Pick an ISO 15552 or ISO 6432 bore, set the supply pressure, stroke and cycle rate. Get the real push and pull force, load ratio, free-air consumption per cycle and per minute, peak flow for valve sizing, cushioning energy and the rod buckling limit.
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TorqueMath.com · Pneumatic Cylinder Calculator
Bore · ISO 6432 minis (8–25) and ISO 15552 (32–320)
bore mm
mm
ISO 15552 rod for Ø63 is 20 mm.
bar(g)
mm
1/min
–
η covers seal friction: about 0.9 for ISO 15552 cylinders at 6 bar, 0.8–0.85 for small bores, low pressure or worn seals.
Action
N
N
From the maker's data. Pre-filled with 5 % and 10 % of the theoretical force; the extended value is subtracted from the push.
Orientation (load on the rod)
kg
N
Load ratio limit (makers' rule of thumb)
m/s
Used for stroke time, peak flow (valve size) and cushioning energy. For cushioning, the speed at impact matters, and it is usually higher than the average speed – enter the higher value to check the end of stroke. Leave empty to skip.
m
mm
Tube between valve and cylinder is filled and emptied every stroke. Common sizes: 6 mm OD → 4 mm ID, 8 → 6, 10 → 7 or 8, 12 → 9.
mm
J
Take both from the cylinder catalogue (cushioning type, bore and speed matter). Leave the energy empty if you don't have it yet.
Mounting (for rod buckling)
Extending: air in at the cap end
Method and assumptionsMethod: Theoretical force p·A (gauge pressure) with efficiency η and spring for single-acting; load ratio vs. theoretical force; free-air consumption from swept volume ×(p+patm)/patm plus tube dead volume ×p/patm; peak flow A·v·(p+patm)/patm; cushioning ½mv² (+mg·Lc lowering); rod buckling Euler / Johnson, SF 3.5Basis: patm 1.013 bar abs, 20 °C, isothermal (SMC L(ANR) convention; ISO 8778:2003 ANR is 100 kPa → ×1.013); η default 0.9; load ratio 0.5 dynamic / 0.7 slow as makers' rule of thumb; ISO 15552 and ISO 6432 bores and rods; L_k = K·(stroke + 1.5·D), E 210 GPa, Re 400 MPaLimits: No pressure-buildup simulation: real speed depends on valve, tubing, load and back-pressure; internal dead volume of cylinder and valve not included; valve rule qnN ≥ 1.5× peak flow is a rule of thumb, no ISO 6358 conductance model; cushioning ignores drive pressure during the cushion stroke; buckling checks the rod onlyReferences: ISO 15552 · ISO 6432 · ISO 8778Formulas · How this calculator was checked · TorqueMath v2.7
How it is calculated
D is the bore, d the rod, s the stroke, p the supply pressure as gauge pressure (above atmosphere), patm = 1.013 bar absolute. Force comes from the pressure difference across the piston, so it uses gauge pressure. Air consumption is a quantity of air, so it uses absolute pressure. The two are never mixed.
Areas A₁ = π·D²/4 (cap side), A₂ = π·(D² − d²)/4 (rod side)
Theoretical force F_th = p·A₁ (extend), p·A₂ (retract) N = bar · 0.1 · mm²
Effective force F = η·F_th − F_spring,extended (single-acting) η ≈ 0.9
Required force F_req,ext = F_load + m·g (lifting) or F_load − m·g (lowering, floor 0)
F_req,ret = m·g when retracting lifts the load (rod-down mounting), else 0
Load ratio LR = F_req / (F_th − F_spring), keep ≤ 0.5 fast/dynamic, ≤ 0.7 slow/static
Air per stroke V_free = A·s·(p + p_atm)/p_atm + V_tube·p/p_atm V_tube = π·d_t²/4 · L_t
Air per minute Q = (V_ext + V_ret)·n single-acting: V_ext only
Peak flow q = A·v·(p + p_atm)/p_atm (upper estimate while moving)
Stroke time t = s / v
Cushioning E = ½·m·v² (+ m·g·L_c when the rod moves downwards)
Rod buckling Euler F_k = π²·E·I/L_k², I = π·d⁴/64, E = 210 GPa, L_k = K·(s + 1.5·D)
below λ_T = π·√(2E/R_e) (λ = 4·L_k/d, R_e = 400 MPa): Johnson σ_k = R_e − (R_e·λ/2π)²/E
safe push = F_k / 3.5
Method and assumptions
Swept volume vs. tube volume. The working chamber starts at atmospheric pressure (it has just exhausted) and ends at full supply pressure. The swept volume A·s arrives from empty, so it takes (p + patm)/patm times its volume of free air. The tube already holds air at atmospheric pressure, so it takes only p/patm times its volume. Many simple calculators use the absolute ratio for both and overstate tube air by about 17 % at 6 bar.
Free air reference. Volumes are free air at 1.013 bar absolute and 20 °C (SMC's "L (ANR)" convention), shown as Nl (catalogues often write Nl or l (ANR) for this). Normal litres in the strict DIN 1343 sense (0 °C, 1.01325 bar) are 6.8 % fewer: multiply by 0.932. ISO 8778:2003 defines the standard reference atmosphere (ANR) as 100 kPa, 20 °C and 65 % RH. Against that reference, multiply our figures by 1.013. scf and scfm are the same quantity in cubic feet (1 ft³ = 28.317 l). Filling is taken as isothermal, and every stroke reaches full supply pressure.
Load ratio is the required force divided by the theoretical force, as in Festo, SMC and Parker sizing guides. The 0.5 and 0.7 limits are a rule of thumb, not a standard. The spare force accelerates the load and overcomes back-pressure from the exhausting chamber.
Peak flow assumes the driving chamber is at full supply pressure while moving, so it is an upper estimate. Real speed depends on the valve, tubing, fittings, flow controls, load and exhaust back-pressure. Valves are rated by their standard nominal flow qnN at 6 bar inlet and 1 bar pressure drop (6 → 5 bar). Picking qnN at least 1.5 × the peak flow is our starting rule, not a standard. Confirm the choice with the maker's sizing software; full ISO 6358 sonic-conductance modelling is outside the scope of this tool.
Bores and rods follow ISO 15552 (Ø32–320) and ISO 6432 (Ø8–25). The rod can be edited for non-standard cylinders.
Limitations
The model is static and quasi-static. It does not simulate how pressure builds up, so it cannot predict the real piston speed or stroke time. Use the target speed as a design value and check it with the maker's software.
The internal dead volume of the cylinder (end caps, cushioning chambers, ports) and of the valve is not included. Add it as extra tube length if you know it. Real consumption is a few percent higher.
Friction is a single efficiency factor. Breakaway friction, stick-slip at very low speed and seal wear are not modelled.
Cushioning energy covers only the moving mass and gravity. The drive pressure acting during the cushion stroke, and the maker's own energy rating, decide the result.
The buckling check covers the rod only, with the buckling length K·(stroke + 1.5·D). With clevis mountings at both ends, the whole extended cylinder acts as the column, which can be about twice as long. It ignores side load, the tube and eccentricity, and assumes a rod yield strength of 400 MPa. Use the maker's buckling chart.
Not covered: compressor sizing, leakage, pressure drop in long supply lines, and temperature effects.
Moving mass should include the piston and rod (and any tooling) for the cushioning check.
For horizontal motion the load ratio only includes what you enter as load: add guide or slide friction μ·m·g yourself.
Rod buckling assumes a rod yield strength of 400 MPa. Stainless rods (for example 1.4301) can be 200–350 MPa, so use the maker's buckling chart for them.
The valve rule (qnN ≥ 1.5 × peak flow) assumes about 6 bar supply. At 2–4 bar the pressure drop across the valve takes a much larger share of the supply, so a larger valve is needed.
This calculator sizes a pneumatic cylinder: extend and retract force at your supply pressure with seal friction, load ratio and the smallest ISO bore that does the job, free-air consumption per cycle and per minute in Nl/min, m³/h and scfm, peak flow for the valve, stroke time, cushioning energy and rod buckling. It covers ISO 15552 cylinders (Ø32–320) and ISO 6432 mini cylinders (Ø8–25), double- or single-acting with a spring return, horizontal or vertical. Automation engineers, machine builders and maintenance technicians use it to choose a bore, size the valve and tubing and estimate how much compressed air a machine will use.
Worked example: Ø63/20, 6 bar(g), 200 mm stroke, 10 cycles/min
Theoretical force: extend 6 × 0.1 × 3117.2 = 1870 N, retract 1682 N. Both match the Festo DSBC-63 data sheet values. With η = 0.9 the effective forces are 1683 N and 1514 N.
Load ratio: a 500 N horizontal load gives 500 / 1870 = 0.27, under the 0.5 limit for fast motion. The smallest ISO bore at 0.5 would be Ø50 (1178 N theoretical).
Tube volume: π·6²/4 × 1000 mm = 28.3 cm³ per side.
Air per cycle = 8.53 Nl. At 10 cycles/min that is 85.3 Nl/min (5.12 m³/h, 3.01 scfm).
Peak flow at 0.5 m/s: 3117.2 mm² × 500 mm/s = 1.559 l/s = 93.5 l/min, × 6.923 = 647 Nl/min (retract 582). A valve with qnN of about 970 Nl/min or more is a sensible start. Air speed in the 6 mm tube while extending is 1.559 l/s ÷ 28.3 mm² = 55 m/s, so a larger tube would help.
Stroke time 0.2 m / 0.5 m/s = 0.40 s. One cycle needs at least 0.8 s, and 6 s are available.
Cushioning: ½ × 20 kg × 0.5² = 2.5 J (horizontal, so gravity adds nothing). Compare this with the maker's chart.
Buckling, pinned–pinned: Lk = 200 + 1.5 × 63 = 294.5 mm. λ = 4 × 294.5 / 20 = 59, which is below λT = 102, so Johnson applies: σk = 333 MPa, Fk = 104.6 kN, safe load 29.9 kN. The 1870 N push is 6 % of that. Euler alone would give 53.6 kN and overstate the safe load.
The Ø63 cylinder pushes 1683 N and pulls 1514 N after friction, uses 8.5 Nl per cycle or 85 Nl/min, and needs a valve flowing roughly 650 Nl/min at peak (start with qnN ≈ 1000 Nl/min) and a larger tube than 6 mm ID for 0.5 m/s.
FAQ
How do I calculate the force of a pneumatic cylinder?
Multiply the gauge pressure by the piston area: F = p × A. At 6 bar a Ø63 bore gives 6 × 0.1 × 3117 mm² = 1870 N pushing. Pulling uses the ring area (bore minus rod), so a Ø20 rod leaves 1682 N. Seals take roughly 5–15 %, so the calculator applies an efficiency factor (0.9 by default).
What load ratio should I size a pneumatic cylinder for?
Makers recommend that the load needs no more than about 50 % of the theoretical force for fast, dynamic motion and about 70 % for slow or static clamping. The rest of the force accelerates the load and overcomes friction and back-pressure. The calculator shows the smallest standard bore that meets the ratio you pick.
How is air consumption in Nl/min calculated?
Each stroke fills the swept volume to supply pressure, so the free air used is V × (p + p_atm) / p_atm. The tube between valve and cylinder is also filled every stroke and adds V_tube × p / p_atm. Add both strokes for a double-acting cylinder and multiply by the cycles per minute. Nl here means litres at 1.013 bar absolute and 20 °C.
Why is gauge pressure used for force but absolute pressure for air consumption?
Force comes from the pressure difference across the piston, and the other side is at atmosphere, so gauge pressure is correct. The amount of air in a volume depends on absolute pressure, so the ratio (p_g + 1.013)/1.013 converts the cylinder volume to free air. Mixing the two is a common error that overstates force or understates air use.
Can this calculator predict the real piston speed?
No. Real speed depends on the valve flow, tube length and size, load, back-pressure and how fast pressure builds up. Enter the speed you want; the calculator gives the air flow needed for it and the stroke time, and suggests a valve flow rate to start from. Check the final design with the maker's sizing software.
When does a pneumatic cylinder need cushioning or shock absorbers?
When the kinetic energy ½·m·v² (plus the work of gravity when lowering) exceeds what the cylinder's end cushioning can absorb. Makers list the permissible energy for each bore; enter it and the calculator compares. Above about 1 m/s or with heavy masses, external shock absorbers are often needed.
Tools for this job
What you need to build, measure or check the result.
ISO 15552 pneumatic cylinder
Push-in tube fittings and PU tubing
Air pressure regulator with gauge