How to use this calculator
- Read the nameplate input. BTU/h on gas, element watts on electric — and the efficiency class (~80% atmospheric, 90%+ condensing, ~98% electric).
- Set the real rise. Setpoint minus the coldest inlet of the year — winter inlet, not summer.
- Compare recovery to demand. Recovery must beat the sustained draw; the tank covers the bursts.
- Sanity-check first hour. Usable draw + an hour of recovery against the peak hour (back-to-back showers).
How it works
A water heater is a heat balance: every litre per hour of recovery costs the same energy — the specific heat of water times the rise — so the rate falls straight out of the input power:
recovery = P·η / (c_p·ΔT) · gph = BTU/h × η / (8.33 × ΔT°F)
Both forms are the same equation (c_p = 4186.8 J/kg·K is exactly 1 Btu/lb·°F). The tank-side plumbing connects here too: thermal expansion from that heated volume is the expansion tank calculator's job, distribution sizing the pipe size by flow calculator's, and circulation losses the pipe heat loss calculator's.
Worked example
Verified against the live calculator
A 40,000 BTU/h (11.7 kW) gas heater at
80% efficiency, 90°F (50°C) rise,
40 gal (150 L) tank:
recovery = 40,000 × 0.80 / (8.33 × 90) ≈ 42.6 gal/h (161 L/h) · full tank in ≈ 56 min
The first-hour estimate lands at 70 gal (266 L): 70%
of the stored 40 gallons plus the 42.6 the burner adds during the
hour. That is why a modest gas heater keeps up with a busy morning —
and why the same tank on a 4,500 W element (15,354
BTU/h at ~98%) recovers only about 20 gal/h and leans much harder
on storage.
Frequently asked questions
How do you calculate water heater recovery rate?
Heat balance on the water: recovery = input × efficiency ÷ (8.33 × temperature rise) in gph with BTU/h, or P·η/(4186.8·ΔT) in SI. A 40,000 BTU/h gas heater at 80% through a 90°F rise recovers 42.6 gal/h (161 L/h).
How long does a water heater take to recover?
Tank volume × specific heat × rise ÷ delivered heat. The 40-gallon (150 L) example heater lifts a full cold tank 90°F in about 56 minutes. Electric units recover slower per nameplate watt — a 4,500 W element is only 15,354 BTU/h, about 20 gal/h at the same rise.
What is first-hour rating versus recovery rate?
Recovery is steady-state production; first-hour delivery adds the hot water already stored. The estimate here is usable draw (≈70% of the tank) plus one hour of recovery — about 70 gallons for the example heater. The FHR on the EnergyGuide label is the standardized test version of the same idea.
Does a heat pump water heater follow this formula?
Yes, but enter the HEAT OUTPUT, not the compressor draw — a COP-3 unit moving 1,500 W of electricity delivers ~4,500 W of heat. Using nameplate watts directly understates heat-pump recovery by the COP factor.
Method & assumptions
- Pure heat balance at c_p = 4186.8 J/kg·K and 1 kg/L — no standby loss, scale derating or cycling; nameplate recovery tables embed the same arithmetic.
- Efficiency is the recovery/thermal figure, not UEF — UEF folds in standby and draw patterns and belongs to the EnergyGuide test.
- The first-hour output is an arithmetic estimate (usable draw + one hour of recovery); the listed FHR is a standardized test rating.
- Demand-side sizing (fixture units, peak-hour demand tables) is code/ASHRAE territory beyond this screen.