Tankless Sizing by Temperature Rise and Flow
Why this matters
A tankless heater that is undersized does not run out of hot water the way a tank does. It delivers a steady stream that is not hot enough, and the customer calls in January about a unit that worked fine when it went in during August. Nothing is broken. The heater was sized against the water temperature on the day of the visit, and the ground has since cooled by about fifteen degrees. This card is the arithmetic that prevents that call, laid out as the sheet you fill in at the kitchen table, with the reasoning for each line.
The one equation and where the 500 comes from
Heating water at a steady flow takes:
Output (Btu/h) = gpm x 500 x temperature rise (F)
The 500 is not a fudge factor. A gallon of water weighs about 8.33 lb, there are 60 minutes in an hour, and it takes 1 Btu to raise 1 lb of water 1 F. 8.33 x 60 = 499.8, which rounds to 500. So 1 gpm raised 1 F needs about 500 Btu/h of heat delivered into the water. The constant holds for water near room temperature; it is close enough across the domestic range that nobody corrects it.
That figure is OUTPUT, the heat that ends up in the water. The burner's rating plate states INPUT, the gas burned. The two are linked by the heater's efficiency:
Input (Btu/h) = output / efficiency
A condensing tankless commonly runs in the mid 90s percent; a non-condensing unit commonly runs in the low 80s. Use the efficiency from the maker's literature for the model you are quoting, not a remembered class figure, and size against input because input is what the gas piping, the plate and the price sheet all talk about.
The sizing sheet
TANKLESS SIZING SHEET job: 2-bath ranch
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1 fixtures at once shower + lavatory
2 flow, each shower 2.0 lav 1.5 gpm
3 design flow 2.0 + 1.5 = 3.5 gpm
4 outlet set point 120 F
5 design inlet 50 F (coldest month)
6 rise 120 - 50 = 70 F
7 output needed 3.5 x 500 x 70
= 122,500 Btu/h
8 efficiency (maker) 0.95
9 input needed 122,500 / 0.95
= 128,947, call it
129,000 Btu/h
10 check, other way 129,000 x 0.95
= 122,550 out
122,550 / (500 x 70)
= 3.50 gpm OK
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inlet measured on visit: 64 F (August, NOT used)
Line 10 is the second direction: take the input you landed on, turn it back into output, and divide by 500 times the rise. If you do not get your design flow back, one of the earlier lines is wrong.
Line by line: the calls that matter
Line 1, what runs at once. Size to the realistic simultaneous draw, not to every fixture in the house. In a two-bath home that is usually one shower plus one other fixture. Two showers at once is a real design case in a house with two full baths and teenagers; ask, and write down what the customer said, because the answer moves the whole sheet.
Line 2, flow per fixture. Use the actual fixture flow, not the supply size. Current showerheads are capped by federal rule at 2.5 gpm at 80 psi and many are rated lower; a WaterSense lavatory faucet is 1.5 gpm or less. If the customer has a rain head or body sprays, read their rated flow off the trim or the box; a multi-outlet shower can double line 2 by itself. The minimum supply pipe size to each fixture is owned by the sibling card on supply sizes; see Minimum Supply Size to Each Residential Fixture.
Line 4, set point. 120 F at the heater is the common residential set point and the one that keeps scald risk down. Shower and tub outlets are limited to 120 F by an ASSE 1016 or 1070 device regardless of the heater set point; see The Pressure and Temperature Numbers on Every Residential Call. A customer who wants 140 F at the heater for a dishwasher without a booster changes line 4 and the rise, not just the dial.
Line 5, the design inlet. This is the line that causes the January callback. Groundwater temperature follows the season with a lag, and the cold supply in a basement or a slab is close to the ground temperature around the service line. The design inlet is the coldest month's groundwater for your area, which your supply house, the heater maker's sizing map or your own winter readings will give you. It is never the reading you take on the visit unless the visit is in the coldest month. In much of the northern US the winter inlet runs in the 40s F; along the Gulf it may stay in the 60s. A shop that keeps a winter inlet reading per service area stops guessing.
Line 6, the rise. Outlet minus design inlet. Every degree of rise costs the same 500 Btu/h per gpm, so at a fixed output, flow and rise are inversely proportional: double the rise and you halve the flow a given heater can deliver.
Worked example: what the August reading would have done
Same house, same fixtures. The tech measured 64 F at the kitchen cold tap on an August visit and was tempted to use it.
Sized on the visit reading. Rise = 120 - 64 = 56 F. Output = 3.5 x 500 x 56 = 98,000 Btu/h. At 0.95, input = 98,000 / 0.95 = 103,158 Btu/h. A unit in that input class would have looked right on the sheet.
What that unit does in January. It delivers 98,000 Btu/h of output at full fire. At the 50 F winter inlet the rise is 70 F, so the flow it can heat to 120 F is 98,000 / (500 x 70) = 98,000 / 35,000 = 2.8 gpm. The house needs 3.5 gpm. The shortfall is 3.5 - 2.8 = 0.7 gpm, which is 0.7 / 3.5 = 20 percent of the design flow. In practice the heater does not refuse to run. It either holds temperature and throttles flow, which the customer reports as weak pressure, or holds flow and lets the outlet sag, which they report as a lukewarm shower when someone washes their hands.
The ratio to remember. 122,500 / 98,000 = 1.25. Sizing on a summer reading 14 F warmer than winter produced a heater with 20 percent less output than this design needed; put the other way, the design needed 1.25 times what it had. The size of that error depends on the gap between your visit reading and the design inlet, so a spring or fall reading misleads less, and a reading taken in the coldest month does not mislead at all.
Sized correctly. At the 129,000 Btu/h input from the sheet, and checking a common larger class: a 199,000 Btu/h input unit at 0.95 delivers 199,000 x 0.95 = 189,050 Btu/h output. At a 70 F rise that is 189,050 / 35,000 = 5.40 gpm. That covers the 3.5 gpm design with 1.9 gpm to spare, enough for a second lavatory or a dishwasher running alongside the shower, and enough to cover two showers at 2.0 gpm each (4.0 gpm) with 1.4 gpm left.
What changes the answer
A mixed-temperature shower draws less than its full flow from the heater. A shower at 105 F mixed from 120 F hot and 50 F cold takes a hot fraction of (105 - 50) / (120 - 50) = 55 / 70, about 79 percent. Of a 2.0 gpm head, that is about 1.57 gpm of hot. Sizing the full 2.0 gpm as hot, as the sheet does, is conservative, which is the right direction to err; do not use the mixed figure to shave a size off unless you are sure what else draws at once.
Electric tankless. The same output math applies, converted to electric: 1 kW is 3,412 Btu/h, and electric resistance heating delivers nearly all its input. 122,500 Btu/h is 122,500 / 3,412 = 35.9 kW. At 240 V that is 35,900 / 240 = about 150 A of heater load, which most existing residential services cannot add. Whole-house electric tankless in a cold-inlet area is an electrical service question first; route it to the electrician before quoting.
Gas supply and venting. A 199,000 Btu/h unit replacing a 40,000 Btu/h tank needs roughly five times the gas, which usually means a larger meter, a regulator check and resized piping. The gas pipe size comes from the adopted edition's table (IFGC or NFPA 54, as adopted), and the vent is the maker's listed system. Neither is solved by the sizing sheet, and both belong on the quote.
Recirculation. A recirculation loop adds standby heat loss and can short-cycle a unit that sees small flows; check the maker's minimum flow and whether the model is designed for a loop.
How to check a quote someone else wrote
Find the design inlet on the quote. If there is none, or it matches the date of the visit in a warm month, recompute line 7 at your area's winter inlet. Then run line 10 backwards from the quoted unit's input and efficiency: if the gpm it gives at the winter rise is below the simultaneous flow the house actually needs, the unit is short, and the customer will find out in the coldest week of the year.
The same equation diagnoses a unit already on the wall. On a January lukewarm-shower call, time a bucket at the shower with only that fixture open, read the inlet and outlet temperatures off the unit's display or with a probe thermometer, and compute what the heater is delivering. Say the bucket gives 3.0 gpm, the inlet reads 46 F and the outlet 112 F at full fire: 3.0 x 500 x (112 - 46) = 3.0 x 500 x 66 = 99,000 Btu/h. Compare that with the rated output (input times efficiency). If the unit is delivering close to its rating, it is undersized for that flow and rise, and the fix is a flow restrictor, a lower set point conversation or a bigger unit. If it is delivering well under its rating, sizing is not the problem: look at gas pressure at the unit under full fire, scale on the heat exchanger, or an inlet filter screen, before anyone blames the original quote. The broader choice between tank, tankless and hybrid, and first-hour rating for tanks, is owned by Water Heater Sizing + Selection Reference.
References
- See related: Water Heater Sizing + Selection Reference
- See related: How to Install a Tankless Water Heater
- See related: The Pressure and Temperature Numbers on Every Residential Call
- IFGC 2021 or NFPA 54, as adopted, for gas pipe sizing tables
- Heater manufacturer's sizing and installation literature, which is part of the listing