What this calculator does
A compressor delivers a steady flow, but a receiver is sized for the opposite question: how much free air it can hand back before the network pressure falls too far. That is what decides whether a tool keeps running between compressor cycles — and what sizes the vessel.
How to use it
- Enter the free air the network actually draws between compressor cycles, not the compressor’s rated output.
- Enter the vessel volume you are considering and the pressures the pressure switch cycles between.
- Enter the atmospheric pressure for your site and the gas temperature inside the receiver.
- The result reports the volume you would need for the run time you asked for, so you can compare it with what you have.
Governing formula
V_free = V × (P₁_abs − P₂_abs) / P_atm Where:
-
V_free= Free air released over the swing, litres -
V= Receiver volume, litres -
P₁_abs, P₂_abs= Maximum and minimum absolute pressure, bar -
P_atm= Atmospheric (reference) pressure, bar absolute
Derived Equations:
m = P·V/(R·T) V_req = Q × t / (ΔP/P_atm) Worked example — 500 L vessel between 6 and 8 bar
The figures below were produced by running this page's own engine with the example inputs (Network free-air demand (L/s), Receiver volume (L), Maximum pressure (bar g), Minimum pressure (bar g), Gas temperature (°C), Atmospheric pressure (bar a), Run time required (min)). If the calculator returns something different for the same numbers, that is a bug, not a rounding difference.
| Free air the vessel releases | 987.17 L |
|---|---|
| Run time available | 98.72 s |
| Volume required for that run time | 911.7 L |
| Compression ratio | 1.29 |
| Usable pressure swing | 2 bar a |
| Air held at maximum | 5.36 kg |
| Cycles per hour | 36.47 1/h |
- A 2 bar swing over 1.013 bar atmosphere gives a compression ratio of 8.89.
- The 500 L vessel releases about 987 L of free air between the two pressures.
- At 10 L/s that is roughly 99 s of run time, short of the 180 s requested.
- A volume near 912 L would be needed for the run time requested.
Assumptions & limitations
Engineering calculation. Receiver volume, free-air delivery and run time from the pressure swing, computed isothermally from Boyle’s law and the ideal gas law.
- Isothermal sizing.
- Receiver AND vessel volume only.
- No pressure vessel code allowance.
- Free air is quoted at the atmospheric pressure entered.
This tool supports professional engineering work; it does not replace a sealed design. Confirm every result against the applicable standard and a licensed engineer before it is built.
References & standards
- Boyle’s law and the ideal gas law — the two relations this tool applies.
- Compressor manufacturers’ receiver sizing guidance, for the isothermal convention.