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). Enter bore, rod and pressure above.

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 .

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?

No — this is the theoretical force from pressure × area. Real output is roughly 85–95% of it after seal friction and back-pressure on the rod side.

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.

Hydraulic Cylinder Force Calculator — Push & Pull (PSI/Bar)

Push and pull force from bore, rod diameter and system pressure — with the rod-area differential shown explicitly. Standard ISO bore sizes. Metric and imperial.

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.

Worked example

A 50 mm bore cylinder with a 22 mm rod at 160 bar (16 MPa). The piston area is ≈ 19.6 cm², so the push force is ≈ 31.4 kN (3.2 tonne, 7,060 lbf). The rod area is ≈ 3.8 cm², so on retract pressure acts on the ≈ 15.8 cm² annulus and the pull force is ≈ 25.3 kN. 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.

Standard cylinder sizes

Standard metric cylinder bore and rod sizes (ISO 6020-2), with the 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.

Standard ISO 6020-2 bore/rod combinations. MM1 = smaller rod (more pull force); MM2 = larger rod (stiffer).
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). Enter bore, rod and pressure above.
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.
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?: No — this is the theoretical force from pressure × area. Real output is roughly 85–95% of it after seal friction and back-pressure on the rod side.
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

Theoretical force from pressure × area — excludes seal friction, back-pressure and dynamic losses. Real mechanical efficiency is typically 0.85–0.95.
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.

Related calculators

Hydraulic Pump Flow & HP Calculator — Pump output flow and hydraulic/shaft power from displacement, speed and pressure.
Pneumatic Air Consumption Calculator — Free-air consumption per cycle and per minute for a pneumatic cylinder.

Hydraulic Cylinder Force Calculator

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