Estimate the cost to heat a swimming pool by size and temperature.
Pool heating cost is set by surface area, not by volume, because almost all the heat leaves through the top. Evaporation alone accounts for the majority of the loss, with radiation and convection making up the rest, and the accepted rule of thumb is about 5 BTU per hour per square foot for every degree Fahrenheit you hold above ambient. That is why a cover is the single most effective measure available — it roughly halves the loss by stopping evaporation, and it costs nothing to run. The heater then determines what that heat costs to replace: a heat pump moves about five units of heat per unit of electricity, an element makes one for one, and a gas heater delivers around 0.82 units per unit of gas, so the fuel comparison depends heavily on the relative price of gas and electricity.
Pool heat loss and running cost
BTU/h = surface area x loss coefficient x degrees above ambient, where the coefficient is 5 uncovered and 2.5 covered; thermal kWh per day = BTU/h x 24 / 3412; energy bought = thermal / COP; cost = energy x rate
Roughly half the heating cost, because evaporation is the dominant loss and a cover stops it. It is the cheapest intervention available and pays for itself within a season on most heated pools.
Because it does not create heat, it moves it from the air into the water, delivering four to six units of heat per unit of electricity. The trade-off is slow recovery and falling output as the air gets colder.
It takes longer to reach temperature because there is more water to warm, but holding temperature costs the same, since losses happen at the surface. Only the initial heat-up is affected by depth.