Hydraulic Cylinder Calculator

Calculate push and pull force for a hydraulic cylinder, plus extend and retract speed from pump flow — before you pick the bore.

Calculator

Calculate

Bore diameter (in) Example: 3.000 in bore, a common NFPA mid-size cylinder.

Rod diameter (in) Example: 1.5 in rod. Enter 0 for a plunger cylinder with equal areas.

System pressure (psi) Pressure at the cylinder port while it moves, not the relief setting.

Pump flow (gpm) Used in Speed mode only. Example: 10 gpm pump output.

About this calculator

This hydraulic cylinder calculator gives theoretical push/pull force and piston speed for one double-acting cylinder. It does not size the pump or the hoses. Air-side work belongs in the pneumatic cylinder sizing calculator; oil-side pump power is next door in the hydraulic pump size calculator.

Calculation Results

14,137 lbf

Push force · pull 10,603 lbf · full bore area 7.0686 in² · annular 5.3014 in²

Formula: F = P × A; A = π/4 × D²

14,137 lbf ≈ 62.9 kN. Switch to Speed mode to add flow.

How to use this result

Theoretical force assumes gauge pressure at the port and no losses. Real output drops with seal friction, hose and valve pressure drop, and back-pressure. For breakaway or holding loads, apply a 25% or larger safety margin before choosing the bore. Speed mode assumes all pump flow reaches the cylinder — metering valves or bypass leakage reduce it.

Continue Your Calculation

Cylinder force does not size the pump. Open the pump size calculator when the next step is pump power or displacement.

Pump size →

Cylinder push force chart (lbf)

Theoretical push force = pressure × full bore area. Pull force is lower by the annular area. Click a preset above to load nearby inputs.

Bore (in)	Area (in²)	1,000 psi	1,500 psi	2,000 psi	3,000 psi
1.5	1.7671	1,767	2,651	3,534	5,301
2	3.1416	3,142	4,712	6,283	9,425
2.5	4.9087	4,909	7,363	9,817	14,726
3	7.0686	7,069	10,603	14,137	21,206
4	12.5664	12,566	18,850	25,133	37,699
5	19.6350	19,635	29,452	39,270	58,905
6	28.2743	28,274	42,412	56,549	84,823
8	50.2655	50,265	75,398	100,531	150,796

Hydraulic cylinder formula

Full bore area: A = π/4 × D². For a 3 in bore, A = 0.7854 × 9 = 7.0686 in².

Annular area (retract side): A_ann = π/4 × (D² − d²). With a 1.5 in rod: 0.7854 × (9 − 2.25) = 5.3014 in².

Push force: F_push = P × A. At 2,000 psi: 2,000 × 7.0686 = 14,137 lbf. Pull force: 2,000 × 5.3014 = 10,603 lbf.

Speed: v = Q × 231 / 60 / A (in/s, Q in gpm). At 10 gpm: extend 10 × 231 / 60 / 7.0686 = 5.45 in/s (327 in/min); retract 7.26 in/s (436 in/min).

Metric row: 14,137 lbf × 4.44822 = 62.9 kN = 6.4 tonnes-force. Pull: 10,603 lbf = 47.2 kN. One cubic inch of area at 1,000 psi gives 1,000 lbf, or about 4.45 kN.

Need the pump power behind this cylinder? Use the hydraulic pump size calculator. Air cylinders: pneumatic cylinder sizing.

Which fluid-power task this is

Question	Use
Cylinder push/pull force or piston speed	This page
Pump horsepower, input kW, displacement	Hydraulic pump size calculator
Air cylinder force at 90–120 psi	Pneumatic cylinder sizing
Electric motor torque at cylinder duty cycle	Motor torque calculator
Motor horsepower in kilowatts	HP to kW

Frequently Asked Questions

How do you calculate hydraulic cylinder push force?

Multiply pressure by full bore area. A 3-inch bore has an area of 7.0686 in², so at 2,000 psi the push force is 14,137 lbf (about 62.9 kN).

Why is pull force lower than push force?

The rod takes up bore area on the retract side. A 3-inch bore with a 1.5-inch rod leaves an annular area of 5.3014 in², so pull at 2,000 psi is 10,603 lbf instead of 14,137 lbf.

How do I convert cylinder force from lbf to kN or metric tons?

1 lbf = 4.44822 N. Divide lbf by 224.8 for kN or by 2,204.6 for tonnes-force. The example: 14,137 lbf ≈ 62.9 kN ≈ 6.4 t.

How fast will the cylinder extend and retract?

Speed = flow × 231 / 60 / area. At 10 gpm the example extends at 5.45 in/s (327 in/min) and retracts at 7.26 in/s (436 in/min) — the annular area is smaller, so retract is faster.

Why is the measured force lower than the calculated value?

The formula is theoretical. Seal friction, pressure drop in hoses and valves, and back-pressure all subtract from it. Keep a 25%+ safety margin for breakaway loads.

Does the rod diameter change push force?

No. Push force uses the full bore only. Rod diameter lowers pull force and speeds up retraction.

What bore diameters are standard?

ISO 6020-2 compact cylinders use metric bores from 25 to 250 mm. NFPA-style North American cylinders run roughly 1.5 to 8 in bores. Both series appear as area×pressure in the chart above.

How is this different from a pneumatic cylinder calculator?

Same area math, different pressure class: hydraulics run 700–3,000 psi, shop air 90–120 psi. The same bore makes roughly 20× more force on oil. Use the pneumatic cylinder sizing calculator for air-side sizing.

Review & sources

Reviewed: CalcPanel Fluid Power Team

Updated: 2026-11-10