Why a closed system builds pressure at all
Water expands when it is heated. Not much — heating a system from 50 to 140 degrees grows it by about 1.7 percent — but water is also very nearly incompressible, so that 1.7 percent has to go somewhere or the pressure goes up instead. In an open system it goes backwards into the street main, which absorbs it without noticing. That is why houses managed without expansion tanks for a century.
A check valve, a backflow preventer or a pressure reducing valve with an integral check closes that door. The system becomes a sealed vessel, the expanding water has nowhere to retreat to, and the pressure rises until something gives. In a genuinely rigid vessel it would rise absurdly — the bulk modulus of water puts the figure in the thousands of psi for that 1.7 percent. In a real house the pipe stretches slightly and then the relief valve opens, which is exactly what it is for and is the noise the whole arrangement is trying to avoid.
The two-step arithmetic
First, how much water is there to absorb. Take the density of water at the cold temperature, divide by the density at the hot temperature, subtract one, and multiply by the total system volume. Working it from densities rather than from a single expansion coefficient matters, because the coefficient roughly doubles between 60 and 160 degrees and a constant will be wrong at one end or the other. Fifty gallons heated from 50 to 140 gives 0.84 gallons.
Second, how large a tank holds that. A tank is a sealed vessel with a bladder or diaphragm: air on one side, system water on the other. Precharged to the supply pressure it sits with no water in it at all, and as pressure rises the air compresses and water enters. Boyle law says the air volume falls in inverse proportion to absolute pressure, so the fraction of the tank that can fill with water between the fill pressure and the ceiling is one minus the ratio of those two absolute pressures. From 60 psig fill to an 80 psig ceiling, that is one minus 74.7 over 94.7, or about 0.211. Divide the 0.84 gallons by 0.211 and the tank is about four gallons.
The absolute pressures are not optional. Working the ratio in gauge pressure gives 1 minus 60 over 80, or 0.25, which understates the tank by nearly twenty percent — an error in the direction that leaves the relief valve still weeping.
What moves the answer
| Input | Direction | Why |
|---|---|---|
| Colder incoming water | Larger tank | A bigger temperature rise means more expansion; winter is the sizing case |
| Higher setpoint | Larger tank | Same reason, from the other end |
| Higher supply pressure | Larger tank | Less room between fill and ceiling, so a smaller share of the tank is usable |
| Lower ceiling | Larger tank | Same squeeze from the other side |
| More piping volume | Larger tank | Expansion is a percentage of everything on the closed side, not just the heater |
| Precharge below supply pressure | Smaller tank, but water sits in it | The bladder is already partly displaced at rest, which wastes capacity in practice |
Piping volume is the input most often guessed at and it is worth actually working out, because on a large house with long runs it is not a rounding error. The pipe volume calculator turns lengths and sizes into gallons for exactly this purpose.
Precharge, and the tank that quietly stopped working
The precharge is set with the tank isolated or before it is connected, using a tyre gauge on the air valve, and the convention is to match it to the system fill pressure so that the tank sits empty of water at rest and every bit of its volume is available for expansion. Set it low and water permanently occupies part of the tank, so less capacity is left for the job. Set it high and the tank does nothing until the pressure has already climbed past the precharge.
Tanks lose their precharge slowly, and a bladder eventually fails. The symptom is the original one returning: a relief valve that starts weeping again on a system that was fine for years. The quick field check is to tap the tank — a healthy one rings hollow at the top and sounds dull at the bottom, and one that is full of water sounds the same all the way up and is unexpectedly heavy. Depressing the air valve on a failed bladder brings water out instead of air. Neither test is a substitute for a gauge, and neither is work to do without shutting the water off first.
What this page will not decide
The ceiling pressure in the form is a number you supply and the arithmetic is only as meaningful as it is. What your piping, fittings, fixtures, appliances, heater and relief valve are actually rated for comes from those products and from your jurisdiction, and the pressure a system may be operated at is a code question rather than an arithmetic one. This page will not tell you what setpoint to run, either — that is a scald and bacterial-growth trade-off that belongs with a plumber and is discussed on the shower mixing calculator.
Nor is any of the physical work homeowner territory in most places. An expansion tank is cut into live supply piping at the heater. The check valve or pressure reducing valve that made the system closed is at the water service. The relief valve and its discharge piping are safety components whose behaviour on a system that has been over-pressuring is not something to assume. Size it here so you know what you are talking about, then have it done by someone licensed to do it — and while the heater is being looked at, the water heater sizing calculator is the page for whether it is the right size at all.
Questions people ask
Why does my water heater relief valve drip?
Most often because the system is closed and the water has nowhere to expand to when it is heated. A check valve, a backflow preventer or a pressure reducing valve with an integral check stops water from pushing back into the main, so the 1.7 percent or so of expansion from a heating cycle raises the pressure until the relief valve lifts. The signature is a weep or a small puddle in the hours after the heater has run, rather than a continuous leak. The other possibilities are a relief valve that has failed to reseal, often after doing this for months, or genuine overheating, which is a different and more serious problem. Any of them is a reason to get it looked at rather than to cap the discharge, which is never the answer.
How do I size a thermal expansion tank?
Two steps. Work out the expansion volume: system volume multiplied by the density ratio between the cold and hot temperatures minus one, which for 50 gallons going from 50 to 140 degrees is about 0.84 gallons. Then divide it by the acceptance factor, which is one minus the ratio of the absolute fill pressure to the absolute ceiling pressure. From 60 psig to an 80 psig ceiling that is one minus 74.7 over 94.7, about 0.211, giving a tank of roughly four gallons. Use absolute pressures, not gauge; the gauge version understates the tank by close to twenty percent. And include the piping in the system volume, because on a large house it is not negligible.
What pressure should the expansion tank be precharged to?
The usual arrangement is to match it to the system fill pressure, measured downstream of any pressure reducing valve, and to set it with the tank isolated rather than under system pressure. The logic is that the tank should sit with no water in it at rest, so its entire volume is available to absorb expansion. Precharged too low, water permanently occupies part of the tank and the usable capacity falls. Precharged too high, nothing enters the tank until the system pressure has already climbed past the precharge, which defeats the point. Since it is set on a tank connected to live water piping at a heater, it belongs with the same visit as the installation.
Do I need an expansion tank if I do not have a check valve?
If the system is genuinely open to the street main, expansion pushes back into the main and there is nothing to absorb. That was the normal state of things for a long time. The difficulty is that many systems became closed without anyone deciding to close them: meters with integral check valves, backflow preventers required at the service, and pressure reducing valves that include a check are all common retrofits, and none of them announce themselves. A relief valve that started weeping after a water company visit or a new pressure reducing valve is telling you exactly this. On a well system with a pressure tank there is generally somewhere for the expansion to go already, and the pressure tank is doing the job — the well pressure tank calculator covers that side.
How can I tell if my expansion tank has failed?
The original symptom returns: a relief valve that starts weeping again on a system that has been fine. A failed tank is full of water, so it is noticeably heavier than it should be and it sounds the same tapped at the top as at the bottom, where a healthy one rings hollow above the water line and dull below it. Pressing the air valve on a failed bladder brings water out rather than air. Losing precharge without an outright bladder failure is more gradual and shows up as a gauge reading below the system fill pressure. All of these checks involve a vessel under system pressure at a water heater, so the water gets shut off first, and replacing one is plumbing work.