Water Heater Size Calculator — First-Hour Rating
Tank gallons is the wrong number to shop on. What decides whether the last shower runs cold is first-hour rating — roughly 70% of the tank plus one hour of recovery — measured against the busiest hour the house actually has. Count the uses in that hour below and this returns the smallest tank that covers it.
Size your water heater
Uses in the busiest hour
Gallons of hot water per use, from the US DOE first-hour-rating worksheet.
Electric: watts × 3.412. A 4,500 W element ≈ 15,400 BTU/h.
Atmospheric gas ~80%, electric ~98%.
Use the winter figure, not the annual average.
140 °F stored, tempered to 120 at the fixtures.
Recommended tank size
Smallest stocked tank whose first-hour rating covers a 66 gallon peak hour, with 4.7 gallons to spare.
Peak-hour demand
66 gal
First-hour rating
70.7 gal
No stocked tank covers this peak
Raise the burner input, spread the demand across the hour, or move to two heaters or a tankless unit.
See the breakdown
Planning estimate. Standby loss, pipe run and recirculation are not modelled, and a real heater's published first-hour rating is measured under a DOE test procedure rather than computed. A licensed plumber has final say.
The formula, explained in plain English
Three steps: what the house wants in an hour, what the heater can make in an hour, and what it already has in the tank.
Recovery beats storage
In the defaults the tank contributes 28 gallons of usable storage and recovery contributes 42.7 — recovery is 60% of the first-hour rating. That is exactly why a 40-gallon gas heater out-delivers a 50-gallon electric one.
Rise is inversely proportional
Double the temperature rise and you halve the recovery. A heater that recovers 54.9 gph on a 70 °F summer rise makes only 38.4 gph on a 100 °F winter rise — a 30% loss from nothing but the season.
The 0.70 is mixing, not margin
Cold entering the bottom mixes with hot leaving the top, so usable output falls below temperature well before the tank empties. It is a physical limit, not a safety factor you can argue away.
Store hot, deliver warm
Storing at 140 °F and tempering to 120 with a mixing valve suppresses Legionella, prevents scalding, and stretches the tank — because every tempered gallon delivered is part cold water.
Worked examples
The defaults, the same house on electric, and a northern winter that changes the answer.
Family morning, 40,000 BTU gas
demand = 66 gal
recovery = 40,000 × 0.80 ÷ (8.33 × 90) = 42.7 gph
40 gal: FHR = 0.70 × 40 + 42.7 = 70.7 gal ✓
30 gal: FHR = 63.7 ✗
Result: a 40-gallon tank, with 4.7 gallons of headroom. Note the 30-gallon tank fails by only 2.3 gallons — first-hour rating is a much finer instrument than tank size.
The same house on electric
A 4,500 W element is 15,354 BTU/h at 98% efficiency — a third of the gas burner.
50 gal: FHR = 35 + 20.1 = 55.1 ✗
60 gal: FHR = 42 + 20.1 = 62.1 ✗
75 gal: FHR = 52.5 + 20.1 = 72.6 ✓
Result: the same 66-gallon peak needs a 75-gallon electric tank against a 40-gallon gas one. Nearly twice the storage, purely because the element cannot recover fast enough — this is the single biggest reason electric tanks are physically larger.
Northern winter — 40 °F inlet
recovery = 40,000 × 0.80 ÷ (8.33 × 100) = 38.4 gph
40 gal: FHR = 28 + 38.4 = 66.4 gal against a 66 gal demand
→ 0.4 gallons of margin
Result: the same heater that had 4.7 gallons spare in the shoulder season has essentially none in January. Size on the winter inlet temperature — a heater sized on an annual average will disappoint exactly when it matters.
First-hour rating by tank size
At the default 40,000 BTU, 80% efficiency and 90 °F rise — 42.7 gallons per hour of recovery. Computed from the same code the calculator runs.
| Tank | Usable storage (70%) | Plus recovery | First-hour rating |
|---|---|---|---|
| 30 gal | 21.0 gal | 42.7 gal | 63.7 gal |
| 40 gal | 28.0 gal | 42.7 gal | 70.7 gal |
| 50 gal | 35.0 gal | 42.7 gal | 77.7 gal |
| 60 gal | 42.0 gal | 42.7 gal | 84.7 gal |
| 75 gal | 52.5 gal | 42.7 gal | 95.2 gal |
| 80 gal | 56.0 gal | 42.7 gal | 98.7 gal |
| 100 gal | 70.0 gal | 42.7 gal | 112.7 gal |
What the season does to recovery
The same 40,000 BTU heater storing at 140 °F, across the range of groundwater temperatures a US house sees.
| Inlet temperature | Rise to 140 °F | Recovery | 40 gal tank FHR |
|---|---|---|---|
| 40 °F | 100 °F | 38.4 gph | 66.4 gal |
| 50 °F | 90 °F | 42.7 gph | 70.7 gal |
| 60 °F | 80 °F | 48.0 gph | 76.0 gal |
| 70 °F | 70 °F | 54.9 gph | 82.9 gal |
Sources & standards: per-use hot water figures and the first-hour-rating method from the US Department of Energy water heater sizing guidance; recovery derived from the specific heat and density of water (8.33 lb/gal). Storage and delivery temperature practice, including thermostatic mixing to limit scalding, follows IPC 607 and ASSE 1017/1070 valve standards. A published first-hour rating is measured under the DOE test procedure; this computes an equivalent. Local amendments override the model code.
Frequently asked questions
Common questions about water heater sizing, first-hour rating, and recovery.
What size water heater do I need?
Size it on peak-hour demand, not on house size or bedroom count. A morning with three showers, a dishwasher, a clothes washer and two hand-washings comes to 66 gallons. A 40,000 BTU gas heater at 80% efficiency with a 90 °F rise recovers 42.7 gallons an hour, so a 40-gallon tank gives a 70.7 gallon first-hour rating — enough, with 4.7 gallons spare.
What is first-hour rating and why does it matter more than gallons?
First-hour rating is how much hot water the heater can actually deliver in one busy hour: roughly 70% of the tank (the usable part before cold mixing spoils it) plus one hour of recovery. It is the number on the yellow EnergyGuide label and the one that decides whether the last shower is cold. A 40-gallon gas heater can out-deliver a 50-gallon electric one because recovery does more work in that hour than ten extra gallons of storage.
Why only 70% of the tank?
Because as you draw hot water off the top, cold water enters the bottom to replace it, and the two mix at the boundary. Long before the tank is empty the delivered water has dropped below usable temperature. The 0.70 factor is the long-standing allowance for that — it is not a safety margin, it is physics.
What is recovery rate?
Gallons per hour the burner or element can heat through your temperature rise: BTU input × efficiency ÷ (8.33 × rise). At 40,000 BTU, 80% efficiency and a 90 °F rise that is 42.7 gallons per hour. Electric heaters recover far more slowly — a 4,500 W element is only about 15,400 BTU, giving 20.1 gallons an hour at the same rise against the gas burner's 42.7, which is why electric tanks have to be bigger.
Does the inlet temperature really matter?
A great deal, and it is seasonal. Groundwater at 40 °F in a northern winter needs a 100 °F rise to reach 140; the same house in summer at 65 °F needs only 75. Recovery is inversely proportional to rise, so the identical heater loses a quarter of its recovery between summer and winter. Size for the winter case.
Should I store hot water at 140 °F?
There is a genuine tension here and it is worth stating plainly. Storing at 140 °F suppresses Legionella, which grows between roughly 77 and 113 °F. But 140 °F water scalds in about five seconds. The usual resolution is to store hot and temper down to 120 °F at the fixtures with a thermostatic mixing valve — which also stretches the effective capacity of the tank, since you are blending in cold.
Is a bigger tank always safer?
No. A larger tank has more standing surface area losing heat around the clock, which shows up on every bill whether the water is used or not. Get the first-hour rating right for the real peak hour and stop there — the aim is to cover the busiest hour of the day, not to store a day's supply.
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