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05 Water, Air and Heat

Water Heating Energy Calculator

Card No. 05·0026 · Updated · Standard formula, shown below

Energy needed 9,418.5 kJ
Energy needed
2.616 kWh
Result
Energy needed
8,927 BTU
Result
Heating time (no losses)
52.3 min
Result
You enter
Water volume, Start temperature, Target temperature, Heater power
You get
Energy needed, Energy needed, Energy needed, Heating time (no losses)
Rounding
1 dp · 3 dp · 0 dp

This calculator finds the energy needed to heat water: enter the volume, the starting and target temperatures and the heater power. You get the energy in kilojoules, kilowatt-hours and BTU, and how long the heater needs if no heat is lost.

Formula

Heat Q = m × c × ΔT. For water, 1 litre has a mass of about 1 kg and the specific heat c is about 4.186 kJ/(kg·°C). ΔT = target − start. 1 kWh = 3,600 kJ and 1 BTU = 1.05506 kJ. Time = energy ÷ power.

  • vol: litres of water (US gallons × 3.785)
  • t1, t2: start and target temperature, °C
  • kw: heater power, kW

Worked Example

50 L from 15 °C to 60 °C with a 3 kW heater.

  1. ΔT = 60 − 15 = 45 °C
  2. Q = 50 × 4.186 × 45 = 9,418.5 kJ
  3. 9,418.5 ÷ 3600 = 2.616 kWh; 9,418.5 ÷ 1.05506 = 8,927 BTU
  4. Time = 2.616 ÷ 3 = 0.872 h = 52.3 min

Limits and common mistakes

  • If the target is below the start temperature the water is being cooled, not heated, and the calculator shows “Cannot compute”.
  • Real heaters lose heat to the tank and pipes, so expect a longer time; divide by the heater efficiency if you know it.
  • The formula is for liquid water. Melting ice or boiling water needs extra latent heat (334 kJ/kg to melt, 2,257 kJ/kg to boil).
  • Fahrenheit: a 1 °F rise is 5/9 of a 1 °C rise.
Formula used
in vol | Water volume | L | 50 | 0
in t1 | Start temperature | °C | 15 | 0 | 100
in t2 | Target temperature | °C | 60 | 0 | 100
in kw | Heater power | kW | 3 | 0
out q | Energy needed | kJ | vol * 4.186 * (t2 - t1) + 0 * sqrt(t2 - t1) | 1
out kwh | Energy needed | kWh | q / 3600 | 3
out btu | Energy needed | BTU | q / 1.05505585262 | 0
out tmin | Heating time (no losses) | min | kwh / kw * 60 | 1

Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work

Photo collage: a steaming kettle on a stove and a copper hot water tank.
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Method: the standard formula for this calculation, rounded as each result states. See how the calculators work or report an error.

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