SizingKitMechanical · Air actuators
Pneumatic cylinder force and the air it costs
Bore, rod diameter and regulated pressure give the extend and retract force in pounds and newtons, and the same three numbers plus a cycle rate give the thing that actually decides whether the machine runs: free air per cycle and continuous SCFM, set against what your compressor is rated to deliver. Because the working fluid is a gas, the page also reports the stiffness of the column trapped behind the piston, which is why a pneumatic cylinder gives under a rising load where an oil one does not. Free, no signup, and every pressure field says gauge in its own label.
- 100% free
- No signup
- Force and SCFM together
- Gauge, never psia
- Altitude corrected
The cylinder and the supply
Three sizes and two pressures give the force. Cycle rate and altitude turn that into an air bill, which is the half of this question a bore-times-pressure calculator leaves out.
A unit typed after a number beats this one, so a 63 mm bore and a 12 in stroke resolve together without converting either.
Every pressure box below is a gauge reading — what the regulator on the wall shows, with the atmosphere already subtracted.
The tube inside diameter, not the outside of the barrel. Force goes with its square: stepping 1-1/2 in up to 2 in is 78% more push.
Takes the rod-end area away, so the return stroke is weaker and also cheaper — the rod occupies part of the volume that would otherwise have to be filled.
Does not change the force at all. It changes everything about the air, because consumption is a volume per cycle.
Regulated pressure at the cylinder, not at the receiver. Long small-bore tubing between the two loses several psi while the valve is open.
Whatever the exhausting side has to push against. Meter-out speed control builds this deliberately, and it comes straight off the force.
Complete out-and-back cycles. A clamp that closes once a shift and holds costs nothing; an indexer at 60 a minute is the whole compressor.
14.7 psia there, against 14.7 psia at sea level.
From the machine’s own CAGI data sheet at your working pressure — not its horsepower, and not the figure printed at 40 psi. This site carries no table of compressor outputs, because delivery is a curve per model.
Where the piston is when the load changes. The trapped column behind it is what gives, and the further out it is the longer and softer that column is.
Default 1.4 — The ratio of specific heats of dry air, γ = cp/cv = 1.400 at room temperature, which is the exponent for a compression fast enough to be adiabatic. Runs from 1.0 for a change slow enough to stay at ambient temperature to 1.4 for one fast enough to trap the heat. A press dwelling on a part is near the bottom of that band; an impact is at the top. The stiffness below is directly proportional to it, so the two ends differ by 40%.
EXTEND FORCE
283 lbf
1,258 N
RETRACT FORCE
255 lbf
1,135 N
AIR DEMAND
7.39 SCFM
3.49 L/s free air
| Piston area, cap end | 3.1416 in² 2026.8 mm² |
|---|---|
| Piston area, rod end | 2.8348 in² 1828.9 mm² |
| Extend force | 283 lbf 1,258 N |
| Retract force | 255 lbf 1,135 N |
| Supply pressure, absolute | 104.7 psia 7.219 bar a |
| Compression ratio | 7.12:1 barometric 14.7 psia |
| Swept volume per cycle | 59.76 in³ 0.979 L |
| Free air per cycle | 426 in³ 6.977 L |
| Continuous demand | 7.39 SCFM 3.49 L/s |
| Trapped column rate | 92.1 lbf/in 16.1 N/mm |
The return stroke is the cheap one: the rod occupies 9.8% of the volume the cap end has to fill, so retracting costs 0.465 L against 0.515 L going out. That asymmetry is why a machine designed to do its work on the pull stroke can run on a smaller compressor than the same machine pushing.
At 50% extended the column behind the piston is 5 in long and behaves as a spring of 92.1 lbf/in. Add a tenth to the load — 28.3 lbf — and the piston gives 0.307 in before the pressure catches up. That is the difference between air and oil in one number, and it is why a pneumatic cylinder cannot hold a position against a varying load. Compare it with a steel spring of the same rate and the numbers are of the same order, which is the point.
Free air is referenced to 14.696 psia. CAGI and PNEUROP rate compressors against 14.5 psia, 68 °F and 36% relative humidity; ISO 1217 uses 1 bar, 20 °C and dry air. Against the 14.696 psia used here those references read about 1.4% higher for the same mass of air, which is smaller than the leakage in any system that has been in service a year. The letter S in SCFM is that reference; a plain CFM figure at the cylinder is a different and much smaller number, which is the distinction the airflow page works in the other direction for ductwork. Barometric pressure at altitude follows US Standard Atmosphere 1976, troposphere: p = 101.325 kPa × (1 − 2.25577 × 10⁻⁵ h)^5.25588 with h in meters. Gives 14.70 psia at sea level, 12.23 psia at 5000 ft and 10.11 psia at 10 000 ft, matching the published tables. It is the standard-day atmosphere, not today's weather — a deep low runs about 0.5 psi below it, which is another foot of head off the suction side.
Two real costs are outside this arithmetic. The tubing between the valve and the cylinder is charged and dumped every cycle: 6 ft of 1/4 in bore on each port is 7.1 in³ at supply pressure, which on the worked example above is another 12% of free air for nothing. And a cushioned end cap holds a volume that never does work. Both push the real figure up, so treat the demand above as the floor. Where the load has to be held rather than moved, oil is the answer instead — the same geometry with an incompressible fluid gives up the compressibility and buys back stiffness and pressure.
The forces above are the pressure acting on the piston faces and nothing else. Seal drag, rod-bearing friction and the mass of the tooling all subtract, and the number that matters for a clamp is what is left at the end of the stroke rather than what the bore multiplies out to. Nothing here is a stamped design: the cylinder’s own rated working pressure, the rod’s column strength on a long stroke and the guarding around a moving load are decisions for the cylinder manufacturer and a qualified engineer.
How to size an air cylinder and its compressor at the same time
Force takes one multiplication. What it costs per minute is the question that gets machines sent back.
Enter the three sizes and the pressure your regulator shows
Bore is the tube inside diameter, rod is the piston rod, and stroke is the working travel. Every pressure box on the page is a gauge reading, which is what a regulator is marked in and what the shop gauge on the wall shows. If a data sheet quoted you an absolute figure, subtract the barometric pressure before typing it: this page will not accept psia, because a number on its own cannot tell the calculator which datum it was measured from.
Give it a cycle rate and the site altitude
Neither changes the force by a pound. The cycle rate turns a volume per stroke into a continuous demand, and the altitude sets the barometric pressure that the gauge reading is measured against. At 5,000 ft the atmosphere is 12.23 psia rather than 14.70, so the same 90 psi gauge is 102 psia rather than 105: the cylinder fills to a slightly lower absolute pressure and needs about 2% less air by mass, while the compression ratio the compressor has to work through rises 17%, from 7.12 to 8.36. The cylinder gets marginally cheaper and the machine feeding it gets meaningfully more expensive.
Read the demand against the compressor, then look at the column
Type the machine's rated delivery in SCFM from its own data sheet and the page prints what fraction of it this one actuator takes, leaving the rest for the leaks and every other cylinder on the header. Then look at the trapped-column rate at the bottom of the table: that is the spring the piston is sitting on. It is what a pneumatic clamp gives when the load rises, and it is the reason a job needing a held position gets oil rather than air.
Technical specifications
| Force model | Extend = p·(π/4)·D² minus the exhaust-side gauge pressure acting over the annulus; retract = p·(π/4)·(D² − d²) minus the exhaust-side pressure over the full bore. Seal drag and rod-bearing friction are not modeled and always subtract |
|---|---|
| Pressure datum | Gauge throughout, stated in each field's own label. An entry written psia is refused rather than silently read as gauge — the difference at sea level is 14.70 psi. The absolute figure the gas laws need is built from the gauge reading plus the barometric pressure and printed in its own row |
| Free-air reference | 14.696 psia, the standard atmosphere defined as exactly 101,325 Pa by the CGPM in 1954. CAGI and PNEUROP rate against 14.5 psia at 68 °F and 36% RH, ISO 1217 against 1 bar at 20 °C dry; both read about 1.4% higher for the same mass |
| Barometric pressure with altitude | US Standard Atmosphere 1976 troposphere formula — 14.70 psia at sea level, 12.23 psia at 5,000 ft, 10.11 psia at 10,000 ft. Standard-day, not today's weather: a deep low runs about 0.5 psi under it |
| Trapped-column stiffness | n·p_abs·A²/V for the driving side with the port blocked, with n editable between 1.0 for a slow isothermal change and 1.4 for a fast adiabatic one — the ratio of specific heats of dry air. Supply line and receiver volume are excluded and soften it further |
| Input ranges | Gauge pressure 0–500 psi, cycle rate 0–2,000 per minute, altitude 0–15,000 ft, polytropic exponent 1.0–1.4. Rod diameter must be smaller than the bore; the page refuses rather than returning a negative area |
| Worked example | 2 in bore, 5/8 in rod, 10 in stroke, 90 psi gauge, 30 cycles per minute at sea level: 283 lbf extend, 255 lbf retract, 7.12:1 compression, 426 in³ of free air per cycle, 7.4 SCFM continuous, and 92 lbf/in of column rate at mid-stroke |
| Deliberately outside the arithmetic | Port, hose and cushion volume, all of which are refilled every cycle: 6 ft of 1/4 in bore on each port adds 12% to that example. Treat the SCFM figure as the floor for the actuator alone, before leaks and before every other device on the header |
Frequently asked questions
Is SCFM the same as CFM, and which one is on my compressor's nameplate?
They differ by the compression ratio, which on a 90 psi system is a factor of seven. CFM is a volume of air measured wherever it happens to be; SCFM is that volume corrected back to a standard atmospheric condition, so it is really a measure of mass. A cylinder swallowing 60 in³ of swept volume per cycle at 90 psi has taken 426 in³ of atmosphere to fill, and it is the second figure a compressor has to produce. Nameplates and CAGI data sheets are in SCFM, but check the pressure the rating was taken at — a rotary screw quoted at 40 psi delivers considerably less at 125.
I turned the regulator up and the cylinder is no faster. Why?
Because speed is a flow question and pressure is a force question. How fast the piston travels is set by how quickly air can get in and out of it — valve flow coefficient, port and fitting size, tubing bore and length, and above all whether the exhaust can leave freely. Once the cylinder is already moving the load with margin, extra pressure raises the force it applies to nothing and raises the air bill proportionally. Fit a larger valve, shorten the tube run and put quick-exhaust valves at the ports before touching the regulator.
Why does the return stroke use less air than the out stroke?
The rod is in the way. On the return, the rod occupies part of the volume that has to be filled, so a 2 in bore with a 5/8 in rod fills 28.3 in³ coming back against 31.4 in³ going out — about 10% less air for the same travel. It is a small saving per cycle and a real one over a shift, and it is the same geometry that makes the return the weaker direction. Where a machine can be arranged to do its work on the pull rather than the push, it costs less to run as well as being easier to guard.
Does altitude change what a cylinder can push?
No, and this is worth being clear about because it is counterintuitive. A gauge measures the difference between the air inside and the air outside, and the cylinder is being pushed by exactly that difference, so 90 psi gauge produces the same force in Denver as at sea level. What altitude changes is the compressor's side of the deal: at 5,000 ft the atmosphere is 12.23 psia instead of 14.70, so reaching the same gauge pressure is a larger compression ratio, more work per cubic foot, and a reciprocating machine that also has less dense air to take in.
Can I park a load in mid-stroke by centering the valve?
You can stop it there; you cannot hold it there. A closed-center valve traps the air on both sides, and trapped air is a spring — 92 lbf/in at mid-stroke on the worked example here, so a 10% rise in load, 28 lbf on a 283 lbf push, lets the piston back off about 5/16 in before the pressure catches up. Add seal leakage past the piston, which is never zero, and the position drifts over minutes as well as sagging under load. A mechanical stop, a rod lock or an oil circuit are the three ways to actually hold a position.
Does meter-out speed control cost me force?
Yes, and that is exactly how it works. Metering the exhaust builds a back pressure on the opposite side of the piston, and that pressure acts over the opposite area and subtracts from the net push. The trade is worth making because meter-out is the only way to get smooth motion against a load that could run away — meter-in lets the piston lunge as soon as it breaks free. There is no figure to predict here, because the back pressure settles wherever the restriction and the load put it: tighten the needle and it climbs until the escaping flow matches what the piston demands. Put a gauge on the exhaust port, type what it reads into the box provided, and the force column shows what it leaves.
How much does the tubing between the valve and the cylinder add?
More than most people expect, because it is charged and dumped every single cycle. Six feet of 1/4 in bore tube on each of the two ports holds 7.1 in³ at supply pressure, which on the 2 in cylinder worked through above is another 12% of free air doing no work whatever. Cushion volume at the end caps behaves the same way. Both are why the demand figure on this page should be read as a floor rather than an estimate, and why mounting the valve on the cylinder is a real saving rather than a tidiness preference.
About compressed air as a working fluid
The force half of this question is trivial and every calculator on the web answers it: pressure times the area it acts on. What makes air different from every other actuator is everything downstream of that multiplication. Air is bought by the cubic foot at atmospheric pressure and used by the cubic inch at line pressure, so the swept volume of a cylinder is not what it consumes — it consumes that volume multiplied by the compression ratio, which on an ordinary 90 psi shop system is a factor of 7.12. A 2 in cylinder with a 10 in stroke swallows a quarter of a cubic foot of atmosphere every time it goes out and comes back, and at thirty cycles a minute that one actuator is 7.4 SCFM. It is why a shop adds a machine and finds that everything else has gone slow, and why the interesting number on a pneumatic drawing is never the force.
The second consequence is compressibility, and it is the one that decides whether air is the right choice at all. Oil resists being squeezed and behaves as a solid link between the pump and the load; air does not, so the piston sits on a gas spring whose rate is the trapped pressure times the piston area squared, divided by the volume behind it. That works out at around 92 lbf/in halfway along the worked example above — the same order as a modest steel compression spring, which is a startling comparison until you have felt a clamp cylinder breathe. The rate falls as the cylinder extends, because the column gets longer, so a pneumatic press is at its softest exactly where it is doing the work. Where a position has to be held against a varying load rather than merely reached, the same geometry filled with oil trades the compressibility away for stiffness and for ten to twenty times the pressure.
The last thing worth stating is what SCFM means, because it is the term most often quoted and least often defined. The S is a reference condition, and there are three in circulation: the standard atmosphere of exactly 101,325 Pa used here, the CAGI and PNEUROP basis of 14.5 psia at 68 °F and 36% relative humidity that compressor data sheets are written against, and ISO 1217’s 1 bar at 20 °C dry. They disagree by about 1.4%, which matters far less than the two things people leave out entirely — the tubing between valve and cylinder, refilled every cycle, and system leakage, which the US Department of Energy’s compressed-air tip sheets put at 20 to 30% of a poorly maintained plant’s total output. This page states its reference beside the answer, prints the barometric pressure the compression ratio was taken against, and reports the actuator alone. Sizing the compressor is a separate exercise in adding demands and applying a duty cycle, in the same way that airflow for a room is built from a load rather than from one grille. Nothing here is a stamped design: the cylinder’s rated working pressure, rod column strength on a long stroke and the guarding around a moving load belong to the manufacturer’s catalog and to a qualified engineer.
Where the cylinder you typed in goes
Every number on this page is worked out by JavaScript running in the tab you are reading it in. Nothing you type — loads, lengths, nameplate ratings, the rates your utility charges you — is uploaded, logged or kept, which is also why the calculators carry on working in a mechanical room with no signal.
Bores, pressures, cycle rates and your compressor’s rated output stay in this tab for as long as it is open and are gone when it closes — no account, no saved machine list, and nothing to leak later about what a customer’s line runs at.