Water heater recovery time calculator: gallons per hour, and how many minutes a full tank takes to reheat
Recovery GPH = input x efficiency / (8.33 x temperature rise). A 4,500 W element at a 90 F rise gives 20.5 GPH, so a 40-gallon tank reheats in about 117 minutes.
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Short answer
Water heater recovery is heat input multiplied by efficiency, divided by 8.33 pounds per gallon times the temperature rise: recovery GPH = input BTU/h x efficiency / (8.33 x rise F). An electric element’s input is its watts times 3.412, because the US Energy Information Administration prints 1 kilowatt-hour as 3,412 BTU. One 4,500 W element at a 90 F rise (50 F incoming water, 140 F setpoint) gives 4,500 x 3.412 / (8.33 x 90) = 20.5 gallons per hour, the same figure A. O. Smith prints in its residential electric recovery table, and a cold 40-gallon tank then takes 40 x 8.33 x 90 / 15,354 BTU/h = 1.95 hours, about 117 minutes, by this site’s arithmetic. A 40,000 BTU gas tank at an implied 78 percent efficiency recovers 41.6 GPH, inside the 41 to 43 GPH A. O. Smith prints for its 40,000 BTU ProLine models. The gas formula is printed by the County of San Diego’s water heater sizing guide.
If the shower ran cold and the plan is a bigger tank, stop: the number that decided it was the rise and the element, not the gallons, and a “9,000 W” dual-element heater recovers at 4,500 W because its elements do not run together.
Recovery in gallons per hour, and minutes to reheat the full tank
Formula: GPH = input BTU/h x efficiency / (8.33 x rise), and minutes = gallons x 8.33 x rise / (input x efficiency) x 60. Electric input is watts x 3.412 (EIA: 1 kWh = 3,412 BTU). Enter one element's watts: A. O. Smith's default wiring runs the two elements one at a time. Switching to gas sets 40,000 BTU and 78 percent, this site's rounding of the 77 to 81 percent implied by A. O. Smith's printed ProLine recovery figures; the San Diego County guide's planning default is 75 percent for gas and 98 percent for electric. The reheat time ignores standby loss and any draw, so a real tank takes longer.
What is the formula?
Recovery is the rate at which a storage water heater turns input into hot water, in gallons per hour at a stated rise. State Water Heaters’ glossary defines it as converting BTU or watt input into gallons heated per hour, with “90 rise” meaning the incoming water is raised 90 F.
The rise is the setpoint minus the incoming water temperature. The San Diego County sizing guide defines it as the temperature of water leaving the heater minus the temperature entering, and prints the gas formula this page rearranges: BTU input = GPH x rise x 8.33 / thermal efficiency. Its worked example, 54 GPH x 60 F x 8.33 / 0.75, comes to 35,986 BTU.
| Term | Value | Where it comes from |
|---|---|---|
| Pounds of water per gallon | 8.33 | San Diego County sizing guide, formula 1 |
| BTU per kilowatt-hour | 3,412 | EIA, Energy Units and Calculators Explained |
| Electric efficiency | 100 percent | A. O. Smith’s electric recovery table matches the formula at 100; San Diego’s planning default is 98 |
| Gas efficiency | 78 percent default | This site’s rounding of 77 to 81 percent implied by A. O. Smith’s ProLine recovery figures; San Diego’s default is 75 |
Efficiency is the share of the input that ends up in the water. One opened sheet prints both terms for a gas tank: A. O. Smith’s FCG-100 lists 75,100 BTU input, 80 percent thermal efficiency and 81 GPH at a 90 F rise, and the formula returns 80.1. For the 40,000 BTU ProLine tanks the sheet prints 41 to 43 GPH and no efficiency, so the 78 percent default is implied, not published.
What does a worked example look like?
The calculator opens on one 4,500 W element, a 40-gallon tank, 50 F incoming water and a 140 F setpoint.
| Step | Arithmetic | Result |
|---|---|---|
| Rise | 140 - 50 | 90 F |
| Input in BTU/h | 4,500 x 3.412 | 15,354 |
| Recovery | 15,354 / (8.33 x 90) | 20.5 GPH |
| Heat to fill the tank | 40 x 8.33 x 90 | 29,988 BTU |
| Reheat time | 29,988 / 15,354 | 1.95 hours, about 117 minutes |
A. O. Smith’s residential electric recovery table prints 20.5 GPH for a 4.5 kW element at a 90 F rise, 36.9 at 50 F and 15.4 at 120 F, so the first three rows reproduce the maker’s figure. The reheat time is the same formula rearranged, which no opened document prints, so it is this site’s arithmetic: nothing drawn, no standby loss, the whole tank heating at once.
Why does a dual-element tank recover at one element’s wattage?
A. O. Smith’s electric element sheet says element operation shall be double element, non-simultaneous unless ordered differently, and that simultaneous operation doubles recovery. Simultaneous wiring is a separate circuit type on the same sheet, with a caution that the breaker must carry the higher amperage. Enter one element’s watts unless the nameplate says simultaneous.
On 208 V the same element delivers less than its rating; the element resistance calculator covers that derate.
Why does January look like a failing heater?
Recovery falls in proportion to the rise. The same 4,500 W element that gives 36.9 GPH at a 50 F rise gives 20.5 GPH at a 90 F rise, a 44 percent drop on A. O. Smith’s table, with nothing wrong at the heater.
Rinnai’s groundwater map puts annual average inlet temperatures between 35 and 77 F across the United States, and says local variations and seasonal changes move the actual inlet temperature. No opened source prints a winter figure by region, so measure the cold tap in January. A 140 F setpoint instead of 120 F adds 20 F of rise the same way.
Who should skip this calculator?
A tankless owner: there is no tank to reheat, and the tankless calculator sizes by flow and rise. A heat pump owner: no heat pump document was opened for this page. Anyone choosing a new tank: the first hour rating calculator is the sizing page; this one only times the tank you have. Whether an insulation blanket cuts its standby loss is a separate guide on this site.
Before you call it a bad heater
Do not replace a water heater for slow recovery until the arithmetic above says it is slow for its element and its January rise. If the tank delivers no hot water at all, or recovers far below what the formula returns for its nameplate, the no hot water guide lists slow recovery after a shower as a symptom of a small or failed element or a bad lower thermostat.
Recovery figures are the makers’ published ratings, not tests this site ran. Electrical and gas work follows the manual and the codes adopted where you live.
What owners buy for this
The top picks from Best tankless gas water heater: the maker spec sheets sort them by BTU input, UEF, venting class and the gas line each manual allows, and the gas line decides before the GPM does, compared on published specs and certifications.
Small home, outdoor wall, the lowest input on the page
Rinnai V53DeN (outdoor, natural gas, 5.3 GPM)
Rinnai spec sheet 100000624: 15,500 to 120,000 BTU/h, 0.4 to 5.3 GPM, UEF 0.81, non-condensing, outdoor only, 1/2 in gas line compatible, 3/4 in connections; manual: 10-year heat exchanger, 12 with an isolation valve kit
Outdoor wall, wants no vent to buy, natural gas
Rheem RTG Series 7.0 GPM outdoor, natural gas (RTG-70XLN-3)
Rheem TK-RTG sheet: 11,000 to 160,000 BTU/h, 7.0 GPM at 35 F rise and 4.5 at 67 F, UEF 0.82, non-condensing, outdoor, vent run N/A, 1/2 in gas line compatibility subject to local code, 15-year heat exchanger, 5-year parts, 1-year labor
Same outdoor unit for a propane home
Rheem RTG Series 7.0 GPM outdoor, liquid propane (RTG-70XLP-3)
Rheem TK-RTG sheet: the propane version carries the same 160,000 BTU/h input, 7.0 GPM at 35 F rise and UEF 0.82, model number with P in place of N; the RTG manual sizes propane pipe from its own Table 5 at 2,546 BTU per cubic foot
Frequently asked questions
How long does a 40-gallon electric water heater take to heat up?
With one 4,500 W element and a 90 F rise, A. O. Smith's recovery table gives 20.5 gallons per hour, and this site's arithmetic turns that into about 117 minutes for a cold 40-gallon tank with nothing drawn. A 50-gallon tank on the same element takes about 146 minutes. Real reheat runs longer, because the tank also loses heat while it heats.
Does a dual-element water heater run both elements at the same time?
Not as shipped from A. O. Smith. Its electric element sheet says element operation shall be double element, non-simultaneous unless ordered differently, and that simultaneous operation doubles recovery. Simultaneous wiring is a separate circuit type with a warning about breaker amperage. So a tank with two 4,500 W elements recovers at 4,500 W, not 9,000 W, unless the nameplate says otherwise.
How long does a 40-gallon gas water heater take to recover?
A. O. Smith's ProLine atmospheric vent sheet prints 41 to 43 gallons per hour at a 90 F rise for its 40,000 BTU models, based on performance tests. At 41.6 GPH, this site's arithmetic gives about 58 minutes to reheat a cold 40-gallon tank and about 72 minutes for 50 gallons. The sheet prints no efficiency; those recovery figures imply about 77 to 81 percent.
Why does my water heater recover more slowly in winter?
Colder incoming water raises the temperature rise, and recovery falls in proportion. A. O. Smith's table gives a 4,500 W element 36.9 GPH at a 50 F rise and 20.5 GPH at a 90 F rise, a 44 percent drop with nothing wrong at the heater. Rinnai's groundwater map runs 35 to 77 F by region and says seasonal changes shift the inlet temperature: measure the cold tap in January.
Does this calculator work for a tankless or heat pump water heater?
No. A tankless heater has no tank to reheat; it is sized by flow and temperature rise, which the tankless calculator on this site handles. No heat pump water heater document was opened for this page, so its recovery is not covered here and the watts on its nameplate should not be entered as if they were a resistance element's.
Fact sheet and how to cite this page
- Answer
- Recovery in gallons per hour is heat input multiplied by efficiency, divided by 8.33 times the temperature rise. A 4,500 W element (3,412 BTU per kWh) at a 90 F rise recovers 20.5 GPH, the figure the maker’s electric recovery table prints, and reheats a cold 40-gallon tank in about 117 minutes by this site’s arithmetic. A 40,000 BTU gas tank at an implied 78 percent recovers 41.6 GPH.
- Formula
Recovery GPH = input BTU/h x efficiency / (8.33 x rise F); electric input BTU/h = watts x 3.412; minutes to reheat a full tank = tank gallons x 8.33 x rise / (input BTU/h x efficiency) x 60- Inputs
- Fuel: electric
- Element watts: 4,500 (one element; A. O. Smith’s default wiring runs one at a time)
- Efficiency: 100 percent (A. O. Smith’s electric recovery table matches the formula at 100 percent)
- Tank: 40 gallons
- Incoming water: 50 F, setpoint 140 F, so a 90 F rise
- Output
- 20.5 gallons per hour of recovery, and about 117 minutes to reheat the full 40-gallon tank from 50 F to 140 F with no draw
- Assumptions
- 8.33 is the pounds per gallon of water and 3,412 the BTU in one kilowatt-hour; both constants are as printed by the San Diego County sizing guide and the US Energy Information Administration
- Gas efficiency is not printed on A. O. Smith’s ProLine atmospheric sheet; 78 percent is this site’s rounding of the 77 to 81 percent that sheet’s recovery figures imply, and the San Diego guide’s planning default is 75 percent
- The reheat time is the same formula rearranged, which no opened source prints; real reheat runs longer because of standby loss
- Tankless and heat pump water heaters are out of scope
- Method
- The calculator converts the fuel input to BTU per hour, multiplies by the efficiency the reader enters, divides by 8.33 times the rise between incoming water and setpoint, and prints gallons per hour; it then divides the tank’s heat content by the same input to print minutes. The formula was checked against A. O. Smith’s printed electric recovery table and a printed 80 percent gas example.
- Primary source
- A. O. Smith, Residential Electric Element Availability Sheet and Recovery Table, AOSTD63000 (October 2020) (manufacturer or vendor document)
- Facts verified
- Last updated
- Cite as
- OwnerSpec, "Water heater recovery time calculator: gallons per hour, and how many minutes a full tank takes to reheat", https://ownerspec.com/plumbing/calculators/water-heater-recovery-time-calculator/, facts verified 31 October 2026.
Every figure above also appears, with its source, in the article. All sources ยท How OwnerSpec verifies numbers
Sources
- County of San Diego Department of Environmental Health and Quality, Guidelines for Sizing Water Heaters (PDF) (government or regulatory source)
- A. O. Smith, Residential Electric Element Availability Sheet and Recovery Table, AOSTD63000 (October 2020) (manufacturer or vendor document)
- A. O. Smith, ProLine Atmospheric Vent Residential Gas Water Heaters spec sheet, AOSRG47000 (December 2019) (manufacturer or vendor document)
- A. O. Smith, ProLine High Recovery Atmospheric Vent Residential Gas Water Heaters spec sheet, AOSRG47002 (manufacturer or vendor document)
- A. O. Smith, ProLine 100-Gallon High Recovery Atmospheric Vent Natural Gas Water Heater FCG-100 400, product specifications (manufacturer or vendor document)
- State Water Heaters, Glossary of Terms (manufacturer or vendor document)
- Rinnai, United States Ground Water Temperature Map, Residential Use (PDF) (manufacturer or vendor document)
- US Energy Information Administration, Energy Units and Calculators Explained (government or regulatory source)