Water heater heating time:
formula and worked example

How long until the water is hot?

The question is a practical one: how early do I need to switch on the geyser, and will a smaller element still be quick enough? The answer comes from basic thermal physics. Raising the temperature of water takes a known amount of energy, and the heater delivers energy at a fixed rate in kilowatts.

Dividing the first by the second gives the time. The same approach works for a bucket heater, a storage tank or a process tank, provided the water mass and the temperature rise are known.

It is a minimum time. Heat escapes through the tank walls and pipes, and the thermostat can cut out before the whole volume is evenly warm.

The formula and its units

• Water mass in kilograms; one litre of water weighs about one kilogram, so 100 litres is close to 100 kg.
• Heat capacity in kJ per kg per degree. For water it is about 4.186, meaning each kilogram needs 4.186 kJ per degree rise.
• Temperature rise in degrees, which is the target temperature minus the starting temperature; a change of one degree Celsius equals one kelvin.
• Heater power in kilowatts, the electrical rating of the element, taken as the heat delivered to the water.

With these units the numerator is in kJ, the first division produces kWh and the second divides by the power to give hours.

Worked example: 100 kg, 35 degrees higher, 3 kW element

A storage geyser holds 100 litres at 25 degrees and should reach 60 degrees, a rise of 35. The element is 3 kW.

1. 1Energy in kJ: 100 x 4.186 x 35 = 14,651 kJ.
2. 2Convert to kWh: 14,651 / 3,600 = 4.07 kWh.
3. 3Divide by the power: 4.07 / 3 = 1.357 hours.
4. 4In minutes: 0.357 x 60 is about 21, so the time is roughly 1 hour 21 minutes.

A higher power element would shorten the time in direct proportion: a 6 kW heater would take about 41 minutes under the same assumptions.

Real time versus calculated time

The formula is a best case. Every tank loses heat to its surroundings, and the loss grows as the water gets hotter. A well-insulated cylinder loses little over the heating period, a poorly insulated one in a cold bathroom loses more, and either adds to the time.

Also consider the cut-out. Thermostats sense a point in the tank, and layered water means the top may reach the set-point before the whole volume does. Draw-off during heating adds cold water and extends the cycle.

• Allow extra time rather than expecting the exact figure; a modest margin is usually enough for a well-insulated tank.
• If the measured time is far above the calculated time, check the element and the thermostat for scale or fault.

What a bigger water mass does

A 10% larger tank, 110 kg rather than 100 kg, needs 10% more energy for the same rise. At the same element power the time rises from 1.357 to 1.492 hours.

About eight more minutes for 10 extra litres. This is a straight proportion, so heating a tank half full takes about half the time, which is a useful saving when only a small amount of hot water is needed.

Mistakes that make heating time wrong

• Forgetting the 3600 conversion and mixing kJ and kWh, which gives a figure thousands of times off.
• Using the final temperature as the temperature rise instead of the difference from the starting temperature.
• Ignoring heat loss on a long, cold-weather heating cycle and expecting the ideal figure.
• Using the element rating on a supply with low voltage, so the delivered power is less than rated.

A quick plausibility check is that heating 1 kg of water by 1 degree needs a little over 4 kJ.

Using the time to plan

Work out when to switch on by subtracting the calculated time from when you need the water, then add a margin for losses. For a timer, set it to start well in advance.

Energy use is the same regardless of element size, apart from losses; a bigger element simply delivers it faster. Heating only the water you need is the real saving.