What needs calculating for a pool?
Volume (length × width × average depth) underpins everything: pump flow, heater size, salt and chemical doses all depend on it. Getting average depth right avoids errors everywhere.
For irregular pools, split into zones and add their volumes.
How many hours should the pump run?
Long enough to turn over the full volume at least once a day, more in summer and with heavy use. A variable-speed pump runs longer at lower flow with less energy.
The filter must handle the pump's flow.
How do you heat a pool efficiently?
Size the heat pump for volume and heat-up time, cover the pool at night and shelter it from wind. Maintaining temperature costs far less than reheating from cold.
Saltwater chlorination reduces chlorine handling but needs salinity and pH control.