Hydraulic Cylinder Calculator
Size or check a double-acting hydraulic cylinder. Enter the bore, rod diameter, stroke and working pressure to get push and pull force in lbf, kN and tons; add the pump flow to get extend and retract speeds, cycle time, oil volume and hydraulic power. Works in inches and psi or millimeters and bar.
Last updated:
0 for a single-acting ram with no rod side
For speeds and cycle times
100% = theoretical; seal friction typically leaves 90–95%
How to use the Hydraulic Cylinder Calculator
- Choose the dimension unit and enter the bore, rod diameter and stroke.
- Enter the working pressure at the cylinder (relief setting or actual load pressure).
- Enter the pump flow to get speeds and times (optional).
- Lower the efficiency to about 90–95% for a realistic force with seal friction.
- Read push and pull force, speeds and oil volumes, and check the extend vs retract table.
Hydraulic cylinder formulas
- Bore area: A = π D² ÷ 4; annulus area: A_ann = π (D² − d²) ÷ 4
- Push force: F = p × A; pull force: F = p × A_ann (× efficiency for real seals)
- Speed: v = Q ÷ A (extend) or Q ÷ A_ann (retract)
- US shortcut: speed (in/s) = 3.85 × GPM ÷ area (in²); force (lbf) = psi × in²
- Time per stroke: t = stroke ÷ speed = A × stroke ÷ Q
- Oil volume: V = A × stroke; hydraulic power: P = p × Q (hp = psi × GPM ÷ 1714)
Push force of common bores
| Bore | Area (in²) | 1,500 psi | 2,500 psi | 3,000 psi |
|---|---|---|---|---|
| 2" | 3.14 | 4,712 lbf | 7,854 lbf | 9,425 lbf |
| 2.5" | 4.91 | 7,363 lbf | 12,272 lbf | 14,726 lbf |
| 3" | 7.07 | 10,603 lbf | 17,671 lbf | 21,206 lbf |
| 3.5" | 9.62 | 14,432 lbf | 24,053 lbf | 28,863 lbf |
| 4" | 12.57 | 18,850 lbf | 31,416 lbf | 37,699 lbf |
| 5" | 19.63 | 29,452 lbf | 49,087 lbf | 58,905 lbf |
| 6" | 28.27 | 42,412 lbf | 70,686 lbf | 84,823 lbf |
Theoretical values (100% efficiency). Divide by 2,000 for US tons.
Design tips
- Allow for losses. Seal friction and back pressure usually reduce usable force by 5–10%, and line losses reduce pressure at the cylinder.
- Check rod buckling on long-stroke push applications; a thin rod can buckle well below the hydraulic force.
- Size the reservoir and lines for the retract return flow, which is larger than pump flow by the area ratio when oil leaves the cap end.
- Stay within ratings. Never exceed the cylinder, hose or pump pressure rating, and keep loads guided to avoid side loading the rod.
Frequently asked questions
How do you calculate hydraulic cylinder force?
Force = pressure × area. When extending, pressure acts on the full piston area A = π D² ÷ 4; when retracting it acts on the annulus π (D² − d²) ÷ 4, where d is the rod diameter. A 3 inch bore at 2,500 psi: A = 7.07 in², force = 2,500 × 7.07 ≈ 17,670 lbf, about 8.8 US tons.
Why is the retract force lower than the push force?
The rod takes up part of the piston face on the rod side, so the oil pushes on a smaller annular area. With a rod half the bore diameter the annulus is 75% of the bore area, so the pull force and the retract oil volume are 75% of the extend values.
How fast will my cylinder move?
Speed = flow ÷ effective area. In US units, speed (in/s) = GPM × 3.85 ÷ area (in²). 10 GPM into a 3 inch bore (7.07 in²) extends at about 5.4 in/s. Retraction is faster because the same flow fills the smaller annulus.
How do I convert cylinder force to tons?
Divide pounds-force by 2,000 for US (short) tons, or newtons by 9,806.65 for metric tonnes. A press rated 20 tons (US) needs 40,000 lbf: at 3,000 psi that takes a bore area of 13.3 in², about a 4.12 inch bore.
What pressure should I use?
Use the pressure actually available at the cylinder, typically the relief valve setting minus line losses, to find the maximum force. To find speed under load, use the pump flow at that pressure. Never exceed the cylinder’s rated pressure.
What is a regenerative circuit?
In a regenerative circuit the oil leaving the rod end is routed back into the cap end while extending. The effective area becomes the rod area, so the cylinder extends faster (flow ÷ rod area) but with only pressure × rod area of force. It is used for fast approach strokes.
How much oil does the cylinder need?
Extend volume = bore area × stroke; retract volume = annulus area × stroke. The difference is the rod volume, which the reservoir must absorb when the cylinder extends. A 3 × 24 inch cylinder holds about 170 in³ (0.73 US gal) on the cap side.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.