Physics of Buildings

Expansion tank sizing estimator

Heater, temperatures and pressures in; expanded water, minimum tank size and peak pressure out. An estimate, not a code or sizing guarantee.

Defaults: a 50-gallon heater, 40 °F water heated to 140 °F, 60 psi house pressure, a 100 psi maximum and a 2-gallon tank, which comes out just short. Change any box; the working is shown below the results.

How it is calculated

First the expansion. Water’s density at the cold and hot temperatures comes from NIST’s reference tables [1]; a fixed mass of water grows by the ratio of the two densities. By default the heater’s own steel tank growth (35 millionths of its volume per °C) is subtracted, as Amtrol’s expansion factors do [2][3]:

E = Vh · [ ρ(Tcold) / ρ(Thot) − 1 − βsteel·(Thot − Tcold) ](1)

Then the air cushion. With the tank’s precharge equal to the house pressure PL, Boyle’s law with absolute pressures (gauge + 14.7 psi) gives the tank volume that holds the pressure to Pmax [4][5]. This is Amtrol’s design pressure factor [3]:

Vtank = E × (Pmax + 14.7) / (Pmax − PL)(2)

With any other precharge the estimator uses the general Boyle’s-law form: a precharge below the house pressure lets the house fill part of the tank before heating; one above it means the tank takes nothing until the pressure reaches the precharge. For a tank you already have, it adds the expansion to the water the tank holds at the house pressure and reads the pressure off Boyle’s curve.

Worked example

Amtrol’s own example: a 240-gallon heater at 150 °F, 60 psi line pressure, 125 psi maximum. Its expansion factor from 40 °F is 0.0179, so E = 4.3 gallons; the factor is (125 + 14.7)/(125 − 60) = 2.1; the tank needs 4.3 × 2.1 = 9.0 gallons [3]. Entered here (240, 40, 150, 60, 125) the estimator gives 4.32 gallons and 9.28 gallons, the same calculation without the rounding.

Choosing the maximum

The result depends most on the maximum pressure you allow, and the makers differ. Amtrol’s quick-sizing chart uses the 150 psi relief valve setting [6]; Watts’ calculator says the final pressure should never exceed 85 % of the relief valve’s rating [7]; Watts’ relief valve data sheet says normal operating pressure must not exceed 75 % of its setting, about 112 psi for a 150 psi valve [8]. The default here, 100 psi, is a conservative choice inside all three.

Assumptions and valid range

  • Design case: the whole heater heated from the cold temperature to the thermostat setting with no water drawn. Watts suggests a 90 °F start unless the heater is fully drained on each use, which gives a smaller tank [7].
  • Air at constant temperature (Boyle’s law); diaphragm free to move; tank shell rigid; water density at atmospheric pressure. Only the heater’s water is counted, not the pipes’.
  • Pressures are gauge pressures at the tank. “House pressure” is the static pressure with no water flowing, after any PRV; above 80 psi makers call for a PRV, and recommend 60 psi or less [9].
  • Accepted inputs: heater 1–1000 gal; cold 34–100 °F; hot 60–200 °F; house 10–150 psi; maximum above the house pressure and not above the relief setting; tank 0–500 gal; precharge 0–150 psi. Results are rounded for display; copied results and shared links keep your exact inputs.
  • This is an estimate for understanding and comparison, not a code determination or a sizing guarantee. Choose a listed tank whose volume and acceptance exceed the result, and follow the maker’s instructions and your local code; a licensed plumber decides.

Before anything is changed. Expansion tanks are installed, and their precharge set (tank empty, system cold), by licensed professionals [10]. Never cap or plug the water heater’s T&P relief valve or its drain line [11]; gas water heaters are licensed-professional work.

Sources

  1. Lemmon, E. W., McLinden, M. O. & Friend, D. G. (2025). NIST Chemistry WebBook, SRD 69: Thermophysical Properties of Fluid Systems (water, isobaric data at 0.101325 and 1.101325 MPa, 1–99 °C). National Institute of Standards and Technology. reference data Density of water from the IAPWS-95 formulation, retrieved 2026-11-10 in 1 °C steps: 999.975 kg/m³ at 4 °C, 998.207 at 20 °C, 983.196 at 60 °C. The same query at 1.101325 MPa gives the compressibility used here (about 3.0–3.3 × 10⁻⁶ per psi between 10 and 60 °C).
  2. Ling, S. J., Sanny, J. & Moebs, W. (2016). University Physics Volume 2, §1.3 Thermal Expansion (Table 1.2, thermal expansion coefficients). OpenStax, Rice University. textbook ΔV = βVΔT; steel α = 12 × 10⁻⁶ /°C, β = 35 × 10⁻⁶ /°C; water β = 210 × 10⁻⁶ /°C (near room temperature); water is densest at 4 °C.
  3. Amtrol (Worthington Industries) (2019). Sizing the Therm-X-Trol: For Pressurization and Expansion Control of Hot Water Systems, MC 10007, 9017-112 (03/19). Amtrol, West Warwick, RI. manufacturer sizing guide Check valves, backflow preventers and PRVs make a system that needs expansion control; tank volume = design pressure factor × expanded water; Table 1 expansion factors from 40 °F (120 °F: .0100, 140 °F: .0150, 150 °F: .0179, 180 °F: .0276); Table 2 DPF and the equation DPF = (max + 14.7)/(max − line); worked example 240 gal, 150 °F, 60 psi line, 125 psi max → 4.3 gal × 2.1 = 9.0 gal; precharge equal to static line pressure; a tank left at 40 psi on a 70 psi supply loses room before heating; tank on the cold supply, not the hot outlet.
  4. Flowers, P., Theopold, K., Langley, R. & Robinson, W. R. (2019). Chemistry 2e, §9.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law. OpenStax, Rice University. textbook Boyle's law: at constant temperature and amount, the volume of a gas is inversely proportional to its pressure (PV = constant); ideal-gas assumptions.
  5. 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 Standard atmosphere = 1.01325 × 10⁵ Pa; 1 psi = 6.894757 × 10³ Pa; so 1 atm = 14.696 psi.
  6. Amtrol (Worthington Enterprises) (2025). Therm-X-Trol Water Heater Expansion Tanks brochure, MC4090 (09/25). Amtrol, West Warwick, RI. manufacturer data sheet ST-5 2.0 gal and ST-12 4.4 gal in-line models, 150 psig maximum working pressure, 200 °F, 50 psig factory precharge; vertical models 40 psig factory precharge; quick sizing charts based on 40 °F incoming water, 150 psi T&P, precharge equal to static supply pressure (e.g. 50 gal heater, 140 °F, 40–80 psi: ST-5).
  7. Watts Water Technologies (2026). Expansion Tank Sizing Calculator (Potable). Watts, North Andover, MA. manufacturer sizing tool Inputs: heater gallons, initial (building cold water) pressure, which typically does not exceed 80 psi per the UPC; air precharge should match initial pressure; final pressure should never exceed 85% of the T&P relief valve rating; install a PRV where system pressure exceeds 80 psi; tank on the cold supply upstream of the heater; PLT-5 2.1 gal, PLT-12 4.5 gal; 150 psi maximum; a general guide, not a guarantee.
  8. Watts Water Technologies (2014). Series 1L, 1XL, 10L and 100XL Temperature and Pressure Relief Valves, specification sheet ES-10L/100XL. Watts, North Andover, MA. manufacturer data sheet Temperature relief 210 °F; standard pressure settings 75, 100, 125, 150 psi; ANSI Z21.22 certified; maximum system operating pressure must not exceed 75% of valve set pressure; lever operated at least once a year; if no water flows the valve is inoperative: turn off the heater and call a plumber; 'designed for emergency safety relief and shall not be used as an operating control'.
  9. A. O. Smith (2018). Water Heater Thermal Expansion Tanks, Owner's Manual, Models 2–5 Gallon Capacity, 100306555 200055907 Rev. A. A. O. Smith Corporation (copy hosted at aosmithatlowes.com). manufacturer manual Backflow preventers seal off the system, so an expansion tank is required or the relief valve will discharge on every heating cycle; the tank stores expanded water and returns it when the temperature drops; 150 psi, 200 °F; above 80 psi incoming a PRV is required, 60 psi or less recommended; air charge matched to incoming pressure, read with the system cold; a weeping T&P may be a worn valve, inlet pressure above 60 psi or an air charge not matched to incoming pressure; 'Do not plug the Temperature-Pressure Relief Valve opening.'
  10. Amtrol (Worthington Enterprises) (2024). Therm-X-Trol Thermal Expansion Absorbers, Installation & Operation Instructions, Models ST-5C(DD) through ST-210VC, 9017-091 (04/24). Amtrol, West Warwick, RI. manufacturer manual Must be installed by a licensed professional; precharge set to match cold water supply pressure with the tank empty of water; installed between the water heater and the backflow preventer, check valve or PRV; the air charge keeps water out until system pressure exceeds the precharge, absorbs the expanded water and keeps pressure below the relief valve setting; a licensed contractor should inspect the T&P valve at least every 3 years or if discharge is present; maximum 200 °F.
  11. International Code Council, PMG Membership Council (2022). CodeNotes: Water Heater Safety in the I-Codes (based on IPC 2021 §504.6 and IRC §P2804.6.1). International Code Council. standards body guidance Any discharge from the relief valve indicates a distribution-system problem, a water heater problem or a malfunctioning valve; discharge piping must have no threaded end (so it cannot be capped) and no valves or tees; improper discharge piping can create a dangerous situation that could result in explosion.