Pneumatic Cylinder: Air & Time
Calculate the air consumption of a pneumatic cylinder as standard volume per stroke, per double stroke (cycle) and per minute, plus the approximate extend time from the force balance. Enter piston diameter, rod diameter, stroke, operating pressure and motion data – the calculator returns piston and annulus area, compression ratio, consumption and a load-ratio traffic light live.
Pneumatic cylinder calculator
Note: The extend time is a rough approximation from the force balance (constant acceleration, no flow restriction by valve/throttle). The real time is usually longer.
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Formulas and fundamentals
The air consumption of a pneumatic cylinder is the geometric swept volume converted to standard conditions. On the extend stroke the full piston area A_out = π/4·D² is effective; on the retract stroke only the annulus area A_in = π/4·(D²−d²) with rod diameter d. The swept volume per stroke is V = A·s. Conversion to standard volume uses the absolute pressure ratio (compression ratio) ε = (p_g + p_amb)/p_amb: Q = V·ε in standard litres. Per ISO 6358 the reference pressure p_amb is the standard pressure 1.013 bar; manufacturers such as Festo use a simplified 1.0 bar, which slightly increases the figure.
Per cycle (double stroke) the extend and retract strokes add up to Q_cycle = Q_out + Q_in; at a stroke frequency f in cycles per minute the per-minute consumption is Q̇ = Q_cycle·f in standard l/min. This value drives the sizing of the service unit, tubing cross section and compressor capacity. Because the annulus area is smaller than the piston area, the retract consumption is always smaller than the extend consumption.
The extend time is an approximation: from the force balance F_res = p·A_out − F_load − F_fric = m·a, assuming roughly constant acceleration a = F_res/m, follows t ≈ √(2·s/a) and the end velocity v = √(2·a·s). This assumes the flow is not restricted by valve or throttle and pressure is available instantly. In practice the real extend time is usually longer; the flow-limited design uses the valve's C-value or Kv per ISO 6358. The load ratio (F_load + F_fric)/(p·A_out) shows how far the pressure force is utilised.
Worked example
A pneumatic cylinder with piston diameter D = 50 mm extends a stroke of s = 200 mm at an operating pressure of p_g = 6 bar. The piston area is A_out = π/4·0.05² = 0.0019635 m² = 19.635 cm², the geometric swept volume V = A·s = 0.3927 L.
The compression ratio is ε = (6 + 1.013)/1.013 = 6.923. The air consumption per extend stroke is therefore Q_out = 0.3927 L·6.923 = 2.72 standard litres. With the catalogue convention (1.0 bar) it would be 0.3927·7 = 2.75 Nl – the difference lies solely in the reference pressure.
With a rod d = 20 mm the annulus area is A_in = π/4·(0.05²−0.02²) = 16.49 cm² and the retract consumption Q_in = 2.28 Nl, so 5.00 Nl per cycle. At 30 cycles per minute this yields 150 standard l/min as the sizing figure for the compressed-air supply.
Frequently asked questions
Why is air consumption given in standard litres (Nl)?
A standard litre is the volume of air that occupies one litre under standard conditions (1.013 bar, defined temperature). Because compressed air is compressed, the geometric swept volume corresponds to a multiple of drawn-in ambient air. The compression ratio ε converts the operating volume into this drawn-in standard volume, which is what the compressor must actually deliver.
Why is the retract consumption smaller than the extend consumption?
On the retract stroke only the annulus area is effective, not the full piston area, because the rod occupies part of the area. A_in = π/4·(D²−d²) is therefore always smaller than A_out = π/4·D², and with it the swept volume and the air consumption.
How accurate is the calculated extend time?
It is a rough approximation. The model assumes constant acceleration from the pure force balance and neglects the flow restriction of valve and throttle as well as the pressure build-up in the cylinder chamber. The real extend time is therefore usually longer. For a reliable time design the flow-limited calculation via the valve's C-value or Kv per ISO 6358 is required.
What do the load ratio and the traffic light mean?
The load ratio is the ratio of the braking forces (load plus friction) to the theoretical pressure force p·A_out. Up to about 0.7 (green) the cylinder moves with sufficient margin, up to 0.85 (amber) it becomes tight, above that (red) the pressure force is no longer enough for reliable motion. Typical design: keep the load ratio below 0.7.
Do I enter gauge or absolute pressure?
The input p_g is the gauge pressure as shown on the manometer (e.g. 6 bar from the mains). For the compression ratio the absolute pressure p_g + p_amb is formed internally. The reference pressure p_amb is selectable: 1.013 bar per ISO 6358 (standard) or 1.0 bar per the common catalogue convention.
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