The litres are decided by the pressures, not the system

The expansion tank is the most misunderstood component of the plant room: it is bought «by litres», as if the size depended only on how much water the system holds. But the expanding water is only half the story. The other half is the pressure window the tank works in: between the nitrogen pre-charge and the safety valve setting. Two identical systems, with the same water and the same temperature, can ask for a 12-litre tank or a 48-litre one: four times as much, just for a bar and a half more pre-charge. This calculator puts the four numbers in their place — content, expansion, pre-charge, valve — and returns the minimum tank together with the metric that explains everything: the acceptance factor η.

The formula: the expansion and the window that receives it

The model is that of the closed membrane tank. Heated water grows by ΔV = V·e/100 litres: the «physical» part of the calculation, with the coefficient e turning temperature and fluid into a number — from the scant 2% of underfloor heating to 6% and beyond for glycol systems. That volume must enter the tank without the pressure touching the valve: the fraction of tank actually available is η = (pf − p0)/(pf + 1), the acceptance factor — dimensionless, the same in any currency and any unit. The minimum tank is ΔV/η: the expansion amplified by the inverse of the window. When η is small, every litre of membrane accepts very little water — and the size explodes.

The expansion scale: from underfloor heating to glycol

A 200-litre system, pre-charge 1.0 bar, valve at 3.0; only the coefficient e changes:

The column that does not move is the acceptance factor: 50.0% on every row — the expansion does not touch the pressures. The tank simply doubles the expanded water (η = 0.5), and the scale tells the physics of the regimes: underfloor heating lives with small tanks, glycol quadruples the underfloor demand — which is why solar thermal and glycol heat pumps deserve the computed number, not the tank «that was in the van».

A complete numeric example

A typical system: 200 litres of content — the radiator house with a wall-hung boiler — 3% expansion (flow at 75-80 °C), factory pre-charge at 1.0 bar, valve at 3.0. The expanded water is 200 × 3% = 6 litres; the pressure window is worth η = (3 − 1)/(3 + 1) = 0.5; the minimum tank is 6 / 0.5 = 12.0 litres — 6% of the system. From the catalogue you go to the commercial step above: a nominal 12 if the count is precise, an 18 if the content is estimated. One rule only: round up, never down — the extra litre of membrane costs little, the missing one weeps from the valve.

How to read the acceptance factor

The four bands tell four pressure tunings. Above 45% the pressures are in good tune: more than half the window works, the tank stays small. Between 35 and 45% the tuning is still orderly, but the size grows faster than the system. Between 25 and 35% the window narrows: you are buying tank to compensate for tight pressures. Below 25% the pressures are out of tune: the tank explodes in size, and the problem is not solved in the catalogue — it is solved with the gauge. No band is «forbidden»: η says whether you are paying litres because of the pressures.

The pre-charge: the number nobody checks

The pre-charge p0 is the nitrogen pressure in the membrane, with the tank isolated from the system. Good practice wants it aligned with the static pressure — a tenth of a bar per metre of rise to the highest point — because a pre-charge higher than necessary steals window and gives nothing back. And it is the number nobody checks: nitrogen migrates through the membrane, a tank loses 0.1-0.2 bar a year, and after a few seasons the «right» tank works like a wrong one. The yearly check with the tank isolated is worth more than any litre bought: it is done with a tyre gauge.

The valve: the high bank of the window

The setting pf is the other bank: the higher the valve, the more window there is — at equal pre-charge, going from 2.5 to 4.0 bar takes η from 42.9 to 60%. But the valve is not chosen to make the tank count work: it is chosen to protect the weakest component of the system — the boiler, the exchanger, the cylinder — and its setting is a nameplate figure, not a variable of convenience. The calculator treats it for what it is: a constraint. When η stays low with the right valve, the legitimate lever is the pre-charge; when that too sits at the static minimum, the litres are the honest price of physics.

International perspective: closed vessel, expansion tank and the same membrane

The component is universal, the habits are not. Europe sizes the closed membrane vessel in bar and litres on heating and recomputes it for solar and glycol; North America lives the expansion tank in PSI (1 bar = 14.5 PSI) and fits it as standard on potable water too, where the closed water heater pushes the «thermal expansion tank» after the check valve. Everywhere the physics is this: a volume that grows and a pressure window that receives it. And the factor η compares systems across markets on the same scale, because a ratio between pressures has no units.

Limits of the model and proper use

This is the preliminary sizing of the closed membrane tank: it photographs expansion and pressure window, but does not cover open vessels, steam systems, nor the fine estimate of the water content — which should be measured or computed pipe by pipe on large systems. The pre-charge must then be set on the building's real static head, and the valve setting remains a protection figure. The thermal context is prepared alongside: the heat load calculator says how much power the system must move, and the water heater sizing calculator sizes the domestic side where the American expansion tank is now standard — because the tank is chosen once, but works at every firing.

Inside the window: the two banks that decide the litres

The six sections that follow put the model on the test bench over the two pressures that bound the window. The first is the pre-charge: the low bank, the one you can act on — and the one nobody checks. The second is the valve: the high bank, which is a protection figure and not a lever. The two tables use the same system as the example — 200 litres at 3% — and move one pressure at a time: the cleanest way to see what every quarter bar costs, in litres.

The pre-charge scale: the bank that steals window

200 litres at 3%, valve held at 3.0 bar; only the pre-charge p0 grows:

The progression is not linear: it is a hyperbola. The first steps cost loose litres, then the curve rears up — and the last row tells the pathological case: from 2.0 to 2.5 bar the acceptance factor halves and the tank doubles, from 24 to 48 litres, a quarter of the system inside a membrane. Half a bar: no other knob in the model buys or burns litres at this speed.

Reading the hyperbola: why the last bar costs more than the first

The window's numerator is pf − p0: as the pre-charge climbs towards the valve, every quarter bar removes the same absolute amount of window, but an ever larger fraction of what remains. It is the same mathematics as the draining tank — and the operating lesson is double. First: the right pre-charge is the static head, not «a bit more to be safe» — every tenth of a bar gifted to the nitrogen is paid in litres of membrane. Second: when a quote proposes a huge tank, the right question is not «why so big?» but «at what value did you measure the pre-charge?» — the giant tank is often the symptom of a strangled window.

The valve scale: the bank you do not choose

Same 200 litres at 3%, pre-charge held at 1.0 bar; only the setting pf grows:

The high valve gifts acceptance — from 2.0 to 5.0 bar the tank halves — but the table must be read backwards: you do not choose the valve for the tank; you read the valve the system has, and size accordingly. The right row is the one written on the boiler's nameplate. The table's real value is diagnostic: it shows how the small system with a low valve is structurally hungry for litres — and why the same water content, changing generator, can ask for a different tank.

Maintenance: the right tank stays right only if checked

Sizing is half the work; the other half is keeping the two pressures the count rests on true over the years. The routine is worth ten minutes a year: isolate the tank, drain the water side, measure the pre-charge with a tyre gauge, top up with air or nitrogen to the design value. The symptoms that demand a check now: the valve dripping with the system hot, the gauge swinging wide between cold and hot, frequent top-ups. Almost always the culprit is not the «small» tank: it is the deflated membrane that moved the window — a gauge defect, not a catalogue one.

Before buying: the four-figure checklist

A readable sizing declares the model's four variables. To put in writing: the water content with the criterion used to estimate it (measurement, calculation, nameplate); the expansion coefficient with the maximum temperature and any glycol; the pre-charge with the building's static head beside it; the valve setting read from the generator's plate. Then two questions worth more than any discount: at what value the pre-charge was verified at installation, and who will recheck it in a year. Whoever answers with numbers is selling a stable system; whoever answers with «it is the tank we always fit» is selling a weeping valve.

Frequently asked questions

What expansion tank does my system need?

With the formula Vv = (V·e/100)/η: the expanded water divided by the acceptance factor η = (pf−p0)/(pf+1). A 200-litre system at 3% expansion, with 1.0 pre-charge and a 3.0 bar valve, asks for a 12-litre minimum — then you go to the commercial step above, never below.

What is the acceptance factor?

It is the fraction of tank actually available: η = (pf−p0)/(pf+1). Above 45% the pressures are in good tune; between 25 and 35% the window narrows; below 25% the tank explodes in size because of the pressures, not the system. It is dimensionless: it holds in bar as in PSI.

Why does half a bar of pre-charge change the size so much?

Because the pre-charge steals window: with a 3.0 bar valve, going from 2.0 to 2.5 of pre-charge halves η (from 25 to 12.5%) and doubles the tank from 24 to 48 litres. It is the model's amplifier: litres get expensive when the window is tight.

How do I choose the expansion coefficient?

From the maximum flow temperature and the fluid: 1.5-2% for low-temperature underfloor, 2.5-3.5% for radiators at 70-80 °C, 4-5% for high temperature and solar, 5-8% with glycol — which expands more than water. 30% glycol asks for roughly four times the underfloor tank.

What should the pre-charge be set to?

To the system's static pressure: about 0.1 bar per metre of rise between the tank and the highest point. Higher than necessary it steals window and swells the tank; lower, the membrane works empty. And it must be checked yearly with the tank isolated, with a gauge: nitrogen migrates and 0.1-0.2 bar are lost per season.

Can the safety valve be raised to shrink the tank?

No: the setting protects the weakest component — boiler, exchanger, cylinder — and is a nameplate figure. If η stays low with the right valve, the legitimate lever is the pre-charge; if that too sits at the static minimum, the extra litres are the honest price of physics.

What happens if the tank is too small?

The pressure climbs at every heat-up until the safety valve weeps: lost water, constant top-up, fresh oxygen and corrosion. The valve dripping when the system is hot is the classic symptom — and before replacing the tank, check the pre-charge: often it is just a deflated membrane.

And if the tank is too large?

No technical drama: the tank works lightly stressed and the pressure stays stable. You pay only in money and space. The trade rule stands: commercial step above the computed minimum — the costly mistake is undersizing, not oversizing.

Does the calculator work for the American expansion tank in PSI?

Yes: η is a ratio between pressures and has no units. Just convert (1 bar = 14.5 PSI): a 15 PSI pre-charge and a 45 PSI valve are about 1.0 and 3.1 bar. The membrane physics is identical; only the nameplate changes.

Does it work for the potable tank on a water heater?

Yes, with its own numbers: the thermal expansion tank is sized on the water heater content, with pre-charge equal to the mains pressure and the cylinder's valve. The window is often tighter than in heating: that is why potable tanks look large for the litres they serve.

Does it work for solar thermal and glycol heat pumps?

As preliminary sizing, yes: glycol raises e and the count shows it. But solar adds a requirement of its own — the tank must also receive the collectors' content in stagnation — which this model does not cover: there the designer's dedicated calculation is needed.

What does the calculation NOT cover?

Open vessels and steam systems, solar stagnation, the fine estimate of water content in large systems and the choice of the valve setting, which is a protection figure. It is the preliminary sizing of the closed membrane tank: final confirmation belongs to the designer on the real system.

Updated July 2026