Why tankless sizing is a flow problem, not a volume problem
A storage heater is sized on how many gallons it can hand you in an hour. A tankless heater is sized on how many gallons it can hand you in a minute, forever. There is no reserve: every drop that leaves the unit was heated on its way through, so the burner has to keep up with the tap in real time or the temperature falls.
That single difference changes what you measure. You do not care how much hot water the household uses in a day. You care about the worst simultaneous moment - two showers and a kitchen sink at seven in the morning in February - because that is the flow the unit must hold at the coldest inlet temperature of the year. Size for that and every easier moment takes care of itself.
The second number is temperature rise, and it is the one people get wrong. Groundwater in a cold northern winter can arrive at 40 F; in the deep south it may never fall below 70 F. Heating to a 120 F setpoint is an 80 degree lift in the first case and a 50 degree lift in the second. Because heat demand is directly proportional to the rise, the same house needs 60% more burner in the cold climate for exactly the same shower. This is why an identical unit is advertised as 5 gpm in one place and 8 gpm in another: both figures are true, at different temperature rises.
A tankless unit's rated flow is therefore meaningless without a stated rise. Whenever a manufacturer quotes gallons per minute, look for the delta-T beside it. Quoted at a 35 F rise, almost any unit sounds enormous. Quoted at 77 F, the same unit sounds modest. The physics has not changed.
The formula and the constant 500
The heat needed to raise water is the sensible heat equation: mass times specific heat times temperature change. Water weighs 8.33 lb per US gallon and takes 1 BTU to lift one pound by one degree Fahrenheit, so one gallon per minute raised one degree needs 8.33 BTU per minute, or 8.33 × 60 = 499.8 BTU per hour. The trade rounds that to 500 and calls it the rule of 500: BTU/hr = 500 × gpm × rise.
That result is the heat that has to land in the water. It is not what you buy. A non-condensing gas tankless heater sends 15 to 20% of its fuel up the vent, so you divide by thermal efficiency to get the input rating on the nameplate. A condensing unit recovers much of the latent heat in the flue gas and runs at 93 to 98%, so the same duty needs a smaller nameplate. An electric unit converts essentially all of its input, which is why electric sizing skips the efficiency step and goes straight to kilowatts: 499.8 BTU/hr is 0.1465 kW, so kW = gpm × rise ÷ 6.83.
Run the formula backwards and you get the more useful question answered. Given a unit of known input rating and efficiency, the flow it can hold at a given rise is rating × efficiency ÷ (499.8 × rise). That is the number in the Flow the selected unit holds output, and it is what you compare against your simultaneous demand. Anything above zero in the headroom line means the unit keeps up; anything below zero means the outlet temperature sags when everything runs at once.
One caution about the flow figure: manufacturers publish a maximum flow rate their unit will pass, and above it the unit modulates down rather than delivering less-hot water. Below a minimum activation flow, typically 0.4 to 0.6 gpm, the burner will not fire at all - which is why a slow trickle at a bathroom faucet can come out cold on a tankless system.
Worked example: two showers, 55 F inlet, 120 F setpoint
A house runs two 2.0 gpm showers at the same time. Winter mains temperature measures 55 F and the setpoint is 120 F. The unit under consideration is a 199,000 BTU/hr non-condensing gas tankless heater at 82% thermal efficiency.
- Simultaneous flow. 2 × 2.0 = 4.00 gpm.
- Temperature rise. 120 − 55 = 65 F.
- Heat into the water. 4.00 × 499.8 × 65 = 129,948 BTU/hr.
- Fuel input required. 129,948 ÷ 0.82 = 158,473 BTU/hr.
- Electric equivalent. 158,473 ÷ 3,412 = 46.4 kW, which is 193 A at 240 V - well past what a domestic service will carry, and the reason this duty is a gas job.
- What the 199,000 BTU/hr unit actually delivers. 199,000 × 0.82 = 163,180 BTU/hr into the water; 163,180 ÷ (499.8 × 65) = 5.02 gpm.
- Headroom. 5.02 − 4.00 = 1.02 gpm spare, enough for a lavatory faucet alongside the two showers but not for a third shower.
Now move the same house to a colder climate where mains water arrives at 40 F. The rise becomes 80 F, the same 4 gpm needs 159,936 BTU/hr into the water and 195,044 BTU/hr of input, and the same 199,000 BTU/hr unit holds only 163,180 ÷ (499.8 × 80) = 4.08 gpm. The headroom has fallen from 1.02 gpm to 0.08 gpm on nothing but geography.
Reading the result: what to buy
Compare the required input rating against real nameplates. Residential gas tankless heaters cluster at roughly 140,000, 160,000, 180,000 and 199,000 BTU/hr, the last figure being common because 199,000 sits just under the 200,000 BTU/hr threshold at which many jurisdictions apply commercial appliance rules. If your requirement lands above 199,000, the answer is not a bigger residential unit; it is two units manifolded together, which most manufacturers support and which has the useful side effect of letting one unit carry light loads efficiently.
For electric, the kilowatt figure is usually the deciding constraint rather than the money. A whole-house electric tankless heater at 27 kW draws 112 A at 240 V, typically wired as three 40 A circuits, and needs a 200 A service with little else on it. Above about 4 gpm in a cold climate, electric whole-house tankless stops being realistic in most homes. Point-of-use electric units of 3 to 9 kW serving a single sink remain a good application.
Do not size on the annual average groundwater temperature. Size on the coldest month. A unit that is perfect in October and 30% short in January is a unit the household will complain about, and no amount of setpoint adjustment fixes a shortage of burner. If you are unsure of your winter inlet temperature, run a cold tap for two minutes in midwinter and measure it - that single measurement is worth more than any published map.
Finally, check that the gas supply can carry the load. A 199,000 BTU/hr tankless heater is often two or three times the input of the tank heater it replaces, and the existing gas line is frequently too small. Total the connected load with the gas appliance BTU load calculator and then size the pipe with the natural gas pipe sizing calculator before you order the heater.
Flow a gas tankless heater holds at each inlet temperature
| Inlet water | Rise to 120 F | 150,000 BTU/hr unit | 199,000 BTU/hr unit |
|---|---|---|---|
| 40 F | 80 F | 3.08 gpm | 4.08 gpm |
| 45 F | 75 F | 3.28 gpm | 4.35 gpm |
| 50 F | 70 F | 3.52 gpm | 4.66 gpm |
| 55 F | 65 F | 3.79 gpm | 5.02 gpm |
| 60 F | 60 F | 4.10 gpm | 5.44 gpm |
| 65 F | 55 F | 4.47 gpm | 5.94 gpm |
| 70 F | 50 F | 4.92 gpm | 6.53 gpm |
| 75 F | 45 F | 5.47 gpm | 7.26 gpm |
A single row of this table is the whole marketing argument about tankless capacity. The same 199,000 BTU/hr appliance is a 4.1 gpm heater in Minnesota in January and a 7.3 gpm heater in Florida in August.
Assumptions and limits of this calculation
- Steady state only. The formula covers the unit once it is firing. It does not model the cold slug already sitting in the pipe, which is why a long run to a distant bathroom still delivers cool water for several seconds no matter how the heater is sized.
- Full hot flow is assumed. A shower mixing 120 F water with cold to reach 105 F draws less than its rated flow from the heater. Sizing on full rated fixture flow therefore carries built-in conservatism, which is deliberate.
- Efficiency is treated as constant. Real thermal efficiency varies with firing rate and with return temperature on condensing units. The nameplate figure is close enough for sizing and wrong for annual energy estimates.
- Water properties are taken at ordinary temperature. 8.33 lb/gal and 1 BTU/lb-F are accurate to within about 1% across the domestic range.
- Gas supply and venting are separate checks. Neither the pipe size nor the vent is covered here, and both frequently need upgrading when a tank heater is replaced with a tankless one.
- Recirculation adds load. A hot water recirculation loop imposes a continuous small draw and standing losses that this calculation does not include.
Setpoint, scald risk and the mixing valve
Raising the setpoint does not increase a tankless unit's capacity in any useful way; it increases the rise the unit has to produce, which reduces the flow it can hold, and it raises the temperature at every fixture. Water at 140 F can scald in about five seconds. If a high delivery temperature is genuinely needed - a commercial dishwasher, a long recirculating main - deliver it and then temper the domestic branches with a thermostatic mixing valve, sized with the mixing valve temperature calculator.
The heater is not the only flow constraint: check the water supply too
Everything on this page sizes the burner or element to the flow you enter - it says nothing about whether the water service, well pump or pressure tank feeding the heater can actually deliver that flow at the pressure the fixtures need. The headroom figure this calculator reports assumes the simultaneous demand you specified arrives at the unit's inlet undiminished; if it does not, the heater can have ample capacity to spare and the fixture can still run cold or lose pressure.
On a municipal connection this is rarely the binding constraint, since a city main carries far more than an ordinary residential simultaneous draw. On a private well it can be the real one. A well pump and pressure tank are sized around a duty cycle, not around continuous full-rated flow, and running several fixtures at once for as long as a shower runs can draw the pressure tank down faster than the pump refills it. The result is a pressure and flow sag at the tankless unit's own inlet sensor, even though the burner itself has plenty of input rating in reserve.
The check is separate from anything computed on this page: confirm the well system's continuous flow rate at normal operating pressure meets or exceeds the simultaneous demand entered above, not just the heater's rated capacity. A correctly sized tankless unit fed by an undersized well will still starve on the coldest morning of the year, and the symptom at the fixture - a drop in flow or temperature - looks identical to an undersized heater even though the burner was never the constraint.