Find the energy needed to raise your pool temperature, how long your heater will take, and what it costs in gas.
One BTU raises one pound of water one degree Fahrenheit. Water weighs 8.34 pounds per gallon, so the energy to heat a pool is volume × 8.34 × temperature rise. Real pools lose heat to the air and ground, so we add roughly 20% for losses — more if your pool is uncovered or windy. A pool cover dramatically cuts both heat-up time and running cost.
Raising 20,000 gallons by 10°F: 20,000 × 8.34 = 166,800 lb, × 10°F = 1.67 million BTU, × 1.25 for losses ≈ 2.1 million BTU. A 400,000 BTU/hr heater takes about 5 hours.