Energy and Power Converter

What this converter answers

What an energy or a power is in other units, and how the two connect. Energy converts joules, kilojoules, megajoules, watt-hours, kilowatt-hours, calories, food Calories (kilocalories), foot-pounds, Btu, therms and electronvolts. Power converts watts, kilowatts, megawatts, horsepower (mechanical and metric), Btu per hour and tons of air conditioning. Power × time turns a power and a time into energy (1,500 W for 3 hours is 4.5 kWh), or an energy and a time into an average power.

How to use it

• Convert: choose Energy, Power or Power × time. Each keeps its own numbers, so you can switch back and forth.
• Energy to convert or Power to convert: the number, in the unit chosen under From. Commas between thousands and e-notation both work: 8,500, 1.6e-19.
• From and To: the unit on your bill or spec sheet, such as therms or Btu, and the unit you want, such as kilowatt-hours. Every other unit is listed in the table under the answer; select a unit name there to make it the main result.
• Significant figures: Auto shows up to 12, and whole numbers in full. Choose fewer for a shorter answer.
• Power × time: choose Energy used (power × time) or Average power (energy ÷ time). Enter the Steady power or the Total energy with its unit, the Time from seconds to years, and the unit under Result in.

The Try buttons load an electricity unit in Btu, a food label in kilojoules, a car rating, an air conditioner, a heater and an appliance’s yearly energy, all worked through below.

Energy vs power: the difference between kW and kWh

Power is how fast energy is used; energy is how much is used. A watt (W) is one joule per second, and a kilowatt-hour (kWh) is the energy of 1,000 W kept up for one hour, 3,600,000 J. So kW and kWh can’t be converted into each other without a time: kWh = kW × hours, and kW = kWh ÷ hours.

A 1,500 W heater draws 1.5 kW whenever it runs. On for 3 hours, it uses 4.5 kWh; on for 20 minutes, 0.5 kWh. The power is the same both times and the energy is not. An electric bill counts energy in kWh, while an appliance label, a car’s spec sheet and an air conditioner’s rating in Btu/h or tons all give a power.

How to convert watts to kWh (power × time)

Multiply the watts by the hours and divide by 1,000:

• $P_{\text{W}}$ is the power in watts and $t_{\text{h}}$ the time in hours (minutes ÷ 60).
• In SI units the same rule, $E = P \times t$, gives joules from watts and seconds.

The other way round, average power is energy divided by time. An appliance that uses 400 kWh in a 365-day year averages 400,000 Wh ÷ 8,760 h = 45.6621004566 W. Choose Power × time and Average power for any time, or read the “spread over time” table under an energy conversion.

To cost the energy, multiply the kWh by your price per kWh. For a power in W or kW over a day or less, the Continue in the Electricity Cost Calculator link under the result carries the power and the time as daily use, and that page gives the cost a day, a month and a year.

Energy and power conversion formula

Each unit has a fixed size, $f$, in joules (energy units) or watts (power units). To convert a value $x$:

• $x_{\text{from}}$ is the value you have and $x_{\text{to}}$ the value in the new unit.
• $f_{\text{from}}$ and $f_{\text{to}}$ are the sizes of the two units: 3,600,000 J for a kilowatt-hour, 1,055.05585262 J for a Btu, 745.69987158227022 W for a horsepower.

The steps under each result do exactly this in two lines, into joules or watts and then out again, with each unit’s definition written beside it. Energy and power only meet through time: $E = P \times t$ and $P_{\text{average}} = E \div t$.

Worked example: 85 therms on a gas bill in kWh

A winter gas bill shows 85 therms, and you want it in kilowatt-hours to set beside an electric bill.

1. Therms to joules: 85 × 105,480,400 = 8,965,834,000 J. The US therm is exactly 105,480,400 J, so this step is exact.
2. Joules to kilowatt-hours: 8,965,834,000 ÷ 3,600,000 = 2,490.50944444 kWh. The division doesn’t end, so the page marks the result Rounded.
3. The same energy in Btu: 8,965,834,000 ÷ 1,055.05585262 = 8,497,970.96309 Btu.
4. Spread over a 30-day billing period, it is an average power of 3,459.04 W (3.45904 kW), or 11,802.7 Btu/h. The “Average power of 85 thm spread over time” table under the result gives this row with the hour, day, week and year.

If the gas company counts a therm as 100,000 Btu (see “Therms on a gas bill” below), 85 therms is 8,500,000 Btu, or 2,491.1 kWh: 0.595 kWh more.

kWh, joules and Btu

One kilowatt-hour is exactly 3,600,000 J (3.6 MJ), because a watt is a joule per second and an hour is 3,600 seconds. The Btu in US energy data and heating and cooling ratings is the International Table Btu, exactly 1,055.05585262 J.

EIA’s tables round 1 kWh to 3,412 Btu. That is fine for one kilowatt-hour but adds up on big totals: 1,000,000 kWh × 3,412 = 3,412,000,000 Btu, while the exact figure is 3,412,141,633.13 Btu.

Calories vs kilocalories (food Calories)

The Calorie on a food label is a kilocalorie: 1,000 small calories. For food energy, 1 kcal = 4.184 kJ, which is the thermochemical kilocalorie of 4,184 J. So a label’s 250 Calories are 250 kcal = 1,046 kJ, not 250 cal = 1.046 kJ.

Going back, 1 kJ ≈ 0.239006 kcal. If you type a food-sized number (20 to 5,000) with From set to small calories, the page points out that label Calories are kilocalories. This converter only changes units; how many Calories a person needs is a different question, answered by a BMR or TDEE calculator.

Horsepower to kW and watts (mechanical vs metric)

Mechanical horsepower (hp) is 550 foot-pounds per second, exactly 745.69987158227022 W, or about 745.7 W. Metric horsepower (written PS or CV) is 75 kilogram-force meters per second; with the kilogram-force at 9.80665 N, that is 735.49875 W, which NIST’s table rounds to 735.4988 W. A mechanical horsepower is 1.39% larger, so the same engine has more PS than hp, and a spec sheet should say which one it uses.

From horsepower to kilowatts, multiply by 0.74569987158227022: 100 hp = 74.57 kW, 200 hp = 149.14 kW and 300 hp = 223.71 kW. NIST also lists an electric horsepower of 746 W, within 0.05% of mechanical horsepower; it is not in the unit list here.

Btu per hour and tons of air conditioning

A ton of refrigeration is 12,000 Btu per hour, about 3,516.85 W, and 1 Btu/h is about 0.293071 W. Air conditioners and heat pumps are rated this way:

These ratings are the heat the unit moves, not the electricity it draws. A 3-ton air conditioner moves 36,000 Btu of heat an hour (10.5505585262 kW); its electrical input is a separate figure on the nameplate. The page shows a note whenever Btu/h or tons are involved.

Therms on a gas bill

NIST defines the US therm, the legal unit of the US natural gas industry, as 105,480,400 J: 29.3001 kWh, or 99,976.1 Btu. EIA’s conversion tables use 1 therm = 100,000 Btu instead, which matches NIST’s therm (EC), based on the International Table Btu: 29.3071 kWh, about 0.024% more. On an 85-therm bill the two readings differ by 0.595 kWh. The converter uses the US therm and says so in a note under the answer.

Electronvolts and joules

An electronvolt is exactly 1.602176634 × 10⁻¹⁹ J; NIST lists it as an exact value. So 1 J is 6.24150907446 × 10¹⁸ eV and 1 kWh is 2.24694326681 × 10²⁵ eV. Values this far from everyday sizes are shown in scientific notation, and the steps keep every digit of the definition.

Exact conversion factors

The last two never end as decimals (they are 1,055.05585262 ÷ 3,600 and 12,000 times that), so the converter keeps them as exact fractions and rounds only the answer.

Reading the result

• The headline gives the answer in the To unit, then the equation and whether it is exact or how it was rounded.
• The factor line shows one unit of each in the other. For therms and kilowatt-hours both directions are rounded, 1 thm ≈ 29.3001111111 kWh and 1 kWh ≈ 0.034129563407 thm, so both carry ≈; a defined factor is marked “exactly”.
• How this was calculated converts into joules or watts and out again, with each unit’s definition. In Power × time it converts the power and the time, multiplies or divides, then converts the answer.
• The conversion table lists the value in every unit, each marked Exact or Rounded. Download CSV and Copy table take the whole table.
• The period table under an energy gives its average power over 1 hour, 1 day, 1 week, 30 days and 365 days; under a power, the energy delivered over the same periods in kWh, MJ and Btu. The button under it carries your number into Power × time for any other time.
• Save for comparison keeps up to three results, with the change in kWh (energy) or kW (power) from the first.
• Continue in the Electricity Cost Calculator appears under an energy found from watts or kilowatts over 24 hours or less. This page never prices energy; that one does, at your rate per kWh.

Common mistakes

• Treating kW and kWh as the same thing. A 2 kW heater doesn’t use 2 kWh unless it runs for exactly an hour; for 45 minutes it uses 1.5 kWh.
• Reading food Calories as small calories. A 250-Calorie snack is 1,046 kJ. Entered as 250 cal, it comes out 1,000 times too small.
• Mixing up hp and PS. The same 150 kW engine is 201.153 hp or 203.943 PS; quoting one as the other is off by 1.39%.
• Using an air conditioner’s Btu/h as its electricity use. Btu/h and tons rate the heat moved; the electricity drawn is a separate figure.
• Entering minutes as hours. 2.4 kW for 45 minutes is 1.8 kWh; the same number entered as 45 hours gives 108 kWh.
• Multiplying by a rounded factor. 3,412 Btu per kWh is rounded, so a large total drifts, as the example above shows. The converter uses the exact factor and rounds once, at the end.

Assumptions and limitations

• The factors are exact definitions: the International Table Btu, the thermochemical calorie (and kilocalorie), the US therm, mechanical and metric horsepower and the ton of 12,000 Btu/h. NIST lists several other Btu and calorie definitions; they differ from these by less than 0.5% and aren’t offered.
• A converted value can’t be more precise than the reading it came from: a gas meter read to the nearest therm doesn’t give kilowatt-hours to 12 figures, even though the arithmetic does.
• Power × time assumes a steady power. Equipment that cycles on and off, such as a fridge or a thermostat-controlled heater, uses less than its rating times the hours; enter the time it actually runs, or its average power.
• A year is 365 days (8,760 hours). Months aren’t offered because their lengths differ; enter 30 or 31 days.
• Numbers go from 0 to 10¹⁵ in the unit typed; negative values are not accepted.
• This page converts units only. It doesn’t price energy or estimate how much a person needs; those are separate calculators.