Calculating Water Heater Capacity for a Standard Olympic Size Swimming Pool

Its for sure there wont be a standard calc and you may also be causing confusion with your use of terms

When you say Heater Capacity I think you are looking for the Thermal Duty or Heat Load of the Heater (from your further comments you seem to be assuming electric heaters but all sorts are possible)

The Heat Capacity of a liquid is the energy required to heat a standard mass by a standard temperature rise. for water this is typically 4.18 kJ/kgK or 1 BTU / lb°F in the temperature range that you are looking at for swimming pools.

I would imagine an olympic pool has a standard dimension obviously 50m long but do they have 8 or 10 lanes these days and are there some half lanes either side all of which affects the width. I know the depth of the pool is significant in making the pool swim faster as well as having the pool filled right to the brim and having some guttering system to return the water spilled over the side when the swimmers dive in (Archimedes and all that)

An Olympic Pool must be 25m wide with a depth of 2.0m (min) at all parts of the course and must be 50m in length - between touch panels if they are used. The 25m width is to allow for 8 lanes to be 2.5m wide minimum with 2 spaces of 2.5m wide outside lane 1 and 8.
So this is 2.5 x 8 lanes = 20m + (2.5m x 2) = 25m in total.

There are then two duties for the Heater

a) Maintaining the temp at the specified temp

b) Bringing the pool up to temp from cold.

So looking at a)

Heat losses from the system:

Evaporation from the pool. This is affected by local ambient temperature and humidity; temp of the pool; is it outside (LA 84, Barcelona 92) in which case how windy, is it in direct sunlight etc or indoors (Beijing / London) what is the air con like in the building

Heat losses through the walls of the pool. The pool will be warmer than the surrounding earth (or air) if its an above ground pool and heat conduction through the walls will lose heat. Insulation in the building process and walls and BASE of the pool will minimise this

As mentioned above olympic pools are filled to the brim (so that waves dont bounce of the walls and slow the swimmers) so there is lost water and lost energy. This water is replaced with cold (presumably) water and so has to be heated.

Depending on how hot the pool is ie if it is above body temperature then there would be heat loss to the swimmers

You need to add all these up and quantifying these will involve lots of assumptions but the general equations can be found add in some design margin and there you go.

A for B well I would calculate a then find out how long it would take to heat the pool from cold to operating using the figure gained in a. If it is acceptable (and this depends on usage hopw often the pool has to be heated from cold - can it be used whil its being heated etc) then just go with a. Otherwise back calculate based on how quickly you want to heat the pool. However if B is more than say five times the value for a you might want to consider two separate heaters