squared per second squared. It is small: a kilojoule (1,000 J) or megajoule (1,000,000 J) is usually the convenient size for anything in a kitchen or a house.

The watt is not an energy unit. It is power, the rate of energy flow, and one watt is one joule per second. Confusing the two is the most common mistake in this area. A 60-watt lamp does not "use 60 watts" in total; it uses 60 joules every second for as long as it is on. Multiply power by time to get energy, and divide energy by time to get power.

That relationship is where the kilowatt-hour comes from. One kilowatt sustained for one hour is 1,000 J/s × 3,600 s = 3,600,000 J. Utilities bill in kWh because the joule would produce unwieldy numbers on every statement.

The Conversion Factors That Matter

Unit	Joules	Where you see it
kilowatt-hour (kWh)	3,600,000	electricity bills, battery and EV ratings
watt-hour (Wh)	3,600	phone and laptop batteries
kilocalorie (kcal, food Calorie)	4,184	US nutrition labels, diet trackers
kilojoule (kJ)	1,000	food labels in Australia, the EU and elsewhere
British thermal unit (BTU)	1,055.05585262	furnaces, water heaters, fuel heat content
foot-pound-force (ft·lbf)	1.35582	mechanical work in US engineering
electronvolt (eV)	1.602176634 × 10-19	atoms, photons and particles

The calorie in the table is the thermochemical calorie, 4.184 J, one of several versions listed in NIST SP 811; the International Table kilocalorie, 4,186.8 J, differs by less than a tenth of a percent. The BTU is the International Table BTU. The electronvolt has been exact since the 2019 revision of the SI fixed the elementary charge. The Energy Converter uses these factors, so every result below can be reproduced there.

Two units deserve a warning. The "Calorie" on a US food label is a kilocalorie, a thousand of the small calories used in chemistry. And a "BTU" rating on a furnace or air conditioner almost always means BTU per hour, which is a power, not an amount of energy.

Food Energy: Calories and Kilojoules

Example 1: Reading an imported cereal box

Elena picks up an Australian muesli at an import shop. The panel says 1,560 kJ per 100 g, and her tracking app wants kilocalories.

1. Convert to joules: 1,560 kJ = 1,560,000 J.
2. Divide by the joules in one kilocalorie: 1,560,000 ÷ 4,184 = 372.849 kcal.
3. She logs about 373 Calories per 100 g, or scales it by the weight of her bowl.

A useful sanity check: kilojoules are always a bit more than four times the kilocalorie figure. If a label's two numbers do not have roughly that ratio, one of them is per serving and the other per 100 g.

Example 2: A body's energy use expressed in watts

Daniel is 40, 180 cm tall and weighs 80 kg. The Mifflin-St Jeor equation used by the BMR Calculator gives him a basal metabolic rate of 1,730 kcal per day, the energy his body spends at rest.

1. Convert to joules: 1,730 × 4,184 = 7,238,320 J per day.
2. A day has 86,400 seconds, so the average power is 7,238,320 ÷ 86,400 = 83.8 W.
3. In electricity terms, the same daily energy is 2.01064 kWh.

Resting, Daniel runs at roughly the power of a bright incandescent bulb, and a full day of basal metabolism is about two kilowatt-hours. Converting kcal to watts is the quickest way to see that food energy and electrical energy are the same physical quantity.

Heating Fuels: BTU and Therms

According to the EIA, one BTU is the heat needed to raise a pound of water by one degree Fahrenheit, about the energy released by burning a match. Because a single BTU is so small, fuels are quoted in large multiples. The EIA lists these heat contents:

• Electricity: 1 kWh = 3,412 Btu
• Natural gas: 1 cubic foot = 1,036 Btu, and 1 therm = 100,000 Btu
• Motor gasoline: 1 gallon = 120,214 Btu
• Propane: 1 gallon = 91,452 Btu
• Heating oil: 1 gallon = 138,500 Btu

Example 3: A winter gas bill in kilowatt-hours

Marcus heats his house with natural gas. His January bill shows 64 therms, and he wants to compare it with his electricity use.

1. Convert therms to BTU: 64 × 100,000 = 6,400,000 BTU.
2. Convert BTU to joules and then to kWh: 6,400,000 × 1,055.05585262 ÷ 3,600,000 = 1,875.65 kWh.
3. Each therm on its own is 29.3071 kWh, which is the number to divide a per-therm price by to get a price per kWh of heat.

The EIA reports that the average US residential electricity customer bought 10,791 kWh in 2022, about 899 kWh a month. Marcus's January gas alone carried roughly twice that much energy. A fair cost comparison also needs the furnace efficiency, since not every BTU bought ends up as heat in the rooms.

Gasoline shows why the reference figure matters. For its MPGe ratings, the EPA counts a gallon of gasoline as 33.7 kWh. Converted, 33.7 kWh is 114,989 BTU, a few percent below the EIA's 120,214 Btu per gallon of motor gasoline, so the two agencies are evidently not using the same heat-content figure. Quote whichever one your comparison is built on.

Power Ratings: BTU per Hour and Tons

Air conditioners, furnaces and heat pumps are rated by how fast they move or produce heat, so their ratings are power. In the US the label usually says BTU, but it means BTU per hour.

Example 4: Sizing up a window air conditioner

Ingrid is choosing between a 10,000 BTU/h window unit and a portable unit rated in kilowatts.

1. Convert using the Power Converter: 10,000 × 1,055.05585262 ÷ 3,600 = 2,930.71 W, or 2.930711 kW of cooling.
2. Central systems are rated in tons of refrigeration. NIST SP 811 defines one ton as 12,000 BTU/h, which converts to 3.516853 kW.

That cooling figure is not the electricity the unit draws. An air conditioner pumps heat out of a room rather than generating it, so its electrical input is a fraction of its cooling output; the ratio depends on the model.

From Energy to Money: A Laundry Budget

Because electricity is sold per kWh, cost is energy times price. The Laundry Cost Calculator combines that with water and detergent.

Example 5: The Nguyen family's washing

The Nguyens run 5 loads a week. Washing and electric drying together take 2.8 kWh per load at $0.19 per kWh. The washer uses 18 gallons at $0.012 per gallon, and detergent is $0.20 a load.

1. Electricity per load: 2.8 × $0.19 = $0.53.
2. Water per load: 18 × $0.012 = $0.22, so the full cost per load is $0.95.
3. Per week: $4.74. Per year, over 52 weeks: $246.48.

Electricity is more than half of each load's cost, which is why line-drying or a heat-pump dryer moves the total more than switching detergent. Your own rate is printed on your utility bill and is the figure to enter.

Small Stores of Energy: Batteries

Battery capacity is often printed in milliamp-hours, which is charge, not energy. Multiply amp-hours by the nominal voltage to get watt-hours. A phone battery of 3,000 mAh at 3.85 V holds 3 × 3.85 = 11.55 Wh, which is 41.58 kJ. That is roughly the energy in ten food Calories.