Type a line (pneumatic cylinder 63 mm, rod 20 mm, 200 mm stroke, 6 bar, 10 cycles/min) or fill in the fields: the line and the fields stay in step.
Enter the piston diameter, the rod, the stroke, the working pressure and the cycles per minute, and the calculator gives the air a pneumatic cylinder takes: the free air per cycle and per minute, in l/min, m3/h and cfm, for one cylinder or several. It also gives the theoretical force on the rod, extend and retract, and with the tubing between the valve and the cylinder entered, the share of the tubing in the air. It shows the working with your numbers, draws a sketch of the cylinder, and gives a line you can copy or add to a request.
The calculator covers double acting and single acting cylinders in control and service air systems and in pneumatic actuators. It gives no recommended pressures and no sizing margins, and does not size the compressor or the receiver. The force is the theoretical one, the pressure times the area; the force of a return spring is not taken off.
The piston area is A extend = pi x D x D / 4, the area on the rod side A retract = pi x (D x D - d x d) / 4. For D 63 mm and a 20 mm rod: 3117.2 mm2 and 2803.1 mm2. With a 200 mm stroke a double acting cylinder fills 0.6234 l + 0.5606 l = 1.1841 l per cycle; a single acting one only the first.
The swept volume fills at the working pressure, and the ratio of the absolute pressures, (p + pa) / pa, brings it to free air. At 6 bar(g) with pa 1.013 bar(a) it is 6.923: 1.1841 l x 6.923 = 8.20 l per cycle, and at 10 cycles/min 82.0 l/min, 4.92 m3/h or 2.89 cfm.
F = p x A at the gauge pressure: 6 bar(g) is 0.6 N/mm2, so a 63 mm piston gives 1870 N on the extend stroke, and with a 20 mm rod 1682 N on the retract stroke. This is the theoretical force, the pressure times the area.
| Quantity | Relation | Note |
|---|---|---|
| Piston area | A extend = pi x D x D / 4 | D the piston diameter |
| Area on the rod side | A retract = pi x (D x D - d x d) / 4 | d the rod diameter |
| Free air per cycle, double acting | V = (A extend x L + A retract x L) x (p + pa) / pa | L the stroke, p the gauge pressure |
| Free air per cycle, single acting | V = A extend x L x (p + pa) / pa | only the extend stroke takes air |
| Tubing | pi x di x di / 4 x length x lines | two lines or one; added to the swept volume |
| Flow | V x cycles per minute x cylinders | l/min; x 60 / 1000 for m3/h; / 28.3168 for cfm |
| Force on the rod | F = p x A | theoretical; 1 bar = 0.1 N/mm2; pa 1.013 bar(a) unless entered |
| Units | 1 in = 25.4 mm; 1 ft3 = 28.316846592 l | 1 psi = 0.06894757293168 bar |
Free air is referred to an ambient pressure of 1.013 bar(a) (assumed; a barometer reading can be entered). The tube between the valve and the cylinder is filled and vented each cycle: two such lines on a double acting cylinder, one on a single acting one. The dead volume in the cylinder end caps and in the valve is not included.
The free air formula, the swept volume of the piston side and the rod side times the ratio of the absolute pressures (p + pa) / pa, with the piston side alone for a single acting cylinder, is given in two independent engineering methods for the compressed air demand of cylinders; both take the pressure of the standard atmosphere. That the tubing between the valve and the cylinder is filled and vented each cycle and adds to the air used (two lines on a double acting cylinder, one on a single acting one) is described in the technical literature on pneumatics by several authors. The force F = p x A on the extend stroke and p x pi x (D x D - d x d) / 4 on the retract stroke is given in general references on pneumatic cylinders. Inches, feet and psi are converted by the exact unit definitions.
From the swept volume and the pressure. The piston area is A extend = pi x D x D / 4, the area on the rod side A retract = pi x (D x D - d x d) / 4. A double acting cylinder fills both sides each cycle, so the swept volume is (A extend + A retract) x L; at the working pressure it is brought to free air by (p + pa) / pa. For D 63 mm, a 20 mm rod and a 200 mm stroke: 3117.2 mm2 and 2803.1 mm2, 0.6234 l + 0.5606 l = 1.1841 l swept; at 6 bar(g) the ratio is (6 + 1.013) / 1.013 = 6.923, so 8.20 l of free air per cycle. At 10 cycles/min that is 82.0 l/min, 4.92 m3/h or 2.89 cfm.
Free air is the volume the air takes at the ambient pressure. The cylinder fills at the working pressure, so the swept volume holds more air than it would at the ambient pressure; the ratio of the absolute pressures, (p + pa) / pa, gives the free air. The calculator takes pa as 1.013 bar(a), the standard atmosphere rounded, and says so; a barometer reading can be entered instead (atm 0.99 bar).
Only one stroke takes air: the extend stroke, while a spring makes the return. The free air per cycle is A extend x L x (p + pa) / pa, and the rod does not change it. For a 50 mm piston and a 100 mm stroke at 6 bar(g): 1963.5 mm2 x 100 mm = 0.1963 l, times 6.923 is 1.36 l per cycle, or 27.2 l/min at 20 cycles/min. The tubing counts one line instead of two.
As the pressure times the area: F = p x A, with p the gauge pressure. 6 bar(g) is 0.6 N/mm2, so a 63 mm piston gives 0.6 x 3117.2 = 1870 N on the extend stroke, and with a 20 mm rod 0.6 x 2803.1 = 1682 N on the retract stroke. This is the theoretical force. On a single acting cylinder the spring force is not taken off.
Because the tube is filled to the working pressure and vented every cycle, and that air does no work. A double acting cylinder has a line to each port, a single acting one a single line. Two lines of 2 m with a 6 mm inside diameter hold 2 x pi x 6 x 6 / 4 x 2000 mm = 0.1131 l; times 6.923 that is 0.783 l of free air per cycle, 8.7 % of the 8.98 l the cylinder and tubing take together in the example above.
The piston diameter D, the rod diameter d and the stroke L in mm or inches (cm and m are read too); the working pressure in bar, psi, MPa or kPa, gauge or absolute, read as gauge when it has no mark; the cycles per minute (or per hour) and the number of cylinders; the tube length per line and its inside diameter, if wanted; the ambient pressure, 1.013 bar(a) unless entered. It gives no recommended pressures and no sizing margins.
The calculator gives the air and the force of a pneumatic cylinder. When a cylinder, a seal kit or other parts are needed, send the line from the calculator with a photograph of the cylinder plate, and Vessel Core checks the details before an offer goes back.
