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BTU sizing is surface-area math, not gallon guessing.
Pool heaters are sized to hold temperature against surface heat loss, which is why the math runs on surface area, not gallons: BTU/hr = surface sq ft × temperature rise × 12, using the coldest month you intend to swim. This calculator runs the rule, adjusts for wind exposure, and tells you what size unit to quote.
Anyone pricing a heater or heat pump uses this before the sales call: the ×12 surface-area rule gives the honest minimum, so a 400k-BTU quote for a small pool reads as what it is. The solar-cover note saves more money than the calculator itself.
512 sq ft of surface, holding 80°F water against 65°F air (15° rise): 512 × 15 × 12 ≈ 92,000 BTU/hr minimum to maintain. In practice that pool gets quoted a 100–150k heat pump or 250–400k gas heater — gas heaters are oversized deliberately for fast weekend heat-up.
Gas heaters are cheap per BTU and oversized for speed (heating 2–3°F per hour); heat pumps are efficient but slow and sized to maintain temperature continuously. A heat pump also loses capacity as air temperature drops — check the output rating at YOUR coldest swim-month temp, not the 80°F nameplate condition.