Water Heater Sizing & Recovery
First-hour demand by household, the gallons an electric element recovers per hour, how long a cold tank takes to come back, and the kW a tankless needs for your ground water.
Hot water at the tap is about 65% of the tank volume in the first few minutes, and the element is recovering while you use it. That is why a 50 gallon tank handles a 4 person morning.
How the math works
- First-hour demand: 20 gal for the first shower (a 2.5 GPM head runs 10 minutes), 10 gal per additional person in a morning-use pattern, plus 6 gal per GPM of simultaneous fixture flow. A 3 person house with a 3 GPM peak is 48 gal.
- Recovery: watts × 3.412 = BTU per hour; gallons per hour = BTU ÷ (8.34 × temperature rise). A 4,500 W element raising 58°F water to 120°F recovers 31.8 gal/hr.
- Available hot water in the first hour: about 65% of tank volume is delivered in the peak-use window (mixing at 105°F from a 120°F tank), plus the recovery during that hour, which is why a 50 gal tank handles a 3-person morning at a 48 gal demand.
- Tankless sizing: kW = GPM × 8.34 × rise ÷ 1000 ÷ 0.85 (85% on a condensing unit at part load). 3 GPM at a 70°F rise is 21 kW, which is 72,000 BTU/hr, and the 199,000 BTU residential unit is a 8 GPM at 50°F rise machine.
- Energy: 8.34 × rise ÷ 3,412 = 0.17 kWh per gallon at a 70°F rise, so hot water costs about 3 cents a gallon at 17 cents per kWh. Standby loss on a tank adds 10 to 22% to that number.
What size water heater for a 4 person family?
A 3 to 4 person household runs 55 to 65 gal of first-hour demand, so a 50 gal electric tank with a 4,500 W element is the working answer, and a 65 gal or a heat-pump unit is the comfortable one. With a tankless, 21 kW covers 3 GPM in a cold climate.
How long does a water heater take to reheat?
A 50 gal electric tank from 58°F to 120°F at 4,500 W: 50 × 8.34 × 62 ÷ 15,354 = 1.68 hours, 101 minutes. A gas tank with a 40,000 BTU burner does the same in 19 minutes.
Is tankless cheaper to run?
On electric resistance, tankless saves the standby loss (10 to 22%) and costs 2 to 4x to install with a 200 A panel upgrade in many homes. A heat-pump hybrid on an existing 50 gal tank beats both in a warm climate, at 3 to 3.5x the recovery of a resistance element.