# Water Heating Calculator

Created by Luis Hoyos
Last updated: Jul 28, 2022

Welcome to the water heating calculator, a tool that will let you calculate water heating in BTU, joules, calories, and many other units.

With this tool, you cannot only calculate the water heating total energy but also:

• Calculate the time required to heat an amount of water if you know the heater's efficiency and power.
• Calculate the watts to heat a water amount if you know the time required and heater efficiency.
• And many more things!

Keep reading to learn how to calculate water heating by hand, using the different water heating formulas.

## How do I calculate the water heating total energy?

The total energy needed depends merely on the initial and final temperatures. Calculating the water heating (in BTU or any other energy unit) involves two quantities:

1. Sensible Heat: The heat required to raise the temperature.
2. Latent heat: The heat needed to change the phase.

Latent Heat (Qt)

Sensible heat (Qp)

Qt = c × m × (Tf - Ti)

Qp = L × m

where:

where L is the specific latent heat

• c — Specific heat capacity;
• m — Mass of the water;
• Tf — Final temperature; and
• Ti — Initial temperature.

For example, under atmospheric conditions, taking water from 20 to 30°C only involves sensible heat. On the other side, taking it from 20 to 200°C involves sensible and latent heat, as at some intermediate point (100°C), we require some additional energy (latent heat) to evaporate the water.

The total heat (Qtotal) is then the sum of the quantities associated with the latent and sensible heat:

Qtotal = Qt + Qp

There are some essential points to consider about the terms of the previous equations:

• If the phase change involves melting (converting ice to liquid water), the specific latent heat is called enthalpy of fusion or latent heat of fusion. Enthalpy of fusion is a material property that equals 334000 J/kg for water. Therefore, we need 334000 J of heat to melt 1 kg of water (which occurs at 0 °C).
• If the phase change involves evaporation (converting liquid water to steam), the specific latent heat is called enthalpy of vaporization or latent heat of vaporization. Enthalpy of vaporization is a material property that equals 2264705 J/kg for water. Therefore, we need 2264705 J to evaporate 1 kg of water (something that occurs at 100 °C).
• The specific heat capacity is a material property, which equals 2108 J/(kg K) for ice water, 4190 J/(kg K) for liquid water and 1.996 J/(kg K) for steam. Therefore:
• We need 2108 J to heat 1 kg of ice water by one degree (Celsius or Kelvin).
• We need 4190 J to heat 1 kg of liquid water by one degree (Celsius or Kelvin).
• We need 1996 J to heat 1 kg of steam by one degree (Celsius or Kelvin).

As 1 kg of water represents 1 liter, 4190 J is also energy to heat 1 litre of water by 1 degree (liquid water).

## How do I calculate the watts to heat the water?

Once you know the total energy required, calculating the watts to heat the water is simple. You can calculate the power needed for that water heating with the following formula:

Power = Qtotal/(time × efficiency)

We can manipulate the previous equation and obtain the formula for the time required to heat:

time = Qtotal / (Power× efficiency)

## Example: Heating 2 kg water from -20 to 200°C

Heating 2 kg of water from -20 to 200°C involves various steps and types of heat:

1. Sensible heat, to take the ice from -20 to 0°C:
Qt = c × m × (Tf - Ti) = 2108 J/(kg K) × 2 kg × (0°C - (-20°C)) = 84320 J.
2. Latent energy, to melt the ice at 0°C:
Qp = L × m = (334000 J/kg) × 2 kg = 668000 J
3. Sensible heat, to take the liquid water from 0 to 100°C:
Qt = c × m × (Tf - Ti) = 4190 J/(kg K) × 2 kg × (100°C - 0°C) = 838000 J.
4. Latent energy, to evaporate the water at 100°C:
Qp = L × m = (2264705 J/kg) × 2 kg = 4529410 J
5. Sensible heat, to take the steam from 100 to 200°C:
Qt = c × m × (Tf - Ti) = 1.996 J/(kg K) × 2 kg × (200°C - 100°C) = 399200 J.

Then, the total heat needed to take those 2 kilograms of water from -20 to 200°C is the sum of the five heats:

Qtotal = 84320 J + 668000 J + 838000 J + 4529410 J + 399200 J
Qtotal = 6518930 J

It's been a lot of calculations! 😱 We can disagree on many things, but we certainly agree that using the BTU water calculator is more straightforward than all those water heating formulas.

Luis Hoyos
Energy
Mass of water
oz
Initial temperature
°F
Final temperature
°F
Total energy
J
Time
Heating power
W
Efficiency
%
Time
hrs
min
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