How to use this calculator
- Enter the bore and rod diameters. Enter the cylinder bore (piston diameter) and the piston-rod diameter. Use a standard ISO size if you can.
- Enter the system pressure. Enter the actual working pressure the cylinder sees.
- Set efficiency. Use 100 percent for ideal force, or enter a practical mechanical efficiency for usable output force.
- Choose the stroke. Select push (extend) or pull (retract). Pull uses the annulus area, so it is lower by the rod-area differential.
- Read the force. Read the usable force first, then compare it with the theoretical push, pull and rod-area differential. Add a flow to get the stroke speed.
How it works
A hydraulic cylinder’s force is simply pressure acting over an area. On the push (extend) stroke, pressure acts on the full piston face: F_push = P · (π/4) · bore² On the pull (retract) stroke the rod takes up part of that face, so pressure acts only on the annulus — the bore area minus the rod area: F_pull = P · (π/4) · (bore² − rod²)
The difference between the two is exactly the rod-area differential,
P · (π/4) · rod² — the force the rod removes on the pull stroke. This
calculator shows that line explicitly, because it is the number people miss when a
retracting cylinder won’t pull what they expected. The same rod area makes the
cylinder retract faster than it extends for a given flow, since speed = flow ÷ area.
The primary usable-force result multiplies the selected theoretical force by the
mechanical efficiency you enter, so seal friction and pressure-loss allowance is not
left as mental math.
The hydraulic cylinder force
formula guide walks through the same derivation with unit shortcuts and a
worked tonnage conversion.
After force is known, use the hydraulic pressure calculator to work backward from a target load, or the hydraulic pump flow and HP calculator to size pump flow and shaft power. Long compression rods should also be checked in the hydraulic cylinder rod buckling calculator, especially at high stroke or clevis-mounted layouts.
Worked example
Verified against the live calculator
A 50 mm bore cylinder with a 22 mm rod at 160 bar (16 MPa) and 90% mechanical efficiency. The piston area is ≈ 19.6 cm², so the push force is ≈ 31.4 kN (3.2 tonne, 7,060 lbf). The usable push force is ≈ 28.3 kN after the efficiency allowance. The rod area is ≈ 3.8 cm², so on retract pressure acts on the ≈ 15.8 cm² annulus and the theoretical pull force is ≈ 25.3 kN, or ≈ 22.8 kN usable. The shortfall — the rod-area differential — is ≈ 6.08 kN, exactly P × rod area. At 20 L/min the cylinder extends at ≈ 170 mm/s. Load this page and the calculator shows these numbers.
Reference data
Use this cylinder force chart as a quick standard-bore reference before entering the exact working pressure above. Standard metric cylinder bore and rod sizes (ISO 6020-2) are shown with piston and annulus areas and the force each develops at 100 bar. Force scales linearly with pressure — at 200 bar, double these; at 250 bar, multiply by 2.5.
| Bore (mm) | Rod (mm) | Series | Piston area (cm²) | Annulus area (cm²) | Push @100 bar (kN) | Pull @100 bar (kN) |
|---|---|---|---|---|---|---|
| 25 | 12 | MM1 | 4.91 | 3.78 | 4.91 | 3.78 |
| 25 | 18 | MM2 | 4.91 | 2.36 | 4.91 | 2.36 |
| 32 | 14 | MM1 | 8.04 | 6.5 | 8.04 | 6.5 |
| 32 | 22 | MM2 | 8.04 | 4.24 | 8.04 | 4.24 |
| 40 | 18 | MM1 | 12.6 | 10 | 12.6 | 10 |
| 40 | 28 | MM2 | 12.6 | 6.41 | 12.6 | 6.41 |
| 50 | 22 | MM1 | 19.6 | 15.8 | 19.6 | 15.8 |
| 50 | 36 | MM2 | 19.6 | 9.46 | 19.6 | 9.46 |
| 63 | 28 | MM1 | 31.2 | 25 | 31.2 | 25 |
| 63 | 45 | MM2 | 31.2 | 15.3 | 31.2 | 15.3 |
| 80 | 36 | MM1 | 50.3 | 40.1 | 50.3 | 40.1 |
| 80 | 56 | MM2 | 50.3 | 25.6 | 50.3 | 25.6 |
| 100 | 45 | MM1 | 78.5 | 62.6 | 78.5 | 62.6 |
| 100 | 70 | MM2 | 78.5 | 40.1 | 78.5 | 40.1 |
| 125 | 56 | MM1 | 123 | 98.1 | 123 | 98.1 |
| 125 | 90 | MM2 | 123 | 59.1 | 123 | 59.1 |
| 160 | 70 | MM1 | 201 | 163 | 201 | 163 |
| 160 | 110 | MM2 | 201 | 106 | 201 | 106 |
| 200 | 90 | MM1 | 314 | 251 | 314 | 251 |
| 200 | 140 | MM2 | 314 | 160 | 314 | 160 |
Source: ISO 6020-2 mounting & rod-diameter series. Verify against the cylinder manufacturer's catalogue for the exact model.
Frequently asked questions
How do I calculate hydraulic cylinder force?
Force = pressure × area. The push (extend) force uses the full bore area, F = P·(π/4)·bore². The pull (retract) force uses the annulus — the bore area minus the rod area: F = P·(π/4)·(bore²−rod²). The usable result then multiplies that theoretical force by the entered mechanical efficiency.
Why is the pull force less than the push force?
On the retract stroke the rod occupies part of the piston face, so pressure acts on the annulus (bore area minus rod area) instead of the full bore. The shortfall equals pressure × rod area — shown on this page as the rod-area differential.
Can I use this as a cylinder force chart?
Yes. The standard bore/rod table is a cylinder force chart at 100 bar. Force scales linearly with pressure, so multiply the chart value by your pressure divided by 100 bar, then apply any efficiency or back-pressure allowance.
What pressure should I enter?
Use the actual working pressure (relief-valve setting) the cylinder sees, not the pump’s maximum rating. Typical industrial and mobile systems run 100–250 bar (1,450–3,600 psi).
Does this include friction and efficiency losses?
Yes, for a first-pass screen. The main usable-force result applies the mechanical efficiency you enter. Use 100% for ideal theoretical force, or roughly 85–95% when you need a quick allowance for seal friction, back-pressure and other losses.
How is the stroke speed found?
Speed = flow ÷ working area. Extend uses the piston area; retract uses the smaller annulus area, so for the same flow the cylinder retracts faster than it extends.
Does this work in metric and imperial?
Yes — toggle SI/Imperial in the header. Pressure switches between bar and psi, and force is shown in N, kN, lbf and tonne at once.
Method & assumptions
- Usable force is theoretical pressure × area multiplied by the entered mechanical efficiency. The default 90% is a screening allowance, not manufacturer data.
- Theoretical force before efficiency is also shown so the pressure-area math stays visible.
- Pressure is the actual working pressure at the cylinder, not the pump rating.
- Rod buckling (column loading) is not checked here — long rods in compression need a separate stroke/rod-diameter check with the linked rod buckling calculator.