Swimming Pool Heat Loss and Heater Size Calculator (Indoor and Outdoor)

Where a pool loses heat, the heater needed to hold the water temperature, the heat-up time and the heat pump electrical power.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

A pool loses heat from its surface by evaporation, by convection to the air and by radiation to the surroundings, through its walls and floor to the ground, and by the cold make-up water added to replace what evaporates and splashes out. An outdoor pool also gains heat from the sun. The heater must supply the net loss.

Evaporation is the biggest loss, especially indoors. The calculator uses the ASHRAE natatorium equation, in which the evaporation depends on the water surface area, the difference between the vapour pressure at the water temperature and in the air, the air speed over the water and an activity factor. A pool cover cuts evaporation by about 90 percent while it is on.

The heat-up time is the energy to warm the whole pool divided by the heater output left over after the losses. For a heat pump the electrical power is the heat output divided by the COP, which falls as the air gets colder.

Formulas used

  • q_e = F_a A (p_w - p_a)(0.089 + 0.0782 V)
  • q_c = (2.8 + 3V) A (T_w - T_a)
  • q_r = \varepsilon\sigma A (T_w^4 - T_s^4)
  • Q = q_e + q_c + q_r + q_g + q_m - q_s

Worked example

With the default numbers in the calculator above:

  1. Vapour pressure difference driving the evaporation: 1.578 kPa
  2. Evaporation (latent heat): 31.78 kW
  3. Water evaporated: 46.97 kg/h
  4. Convection to the air: -0.65 kW
  5. Radiation to the surroundings: -1.183 kW
  6. Ground and wall loss: 1 kW
  7. Heating the make-up water: 1.212 kW
  8. Heater output needed to hold the temperature (average): 32.16 kW
  9. Energy a day at that rate: 771.9 kWh
  10. Heat pump electrical power: 8.041 kW

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

Why does an indoor pool lose so much heat by evaporation?

Because warm water evaporates strongly into air that is less than fully humid, and each kilogram of water carries off about 2.4 megajoules of latent heat.

How much does a pool cover save?

A cover on when the pool is not in use cuts the evaporation by about 90 percent, which is usually the single biggest energy saving for a heated pool.

What water temperature should I hold?

That is a choice for the pool use: comfort, therapy or sport. Every degree you add raises the evaporation and the heater size, so use the lowest that suits the use.

Related calculators

Further reading: Incropera and DeWitt, Fundamentals of Heat and Mass Transfer; Cengel, Heat and Mass Transfer. ASHRAE Handbook, HVAC Applications (natatoriums).

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