Calculate hot water recovery time, tank volume, water temperature, heater capacity or efficiency from five inputs in gallons, °F, BTU/hr or kW.
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Hot Water Recovery Formula
The calculator uses the heat required to raise a tank of water from the cold water temperature to the hot water temperature. Internally, it converts inputs to hours, US gallons, degrees Fahrenheit, and BTU/hr.
Energy = V*8.34*(T_h-T_c)
t = (V*8.34*(T_h-T_c))/(H*E)
V = (t*H*E)/(8.34*(T_h-T_c))
T_h = T_c + (t*H*E)/(8.34*V)
T_c = T_h - (t*H*E)/(8.34*V)
H = (V*8.34*(T_h-T_c))/(t*E)
E = (V*8.34*(T_h-T_c))/(t*H)
- t = hot water recovery time, in hours before final unit conversion
- V = volume of tank, in US gallons before final unit conversion
- T_h = temperature of hot water, in °F before final unit conversion
- T_c = temperature of cold water, in °F before final unit conversion
- H = heating capacity of the heater, in BTU/hr before final unit conversion
- E = heater efficiency as a decimal, so 80% is entered as 80 and used as 0.80
- 8.34 = approximate weight of 1 US gallon of water in pounds
To calculate hot water recovery time, the calculator first finds the energy needed in BTU, then divides by the effective heater output, which is heating capacity multiplied by efficiency.
If you leave another field blank, the same relationship is rearranged. You can solve for tank volume, hot water temperature, cold water temperature, heating capacity, or efficiency by entering the other five values.
Typical Inputs for Hot Water Recovery Calculations
Use these values as general reference points when checking whether your result is reasonable.
| Input | Common range | Notes |
|---|---|---|
| Residential tank volume | 30 to 80 gal | Larger tanks need more energy to recover from the same temperature rise. |
| Hot water setpoint | 120°F to 140°F | A higher setpoint increases recovery time if heater capacity is unchanged. |
| Incoming cold water | 40°F to 70°F | Colder inlet water increases the required temperature rise. |
| Gas heater input | 30,000 to 75,000 BTU/hr | Only the useful heat after efficiency is applied goes into the water. |
| Electric heater input | 3 to 5.5 kW | 1 kW equals about 3,412 BTU/hr. |
| Unit | Conversion used | Used for |
|---|---|---|
| 1 gallon | 8.34 lb of water | BTU heat calculation |
| 1 kW | 3,412.141633 BTU/hr | Heater capacity conversion |
| 1 liter | 0.264172 gal | Tank volume conversion |
| 1 cubic meter | 264.172052 gal | Tank volume conversion |
| °C to °F | °F = °C*9/5 + 32 | Temperature conversion |
Hot Water Recovery Examples
Example 1: Calculate recovery time
You have a 50 gal tank, 120°F hot water, 60°F cold water, a 40,000 BTU/hr heater, and 80% efficiency.
Energy = 50*8.34*(120-60) = 25020 BTU
t = 25020/(40000*0.80) = 0.7819 hr
0.7819 hr*60 = 46.91 min
The recovery time is about 46.91 minutes.
Example 2: Calculate required heater capacity
You want an 80 gal tank to recover in 70 minutes. The hot water temperature is 120°F, the cold water temperature is 50°F, and the heater efficiency is 90%.
Energy = 80*8.34*(120-50) = 46704 BTU
t = 70/60 = 1.1667 hr
H = 46704/(1.1667*0.90) = 44480 BTU/hr
The required heater capacity is about 44,480 BTU/hr.
Hot Water Recovery FAQ
What does hot water recovery mean?
Hot water recovery is the time it takes a water heater to bring a tank of water back up to the target hot water temperature after hot water has been used. It depends on tank size, incoming water temperature, set temperature, heater capacity, and efficiency.
Why does colder inlet water increase recovery time?
Colder inlet water creates a larger temperature rise. For example, heating water from 50°F to 120°F requires more energy than heating it from 70°F to 120°F. With the same heater capacity and efficiency, more required energy means a longer recovery time.
Should efficiency be entered as a percent or decimal?
Enter efficiency as a percent. For example, enter 80 for an 80% efficient heater. The calculation uses that value as 0.80 internally.
