Water Heater Sizing for Pros: FHR, GPM and Temperature Rise

Two ratings, two sizing methods

The federal test procedure for residential water heaters, 10 CFR 430, Subpart B, Appendix E, defines the two numbers you size with:

• First-hour rating (FHR) applies to tanks and other heaters that don't fire on flow. It estimates the most hot water the heater can deliver in one hour, starting fully heated.
• Maximum GPM rating applies to flow-activated (tankless) heaters. It is the most hot water per minute the unit delivers in the federal test.

Both tests run with supply water at 58 °F and the outlet set to 125 °F, a nominal 67 °F rise, and the maximum GPM formula scales the measured flow to that 67 °F rise. Keep that in mind: a tankless unit's rated flow assumes a 67 °F rise, and many jobs need more.

Tank size in gallons is not the sizing number either. The FHR depends on tank capacity, heat source and burner or element size, according to DOE's Energy Saver sizing page. That page returns a 404 error as of October 4, 2026, so this guide uses the Internet Archive copy captured July 2, 2026.

Sizing a tank: first-hour rating vs. peak-hour demand

DOE's method is to estimate the household's busiest hour of hot water use and choose a model whose FHR is at least that large.

1. Pick the busiest hour of the day (morning, noon or evening) and count who is home then.
2. Count each hot water use in that hour.
3. Multiply each use by its gallons and add them up. That total is the peak-hour demand.
4. Find a model with an FHR at least that high. It is printed at the top left of the EnergyGuide label as "Capacity (first hour rating)" and may also appear in the maker's literature.

DOE's worksheet uses these gallons of hot water per use:

DOE notes that these are estimates based on averages of information published on websites, and that the worksheet does not estimate daily use. If you can measure, measured shower flow × minutes beats a flat 20 gallons.

Worked examples:

• DOE's own example: 3 showers (60) + 1 shave (2) + 1 hand dishwashing (3) = 65 gallons, so look for an FHR of 65 or more. The archived page prints a total of 66, but its lines add to 65.
• A busy morning: 2 showers (40) + a top-loader load (25) + the dishwasher (7) + food prep (3) = 75 gallons.
• Measured: 2 showers at 2.0 gpm for 8 minutes (32) + a front-loader load (15) = 47 gallons.

For heat pump water heaters, DOE notes that the FTC does not require the EnergyGuide label, so take the FHR from the manufacturer's literature.

Recovery, if you want to check a spec sheet. The federal test defines recovery efficiency as the energy delivered to the water divided by the energy content of the fuel used. Gallons recovered per hour = input Btu/h × recovery efficiency ÷ (500 ÷ 60 × rise). Take a 40,000 Btu/h gas tank whose spec sheet lists 78% recovery efficiency, at a 70 °F rise: 40,000 × 0.78 ÷ (8.333 × 70) = 53.49 gallons per hour. A 4,500 W element is 15,354 Btu/h; at 98% it recovers 25.79 gallons per hour. Those efficiencies are examples; use the figures for the unit you're quoting.

Sizing a tankless unit: flow × temperature rise

DOE describes tankless heaters as rated by the maximum temperature rise they can deliver at a given flow. So you need two numbers: flow and rise.

1. List the fixtures that will run at the same time and add up their flow rates. DOE's example is a 0.75 gpm faucet plus a 2.5 gpm showerhead, or 3.25 gpm. If you don't know a flow, DOE suggests timing a bucket for one minute.
2. Find the rise: desired outlet temperature minus incoming water temperature. DOE uses 120 °F for most uses and a 50 °F inlet when you don't know better, which gives a 70 °F rise. It mentions 140 °F for dishwashers without internal heaters and cautions that 140 °F raises the risk of scalding.
3. Output Btu/h = 500 × gpm × rise.
4. Input = output ÷ the efficiency on the spec sheet. For electric units, kW = Btu/h ÷ 3,412.
5. Check the unit's published flow-and-rise data at your rise, not just its maximum GPM. For several fixtures at once, see tankless water heater gpm.

Worked example (DOE's numbers): 500 × 3.25 gpm × 70 °F = 113,750 Btu/h into the water. A gas unit with a 95% thermal efficiency (an example; use the spec sheet) needs 113,750 ÷ 0.95 = 119,736.8 Btu/h of input, about 119,700. An electric unit, assuming 100%, needs 113,750 ÷ 3,412 = 33.34 kW, which is 138.9 amps at 240 V. Circuit and conductor sizing come from the electrical code and the manufacturer, not from this arithmetic.

Working backward from a unit: a 199,000 Btu/h input unit at 95%, with 43 °F water in and 120 °F out (a 77 °F rise), delivers at most 199,000 × 0.95 ÷ (500 × 77) = 4.91 gpm.

DOE's rule of thumb is that gas tankless units can typically manage a 70 °F rise at 5 gpm, and electric ones at 2 gpm. That works out to 175,000 Btu/h and 70,000 Btu/h of output (20.52 kW). Because the rated maximum GPM is scaled to a 67 °F rise, the same heat output at a 70 °F rise gives about 4% less flow (67 ÷ 70 = 0.957).

The Btu and kW formula, and why 500 is rounded

One Btu raises one pound of water by 1 °F (EIA). The heat needed per hour is pounds of water per hour × rise, and pounds per hour = gpm × 60 × pounds per gallon. The constant 500 is that 60 × pounds per gallon, rounded: 500 ÷ 60 = 8.33 lb per gallon.

The federal test procedure uses 8.24 lb per gallon for water at 125 °F and a specific heat of 1.00 Btu per lb per °F, which gives 8.24 × 60 = 494.4. So 500 is a rounded constant, about 1.1% above the test-procedure figure, which errs slightly toward more heater. Our calculator uses 500 everywhere so tank and tankless results agree with each other.

For kW, EIA gives 1 kilowatthour = 3,412 Btu, so kW = Btu/h ÷ 3,412.

Incoming water temperature changes the answer

DOE's 50 °F inlet is a placeholder for when you don't know. In the model estimates below, winter mains water runs colder than that in Minneapolis, Chicago and Boston and warmer in Atlanta and Phoenix. The best number is a measured cold-tap temperature in winter; DOE suggests holding a thermometer under a cold faucet.

The next best is an estimate. NREL's 2014 Building America House Simulation Protocols give an equation for daily mains temperature, based on a location's annual average air temperature and the spread between its warmest and coldest months. NREL says it was fitted to data from multiple locations and reflects pipes buried deeper in colder climates. Plugging in NOAA's 1991–2020 normals gives these model estimates. They come from a model, not from measured water.

Worked example: take DOE's 3.25 gpm to 120 °F in Minneapolis in mid-February. The output needed is 500 × 3.25 × 79.6 = 129,350 Btu/h, 13.7% more than at the 50 °F default (37.91 kW for an electric unit). Flip it around: a unit sized to deliver 113,750 Btu/h gives only 113,750 ÷ (500 × 79.6) = 2.86 gpm at that rise, not 3.25. In Atlanta the model's coldest value is above 50 °F, so the default leaves some margin there.

Where the codes and the manufacturer take over

This is general information, not code or engineering advice. Venting, gas pipe sizing, combustion air, relief valves, electrical circuits and any temperature-limiting devices at fixtures are governed by the adopted codes and the manufacturer's installation instructions. The local building department, as the authority having jurisdiction, has the final word.

You can read the model codes free online: the IPC at ICC Digital Codes, the UPC at IAPMO's read-online library, and the NEC through NFPA free access, which requires an NFPA account. Check which edition and local amendments your jurisdiction has adopted.

Next step

Run the job's numbers in the water heater size calculator. It gives peak-hour gallons for a tank, and Btu/h and kW for a tankless unit, at the inlet temperature you enter. Then use how to price a water heater replacement to turn the unit into a price. If the complaint is a long wait for hot water rather than running out, the heater's size won't fix it; the piping volume will tell you why (gallons in a pipe by size).