Push force (extend)
-Pull force (retract)
-Extend speed
-Retract speed
-All results
| Bore (cap side) area | - |
| Rod area | - |
| Annulus (rod side) area | - |
| Area ratio, bore / annulus | - |
| Push force, theoretical (no losses) | - |
| Push force, usable (with efficiency) | - |
| Pull force, theoretical (no losses) | - |
| Pull force, usable (with efficiency) | - |
| Oil volume, extend stroke | - |
| Oil volume, retract stroke | - |
| Time, extend stroke | - |
| Time, retract stroke | - |
Method and formulas
Steady-state force and flow balance, so every figure can be checked by hand. Force is set by pressure and piston area; speed is set by flow and piston area.
| Quantity | Formula |
|---|---|
| Bore area | Ac = π D² / 4 |
| Annulus area | Aa = π (D² − d²) / 4 |
| Push force | Fpush = η (p Ac − pb Aa) |
| Pull force | Fpull = η (p Aa − pb Ac) |
| Speed | vext = Q / Ac, vret = Q / Aa |
| Volume per stroke | V = A L |
| Stroke time | t = L / v |
| Metric unit shortcut | F (N) = p (bar) × A (mm²) / 10 |
Pressure is gauge pressure. The back pressure term uses the opposite area, so a restricted return line cuts the force. Flow is the pump flow reaching the driven side, with no leakage or compressibility. 1 US gallon = 231 in³.
Worked example: 63 mm bore, 36 mm rod, 160 bar, 20 L/min, 300 mm stroke
Bore area = π × 63² / 4 = 3117.2 mm². Annulus area = π (63² − 36²) / 4 = 2099.4 mm². Theoretical push force = 16 N/mm² × 3117.2 = 49.88 kN, and with 90 % efficiency 44.89 kN. Pull force = 16 × 2099.4 = 33.59 kN theoretical, 30.23 kN usable. Extend speed = 20 × 1 000 000 / (60 × 3117.2) = 106.9 mm/s; retract speed = 158.8 mm/s. Oil needed to extend 300 mm is 0.935 L, taking 2.81 s.
Questions
How do you calculate hydraulic cylinder force?
Force equals pressure times piston area: F = p x A. On the push (extend) stroke the pressure acts on the full bore area A = pi D^2 / 4. On the pull (retract) stroke it acts on the annulus, bore area minus rod area, A = pi (D^2 - d^2) / 4. With p in bar and areas in mm^2, F (N) = p (bar) x A (mm^2) / 10. In US units F (lbf) = p (psi) x A (in^2). Multiply by the cylinder efficiency to get the usable force.
Why is the pull force lower than the push force?
The rod takes up part of the piston area on the rod side, so the annulus the oil acts on is smaller. With the same pressure the pull force is lower by the ratio of the annulus area to the full bore area. The same smaller area also makes the retract stroke faster for the same flow.
How do I find the speed of a hydraulic cylinder?
Speed equals flow divided by the effective piston area: v = Q / A. Extend speed uses the full bore area and retract speed uses the annulus area. For Q in L/min and A in mm^2, v (mm/s) = Q x 1 000 000 / (60 x A). For Q in gpm and A in in^2, v (in/s) = Q x 231 / (60 x A). Cylinder speed is set by flow, force is set by pressure.
What cylinder efficiency should I use?
Seal friction and the pressure needed to break away the load reduce the usable force. Figures of 85 to 95 percent are commonly used for well-made hydraulic cylinders at working pressure, lower at very low pressures or with high-friction seals. Use your supplier's data where you have it. This calculator treats efficiency as one constant factor.
What is back pressure and why does it matter?
The oil leaving the opposite side of the piston has to be pushed through the return line, valves and any counterbalance or flow control, so that side sits at a pressure above tank pressure. That pressure acts on the opposite area and subtracts from the force. Enter the pressure on the exhaust side to include it. Zero means a free return to tank.
Does this work for pneumatic cylinders?
The force equations are the same, so use the gauge pressure of the air supply. Air is compressible, so speed depends on the supply, the valves and the exhaust restriction rather than on a fixed flow, and the flow shown here is the actual volume flow at working pressure, not free air. Treat the speed result as an estimate only for pneumatics.
What does this calculator not cover?
It covers steady-state force, speed and volume. It does not cover rod buckling, side loads, cushioning, acceleration, pressure intensification on the rod side of a differential cylinder with a blocked port, pump or valve sizing, oil compressibility, or heating. A long stroke with a slender rod needs a buckling check, see the column buckling calculator. Verify critical designs.
Engineering aid for guidance. It covers steady-state force, speed and volume and does not cover rod buckling, side loads, cushioning, acceleration, leakage, oil compressibility, pump and valve sizing or temperature effects. Verify critical designs.