Hong Life CalculatorsUnderstanding the hydraulic cylinder force and speed calculator — concept and principle
A double-acting hydraulic cylinder pushes with oil acting on the full piston area and pulls with oil acting on the smaller ring area around the rod. This calculator gives the theoretical push and pull forces from the bore, rod diameter and system pressure, and the extend and retract speeds from the pump flow. It is used to size cylinders for presses, lifts, loaders and fixtures.
How it is calculated
- Piston area: A_b = π D²/4; rod area: A_r = π d²/4 (diameters converted from mm to m).
- Push force: F = p × A_b; pull force: F = p × (A_b − A_r). Pressure in bar × 10⁵ gives Pa, and N ÷ 1,000 gives kN.
- Extend speed: v = Q / A_b; retract speed: v = Q / (A_b − A_r), with Q in L/min ÷ 60,000 = m³/s.
The principle
Pascal's law says pressure in a confined fluid acts equally in all directions, so force is simply pressure times the area it acts on. On the rod side the rod itself takes up part of the piston face, leaving only the annulus. For speed, oil is nearly incompressible, so each litre pumped in must sweep a litre of volume: velocity equals flow divided by area. The smaller annulus therefore makes the cylinder pull with less force but retract faster.
Worked example
- Inputs: bore 80 mm, rod 45 mm, 160 bar, 30 L/min.
- A_b = π × 0.08²/4 = 0.0050265 m²; A_r = π × 0.045²/4 = 0.0015904 m²; ring area = 0.0034361 m².
- Push = 160 × 10⁵ × 0.0050265 = 80,425 N = 80.42 kN.
- Pull = 160 × 10⁵ × 0.0034361 = 54,978 N = 54.98 kN.
- Q = 30/60,000 = 0.0005 m³/s; extend speed = 0.0005/0.0050265 = 0.09947 m/s.
- Retract speed = 0.0005/0.0034361 = 0.1455 m/s.
| Bore (mm) | Push force (kN) |
|---|---|
| 20 | 5.026548246 |
| 40 | 20.10619298 |
| 60 | 45.23893421 |
| 80 | 80.42477193 |
| 100 | 125.6637061 |
| 120 | 180.9557368 |
| 160 | 321.6990877 |
How to read the result
The area ratio here is 1.46, so retraction is 46% faster and pull force about 32% lower than push. Real forces are lower because of seal friction and back pressure on the opposite side, so designers usually leave a margin. Long, slender cylinders pushing a load must also be checked for rod buckling, which can govern well before the hydraulic force limit. Speeds of about 0.1 m/s (6 m/min) are typical of general industrial cylinders; very high speeds may need cushioning.
Common mistakes
- Using the full piston area for the pull force.
- Mixing bar and MPa (1 MPa = 10 bar).
- Assuming the pump's rated pressure is always available at the cylinder; valves and hoses drop pressure.
- Forgetting that a regenerative circuit changes both force and speed.
Frequently asked questions
How do I find the bore for a required force?
Divide the force by the pressure to get the area, then D = √(4A/π), and round up to a standard bore.
What are standard bore and rod sizes?
ISO 3320 lists preferred bores and rod diameters; 80 mm bore with a 45 mm rod is one such pair.
How much power does the cylinder use?
Hydraulic power is pressure times flow: 160 bar and 30 L/min give 8 kW before losses.
Sources: ISO 3320, Fluid power systems and components — Cylinder bores and piston rod diameters