Enter your pool's surface dimensions, desired water temperature, and average air temperature to find the BTU output you need from a heater.
Estimate only — an uncovered pool in wind loses heat faster; a pool cover reduces the BTU needed.
BTU/hr needed = pool surface area × temperature rise × 12 — a standard rule-of-thumb constant covering typical heat loss from an uncovered outdoor pool. We round up to the nearest common gas heater size (100k, 150k, 200k, 250k, 300k, or 400k BTU) since that's what's actually sold. A pool cover, wind-sheltered location, or heat pump instead of gas can all change the real-world number.
It depends on your pool's surface area and how much you need to raise the temperature above average air temperature — enter your numbers above for a specific BTU recommendation.
Yes significantly — a cover cuts evaporative heat loss, often the biggest factor in pool heat loss, so a covered pool can often use a smaller heater or heat faster with the same size.