The pool heating formula
BTU = gallons × 8.34 × °F rise
gas: BTU ÷ (100,000 × 0.80) therms · propane: BTU ÷ (91,500 × 0.80) gal
heat pump: BTU ÷ (3,412 × COP) kWh · resistance: BTU ÷ 3,412 kWh
Every method delivers the same BTUs — they differ only in what a BTU costs. Gas makes heat by burning fuel (fast, works in any weather); a heat pump moves heat from the air (slow but multiplies each kWh 4–6×); electric resistance turns each kWh into exactly one kWh of heat (simple, and almost always the most expensive per degree).
A worked example
Warming 15,000 gallons by 10°F needs 15,000 × 8.34 × 10 ≈ 1.25 million BTU. At $1.20/therm and 80% efficiency, natural gas costs about $18.80. A heat pump with COP 5 uses ~73 kWh — about $12.50 at $0.17/kWh. Electric resistance for the same job: ~$62. Multiply by how often you let the pool go cold, and the heater choice pays for itself (or doesn't) pretty quickly.
Raising vs. holding temperature
This calculator prices the raise; keeping it there is a separate, ongoing bill driven mostly by evaporation. An uncovered pool can lose 3–5°F overnight — effectively re-buying part of this calculation every day. Before upgrading a heater, price a solar cover; it's the rare purchase that beats every energy source above.