Physics of Buildings

How long will my hot water last?

Tank, temperatures, shower and heater in; minutes of hot shower out.

Defaults: a 40-gallon gas heater (40,000 Btu/h, 77 % recovery efficiency) at 120 °F, 50 °F cold water, a 2 gpm shower at 105 °F. Change any box; the working is below the result. The chart runs the same model at many flows: the steep climb near the dashed keep-up flow is where the heater’s output starts to matter during the shower.

How it is calculated

It takes 8.33 Btu to warm a gallon of water by 1 °F (water’s specific heat, 4.184 J/(g·°C), converted with NIST factors) [1][2][3]. The shower valve mixes tank water and cold water, so the share drawn from the tank is

hot share = (Tshower − Tcold) / (Ttank − Tcold)(1)

The heat a heater puts into the water is the burner input times its recovery efficiency (gas) or the element’s power, 3,412 Btu/h per kW (electric; one element runs at a time) [4]. Its recovery rate and the largest shower it can carry on its own follow:

recovery (gal/h) = heat / (8.33 · rise)
keep-up flow (gpm) = heat / (60 · 8.33 · (Tshower − Tcold))(2)

Below the keep-up flow, the shower never runs cold. Above it, the time comes from the same layered tank model as the cut-open heater: cold water enters at the bottom through the dip tube, hot water leaves the top, warm water rises above cooler water, and the heat goes in at the burner or at the element whose thermostat calls, upper first. The answer is the simulated time until the shower first falls more than 1 °F below the temperature you asked for. The model shows why a gas burner adds little during a long shower: it warms the incoming cold water by heat ÷ (60 × 8.33 × hot flow), usually too little to reach shower temperature, so the stored hot water runs out first. In this model an electric tank with half the heat input can last a little longer in one shower than a gas tank: its upper element heats the water near the outlet, where it is drawn next, while the model puts all of the gas heat at the bottom. A real gas flue also warms the upper water, so the real difference is smaller, and the electric tank takes longer to reheat the whole tank afterwards. The essay works through it.

Worked example

The defaults: a 40-gallon gas heater at 120 °F with 50 °F cold water and a 2 gpm shower at 105 °F. The hot share is 55/70 = 0.79, so the tank supplies 1.57 gpm. The burner puts 40,000 × 0.77 = 30,800 Btu/h into the water: a recovery of 41 gallons an hour at a 90 °F rise, which matches the rating A. O. Smith lists for its 40,000 Btu/h, 40-gallon GCBL-40 [5]. Its keep-up flow is 30,800 ÷ (60 × 8.33 × 55) = 1.1 gpm, less than 2, so the shower is limited by the store: about 23 minutes, with about 37 gallons of hot water drawn. With the burner off the same tank gives about 21 minutes.

Assumptions and valid range

  • One steady shower from a fully heated tank; no other hot water in use; the valve mixes exactly to your shower temperature, as a thermostatic valve does; no heat lost in the pipes.
  • The tank is a stack of 30 layers that mix only when warmer water sits below cooler water. Its boundary between hot and cold spreads over a few gallons, so about 86 percent of the tank reaches the shower with the heater off; tanks whose inlet stirs the water deliver less [6]. A gas heater’s heat goes in at the bottom only (the flue’s warming of the water higher up is ignored), which makes the gas result conservative.
  • Recovery efficiency: about 77 percent is typical of a standard atmospheric gas heater (from a 41 gph rating at 40,000 Btu/h); check your heater’s label or specification sheet. Electric elements put all their power into the water.
  • Accepted inputs: tank 10–120 gal; thermostat 90–160 °F; cold water 33–90 °F; shower 0–6 gpm at 60–125 °F; burner 0–100,000 Btu/h at 30–100 %; element 0–12 kW. The model stops at 4 hours. Standard shower heads use 2.5 gpm and WaterSense-labeled ones 2.0 or less [7].
  • This is an estimate for understanding and comparison, not a sizing guarantee or a code determination. For choosing a heater, compare first-hour ratings, which a federal test measures [8].

Before turning the thermostat up. The U.S. Consumer Product Safety Commission urges 120 °F: at 130 °F a 30-second exposure can cause a third-degree burn, at 140 °F six seconds [9]. Store hotter only with thermostatic mixing valves protecting the taps [10]. Gas controls and 240-volt elements are work for a licensed professional.

Sources

  1. Flowers, P., Theopold, K., Langley, R. & Robinson, W. R. (2019). Chemistry 2e, §5.1 Energy Basics (Table 5.1, specific heats). OpenStax, Rice University. textbook Specific heat of liquid water 4.184 J/(g·°C) at 25 °C.
  2. Thompson, A. & Taylor, B. N. (2008). Guide for the Use of the International System of Units (SI), NIST SP 811, Appendix B.8 Factors for units listed alphabetically. National Institute of Standards and Technology. standard Btu_IT = 1055.056 J; Btu_IT/h = 0.2930711 W; US gallon = 3.785412 × 10⁻³ m³; lb = 0.4535924 kg; °F interval = 5/9 K.
  3. U.S. Geological Survey. Water Density (Water Science School). USGS. government reference Density table: 0.99907 g/cm³ at 60 °F (15.6 °C), 0.98870 at 120 °F (48.9 °C), 0.98338 at 140 °F (60 °C).
  4. A. O. Smith Corporation (2021). Installation Instructions and Use & Care Guide: Residential Electronic Thermostat Electric Water Heater (printed 10/21/2021). A. O. Smith, sold through Lowe's (AOSmithAtLowes.com). manufacturer manual Upper and lower element; the control energizes one element at a time and the upper has priority; limp mode with one failed element; troubleshooting 'insufficient hot water': undersized heater, temperature set low, faulty thermostatic mixing valve in a shower control, reversed connections or melted dip tube (soon after installation), leak, failed lower element ('some hot water but not as much as before'; the lower element does most of the work and usually wears out first); 4500/5500 W elements; inspect the anode after six months, then at least annually depending on hardness.
  5. A. O. Smith Corporation. ProLine 40-Gallon Atmospheric Vent Short Natural Gas Water Heater, model GCBL-40 400 (product page). hotwater.com. manufacturer data sheet 40-gallon nominal (38 gal rated storage), 40,000 Btu/h input, 68-gallon first-hour rating, recovery 41 gallons per hour, UEF 0.57.
  6. Abu Hilal, M. (2011). Experimental Energy Study for Domestic Hot Water Storage Tanks. Jordan Journal of Mechanical and Industrial Engineering (abstract via An-Najah National University). journal article Turbulent mixing at the cold inlet must be eliminated to save energy in the tank; a curved cover on the bottom supply line gave about 17% more usable hot water.
  7. U.S. Environmental Protection Agency. WaterSense: Showerheads. EPA. government reference Standard showerheads use 2.5 gpm; WaterSense-labeled showerheads use no more than 2.0 gpm; less shower water reduces demand on water heaters.
  8. U.S. Department of Energy. 10 CFR Part 430, Subpart B, Appendix E: Uniform Test Method for Measuring the Energy Consumption of Water Heaters. Electronic Code of Federal Regulations (eCFR), current as of 2026. federal regulation §1.5 first-hour rating: estimate of the maximum volume of hot water a storage heater can supply within an hour that begins fully heated; §2.3 supply water 58 °F; §2.4 outlet 125 °F; §5.3.3 draws at 3.0 gpm (tanks ≥ 20 gal), each ended when the outlet falls 15 °F below its maximum; electric heaters with two or more elements that do not operate simultaneously; §1.11 recovery efficiency.
  9. U.S. Consumer Product Safety Commission. Avoiding Tap Water Scalds (CPSC Document #5098). U.S. Consumer Product Safety Commission, Bethesda, MD. government safety alert Urges all users to lower water heaters to 120 °F; most adults suffer third-degree burns from 150 °F water in 2 s, 140 °F in 6 s, 130 °F in 30 s, and even 120 °F in 5 min; most injuries are to the elderly and children under five; measure at the tap with a thermometer.
  10. A. O. Smith Corporation (2021). Installation Instructions and Use & Care Guide: Residential Gas Water Heaters, 100341468_2000598643 Rev A (March 2021). A. O. Smith, sold through Lowe's (AOSmithAtLowes.com). manufacturer manual Component diagram (anode, inlet dip tube, T&P valve); every heater has at least one anode rod; rotten-egg odor needs sulfate, little oxygen, sulfate-reducing bacteria and active hydrogen from the anode; less active anode plus chlorination by a service agency; do not remove the anode; condensation sizzling and popping in the burner area is normal; expansion noises are normal; T&P valve must not be plugged; most T&P leakage is thermal expansion in a closed system; thermostatic mixing valves; short repeated heating cycles can raise temperature up to 30 °F above the setting; drain and flush every 6 months.