What formula does this use?

It uses Q = m × Cp × ΔT. For water that simplifies to 8.33 BTU to raise one US gallon by one degree Fahrenheit. Recovery rate in gallons per hour is the heat delivered to the water divided by 8.33 times the temperature rise.

How is gas input converted to heat in the water?

The gas input rating in BTU/h is multiplied by a conversion efficiency, typically 0.75 to 0.80 for an atmospheric tank and 0.90 or more for condensing. The result is the heat actually transferred to the water, which is what drives recovery.

Why does recovery rate depend on temperature rise?

The same burner delivers a fixed BTU/h, so the colder the incoming water and the higher the setpoint, the more energy each gallon needs and the fewer gallons per hour the heater can recover. Manufacturer recovery figures are quoted at a standard rise, often 90 F.

How is recovery time calculated?

Recovery time is the energy to reheat the full tank divided by the heat delivery rate. Energy to reheat is tank gallons times 8.33 times the temperature rise; dividing by the BTU/h delivered and multiplying by 60 gives minutes to bring a cold tank up to setpoint.

Does electric really reheat slower than gas?

Usually yes for residential units. A 4.5 kW element delivers about 15,400 BTU/h to the water, while a common gas tank inputs 40,000 BTU/h and still delivers around 30,000 BTU/h after losses, so the gas tank recovers roughly twice as fast.

Water Heater Recovery Rate Calculator

When a tank of hot water runs out, recovery rate decides how long you wait for more. This calculator turns an electric element rating or a gas input into a real recovery rate in gallons per hour and a reheat time, using the basic heat equation for water.

How it works

Heating water is a simple energy balance, and 8.33 BTU raises one gallon by one degree Fahrenheit:

ΔT            = setpoint − incoming cold temperature
heat to water = electric kW × 3412   OR   gas BTU/h × efficiency
recovery GPH  = heat to water / (8.33 × ΔT)
reheat time   = (tank gal × 8.33 × ΔT) / heat to water × 60   (minutes)

The electric path treats the element as delivering essentially all its power to the water; the gas path applies an efficiency factor for flue and standby losses.

Example and notes

A 40,000 BTU/h gas tank at 80 percent efficiency delivers 32,000 BTU/h to the water. Raising water from 50 to 120 F (a 70 F rise) recovers about 55 gallons per hour and reheats a depleted 40-gallon tank in roughly 45 minutes. The same job on a 4.5 kW electric element recovers only about 26 gallons per hour. Remember that published recovery numbers assume a standard rise, so your real-world figure in a cold-groundwater region will be lower than the spec sheet.