Expansion Tank Sizing Calculator
Work out how much the water in a closed heating system expands when it heats up, and the smallest diaphragm or plain steel tank that absorbs it without lifting the relief valve.
Method reviewed October 26, 2026. Version 1.0.0. How it works
Result
- Minimum tank volume
- 4.61gal
- Water expansion (tank must accept this)
- 1.51gal
Heating 50 gal of water from 50 °F to 180 °F adds 1.51 gal; a diaphragm tank of at least 4.6 gal keeps the pressure at or below 25 psig.
- Set the tank’s air precharge to 12 psig with the tank isolated and empty of water, before filling the system.
- Choose a tank with at least this total volume whose maximum acceptance volume is at least the water expansion. Confirm the selection with the tank manufacturer’s data and your installer.
- Water expansion as a share of system volume
- 3.02%
- Acceptance factor
- 0.327
- Fill pressure, absolute
- 26.7psia
- Maximum pressure, absolute
- 39.7psia
Show the working
- Water density at fill and at maximum temperature (IAPWS table)62.4064 and 60.5783 lb/ft³
- Expansion = system volume × (ρ cold ÷ ρ hot − 1)50 × (1.03018 − 1) = 1.509 gal
- Absolute pressures = gauge + atmospheric26.7 psia and 39.7 psia (atmosphere 14.696 psia)
- Diaphragm tank factor = 1 − Pf ÷ Po (precharged to the fill pressure)1 − 26.7 ÷ 39.7 = 0.3275
- Minimum tank volume = expansion ÷ factor1.509 ÷ 0.3275 = 4.61 gal
Why a closed system needs an expansion tank
Water expands as it heats. In a sealed system that extra volume has nowhere to go, so the pressure rises until the relief valve opens. An expansion tank holds a cushion of air that compresses to make room for the extra water, keeping the pressure between the cold fill pressure and a safe maximum.
How the size is worked out
First, the expansion: the calculator takes water density at the fill and maximum temperatures from an IAPWS water table checked against the NIST Chemistry WebBook. The expanded volume is the system volume × (cold density ÷ hot density − 1). Heating water from 50 °F to 180 °F adds about 3 %.
Then the tank: the air cushion obeys Boyle’s law, so pressure × volume stays constant at constant temperature (with absolute pressures). A diaphragm tank is precharged to the fill pressure, which gives a tank of at least expansion ÷ (1 − fill pressure ÷ maximum pressure). A plain steel tank starts with air at atmospheric pressure, so it has to be larger. These are the same expressions published by R.L. Deppmann for compression and bladder tanks.
Choosing the pressures
- Fill pressure: enough to keep the highest radiator or air vent pressurised. A column of water exerts 0.433 psi per foot of height, so a top floor 20 ft above the tank needs at least 8.7 psig at the tank, plus a margin.
- Maximum pressure: safely below the relief valve setting, so the valve does not weep, and within the boiler’s rating.
- Precharge: on a diaphragm tank, set the air side to the fill pressure before the tank is connected and filled.
Pressure, temperature and relief valve settings come from the boiler manufacturer and local code. A qualified installer should make the final selection.
Worked example
These are the example values the calculator opens with, and the result the engine calculates for them.
Inputs
- Tank type
- Diaphragm or bladder
- Water volume of the system
- 50 gal
- Water temperature when filled
- 50 °F
- Highest operating water temperature
- 180 °F
- Fill pressure at the tank
- 12 psi
- Maximum allowed pressure at the tank
- 25 psi
- Site elevation
- 0 ft
Result
- Minimum tank volume
- 4.61 gal
- Water expansion (tank must accept this)
- 1.51 gal
- Water expansion as a share of system volume
- 3.02 %
- Acceptance factor
- 0.327
- Fill pressure, absolute
- 26.7 psia
- Maximum pressure, absolute
- 39.7 psia
Heating 50 gal of water from 50 °F to 180 °F adds 1.51 gal; a diaphragm tank of at least 4.6 gal keeps the pressure at or below 25 psig.
Assumptions
- Water only. Density from the site’s IAPWS water table (CoolProp 8.0.0, checked against the NIST Chemistry WebBook), interpolated per °F.
- The air cushion follows Boyle’s law at constant temperature. A diaphragm tank is precharged to the fill pressure; a plain tank starts with air at atmospheric pressure.
- Pipe and boiler expansion is ignored. Metal expands far less than water, so ignoring it slightly oversizes the tank, which is the safe direction.
Limitations
- Does not handle glycol solutions: their expansion differs from water and needs the fluid maker’s data.
- The tank must also be rated for the system pressure and temperature. Relief valve and pressure settings are set by the boiler manufacturer and your local code; have a qualified installer make the final selection.
Frequently asked questions
Is a bigger expansion tank always better?
A larger tank keeps pressure swings smaller, which does no harm, but it costs more and takes space. What matters is that the tank volume is at least the minimum and its acceptance (bladder) volume at least the water expansion.
Does this work for glycol (antifreeze) systems?
No. Glycol solutions expand more than water and their properties depend on the mixture, so use the fluid manufacturer’s data and the tank maker’s sizing method.
How do I find the system water volume?
Add the boiler’s water content from its manual, the emitters (radiators or baseboard) from their data, and the piping: each pipe size holds a known volume per foot. If you are unsure, err on the high side.
Sources
- Differences in Compression Tank and Expansion Tank Formula (Part 9) — R.L. Deppmann, Monday Morning Minutes. Minimum tank volume = (fluid expansion − pipe expansion) × system volume ÷ denominator, with absolute pressures; plain compression tank denominator (Pa/Pf) − (Pa/Po) with Pa = atmospheric; bladder or diaphragm tank precharged to fill pressure: 1 − (Pf/Po).
- Compression Tank and Expansion Tank Selection Examples (Part 10) — R.L. Deppmann, Monday Morning Minutes. Worked denominators: fill 30 psig (44.7 psia), maximum 50 psig (64.7 psia): bladder tank 1 − 44.7/64.7 = 0.309, compression tank 14.7/44.7 − 14.7/64.7 = 0.102.
- Chemistry 2e, §9.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law — OpenStax, Rice University. Boyle’s law: at constant temperature and amount, P₁V₁ = P₂V₂ (absolute pressures) — the basis of the tank acceptance factor.
- NIST Chemistry WebBook, SRD 69 — Thermophysical Properties of Fluid Systems (water) — National Institute of Standards and Technology. Saturated-liquid water density and viscosity, e.g. 62.364 lb/ft³ and 1.1211 cP at 60 °F; 61.377 lb/ft³ and 0.46602 cP at 140 °F.
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