Expansion Tank Calculator
Acceptance volume and tank size for a closed domestic hot water system.
What it does
Water is at its densest near 4 C and expands as it warms. In a closed plumbing system with a check valve, a backflow preventer, or a pressure reducing valve, that extra volume has nowhere to go, so the pressure climbs every time the water heater fires. The expansion tank gives the water a place to push against a cushion of air.
The calculation has two parts. First, the thermal expansion percentage, which compares the density of cold water with the density of hot water. Heating 50 gallons from 60 to 140 degrees Fahrenheit expands the water by about 1.61 %, or 0.81 gallons. That amount is the acceptance volume.
Second, the tank size. A bladder tank holds an air charge that is compressed as water enters. The tank must be larger than the acceptance volume because the bladder cannot use its full internal space. The usable fraction depends on the precharge pressure, the supply pressure, and the relief valve setting.
With the precharge matched to the supply pressure, the standard sizing formula gives a total tank near two times the acceptance volume, so the 0.81 gallon acceptance leads to a tank around 1.61 gallons. A 2 gallon tank from the shelf covers the classic 40 to 50 gallon heater in a typical home.
Precharge matters. Air at 60 psi will not admit water until the system pressure exceeds 60 psi, and a lower charge lets the tank fill earlier. When the precharge drops below the supply pressure, the tank still works, but the usable share of its volume shrinks and a larger tank is needed. That is why the precharge field is part of the input.
The relief valve setting caps the calculation. The tank is sized so that expansion is stored before the system reaches the valve setting. A valve set at 150 psi with a 60 psi supply gives the tank more room to work with than a valve at 100 psi, so the same heater can need a different tank.
How to use
- Choose Imperial or Metric.
- Enter the water heater tank volume.
- Enter the cold water supply temperature and the hot water storage temperature.
- Enter the supply pressure at the tank and the tank air precharge, usually matched to supply.
- Enter the relief valve setting.
- Read the expansion percentage, the acceptance volume, and the total tank size.
- Pick the next standard tank size at or above the result.
Formula
- Expansion
- Fractional volume increase from heating, in percent.
- Acceptance
- Volume the tank must absorb, equal to system volume times expansion.
- P1
- Tank air precharge plus atmospheric pressure.
- P2
- Supply pressure at the tank plus atmospheric pressure.
- P3
- Relief valve setting plus atmospheric pressure.
Water density comes from the Kell equation fitted to the international standard values, evaluated at the cold and hot temperatures. Absolute pressures are used in the tank formula, so one atmosphere is added to each gauge reading. When the precharge equals the supply pressure, the formula simplifies to about twice the acceptance volume, which is the familiar rule of thumb.
Worked example
Example: 50 gallon heater, 60 F to 140 F, 60 psi supply
Imperial defaults: 50 gal, 60 F cold, 140 F hot, 60 psi supply, 60 psi precharge, 135 psi relief setting.
- Density of water at 60 F is 999.0 kg/m3 and at 140 F is 983.2 kg/m3.
- Expansion: 999.0 / 983.2 minus 1 = 1.61 %.
- Acceptance: 50 x 0.0161 = 0.81 gallons.
- Tank: 0.81 x (74.7 x 149.7) / (74.7 x (149.7 minus 74.7)) = 1.61 gallons.
- Pick a 2 gallon tank, the nearest standard size above the result.
- Tool shows 0.81 gal acceptance, 1.61 gal tank, and 1.61 % expansion.
Reference table
| Heater | Expansion | Acceptance | Tank |
|---|---|---|---|
| 40 gal | 1.61% | 0.64 gal | 1.29 gal |
| 50 gal | 1.61% | 0.81 gal | 1.61 gal |
| 75 gal | 1.61% | 1.21 gal | 2.41 gal |
| 100 gal | 1.61% | 1.61 gal | 3.21 gal |
Limits
- Assumes the tank precharge matches the supply pressure unless you enter a different value.
- Ignores piping volume in the system; add large piping runs for a closer answer.
- Does not cover commercial recirculation or combination systems with storage loops.
- Uses gauge pressures converted to absolute with one atmosphere; high altitude systems need slight adjustment.
Common mistakes
- Sizing the tank from heater volume alone instead of the expansion percentage.
- Installing a tank with a factory precharge far below the actual supply pressure.
- Capping the tank connection and losing the air cushion.
- Forgetting the tank on a system behind a backflow preventer.
- Setting the relief valve higher to avoid drips instead of fixing the expansion control.
Try it yourself
Quick checks. Answers sit tucked under each question.
50 gallon heater, 60 F to 140 F. What size tank?
Acceptance 0.81 gal and total tank 1.61 gal, so a 2 gallon tank works.
Heating 60 F water to 150 F instead. What changes?
Expansion rises to 1.92 %, acceptance to 0.96 gal, and the tank to about 1.91 gal.
Same 50 gallon case but with a 40 psi precharge?
The acceptance stays 0.81 gal but the tank grows to 2.19 gal because the air cushion starts lower.
Questions
Do I need an expansion tank with a tankless water heater?
Usually not for the heater itself, because there is little stored water. You may still need one on a closed system with a storage tank or where the manufacturer requires it.
What size expansion tank for a 50 gallon water heater?
A 2 gallon tank covers the usual 60 F to 140 F case at 60 psi supply, which needs about 0.81 gallons of acceptance and a 1.61 gallon tank.
How do I set the precharge?
With the system drained and the tank isolated, charge the air side to the supply pressure, usually 60 psi for a 60 psi system. Match the supply pressure when the tank is installed.
Why does my expansion tank keep filling with water?
Either the bladder has failed or the precharge has leaked away. Check the air valve for water and recheck the charge; a failed bladder needs a new tank.
Where does the expansion tank go?
On the cold water side, between the backflow preventer or check valve and the water heater, so the expanded water can push back into the tank.
Is an expansion tank the same as a thermal expansion valve?
No. A valve relieves small amounts of water, while a tank stores the expanded volume and keeps the system closed. Many codes now require the tank on closed systems.
Sources
- ASPE newsletter: thermal expansion tank sizing for domestic water systems
- Wessels: domestic hot water expansion tank sizing and selection
- Kell GS: density, thermal expansivity, and compressibility of liquid water, Journal of Chemical and Engineering Data 1975