Hydraulic Cylinder Calculator
Push and pull force from bore, rod and pressure in bar, psi or MPa, plus extend and retract speed, cycle time, flow for a target speed and hydraulic power.
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About this toolWhat is the Hydraulic Cylinder Calculator?
A hydraulic cylinder turns pressure into force and flow into speed, and the rod makes the two directions different. On the extend stroke oil pushes on the full piston area; on the retract stroke it pushes only on the ring around the rod. This calculator works out both forces from the bore, the rod and the system pressure, then uses the pump flow to give extend and retract speeds, stroke times, the full cycle time and the oil each stroke needs.
The default cylinder is a common 100 mm bore with a 56 mm rod at 200 bar and 40 L/min. It pushes 157.1 kN (about 16 tonnes-force), pulls 107.8 kN, extends at 84.9 mm/s and retracts at 123.7 mm/s, so a 500 mm stroke cycles in 9.9 seconds. Switch to US units and the same panel reads bore in inches, pressure in psi and flow in US gallons per minute.
A target speed field turns the problem around and returns the flow you need for that speed in each direction, and a regenerative row shows what happens when the rod-side oil is routed back to the cap end.
- Extend, retract and regenerative force from bore, rod and pressure
- Pressure in bar, MPa or psi and flow in L/min or US gpm, with exact conversions
- Extend and retract speed, stroke times, cycle time and oil volume per stroke
- Flow needed for a target speed in each direction and hydraulic power in kW and hp
- Metric and US dimensions that convert in place, formula panel, copy and share
How to use the Hydraulic Cylinder Calculator
- Choose metric or US units for the bore, rod and stroke, then the pressure and flow units you work in.
- Enter the bore (piston) diameter, rod diameter and working pressure. Set a force efficiency below 100% if you want to allow for seal friction.
- Enter the pump flow and stroke length to see speeds, stroke times and cycle time.
- Optionally enter a target speed to see the flow needed in each direction and for a regenerative extend.
- Copy the results or share a link with the cylinder filled in.
Worked examples
Press cylinder, metric
Input
100 mm bore, 56 mm rod, 200 bar, 40 L/min, 500 mm stroke
Output
Push 157.1 kN, pull 107.8 kN; 84.9 mm/s out, 123.7 mm/s back; cycle 9.93 s; 13.3 kW
The area ratio is 1.457, so retracting is 46% faster and the return line must pass 58 L/min.
Log splitter, US units
Input
3 in bore, 1.5 in rod, 2,500 psi, 10 gpm, 24 in stroke
Output
Push 17,671 lbf (8.8 tons), pull 13,254 lbf; 5.45 in/s out, 7.26 in/s back; cycle 7.7 s
Hydraulic power is 14.6 hp at full pressure, which is why two-stage pumps drop flow when pressure rises.
Regenerative extend
Input
63 mm bore, 36 mm rod, 160 bar, 20 L/min
Output
Normal extend 106.9 mm/s and 49.9 kN; regenerative 327.5 mm/s and 16.3 kN
Feeding rod-side oil back to the cap end triples the speed and divides the force by the same factor, useful for fast approach strokes.
Background and insight
The maths is Pascal's law. Force equals pressure times area, so a 100 mm piston has π × 100² / 4 = 7,854 mm², and 200 bar is 20 N/mm², which gives 157,080 N. Speed is flow divided by area: 40 L/min is 666,667 mm³/s, which spread over 7,854 mm² moves the piston at 84.9 mm/s. Every number in the calculator is one of those two divisions or multiplications with exact unit conversions (1 bar = 100 kPa, 1 psi = 6.894757 kPa, 1 US gallon = 231 in³ = 3.785411784 L).
The ratio of piston area to annulus area, often called phi (φ), governs the difference between directions. With a 100/56 cylinder φ is 1.46, so it retracts 46% faster than it extends and returns 46% more oil than the pump supplies while retracting. That extra return flow is a common reason for undersized return lines, filters and valves.
Hydraulic power is pressure times flow. In practical units, kW = bar × L/min / 600 and hp = psi × gpm / 1714. Seal friction typically costs 5 to 10% of theoretical force, so the efficiency field lets you derate the forces; it does not change speed, which leakage affects instead.
Common use cases
Sizing a cylinder
Find the bore that gives the force you need at the pressure your power unit can supply, then check the pull force on the rod side.
Matching a pump
Work out the flow needed for a target cycle time and the power that flow costs at working pressure.
Mobile and farm equipment
Check loader, tipper and log splitter cylinders with US units and tractor hydraulic flow in gpm.
Troubleshooting slow machines
Compare measured stroke times with theory to spot a worn pump, a relief valve opening early or internal leakage.
Tips and limitations
- Use the pressure at the cylinder, not at the pump. Valves, hoses and fittings can lose 5 to 20 bar at full flow.
- Back pressure on the outlet side subtracts from force: multiply it by the opposite area and take it off.
- Long rods in push can buckle. Check the rod with a buckling calculation, using the mounting style to set the effective length.
- Cycle time here ignores acceleration, valve shift time and any dwell, so real cycles run longer.
- If the cylinder is meter-in or meter-out controlled, speed is set by the flow control, not the pump.
Frequently asked questions
How do you calculate hydraulic cylinder force?
Multiply pressure by the area it acts on. Extend force = p × π D² / 4, and retract force = p × π (D² − d²) / 4, where D is the bore and d the rod diameter. In metric, bar × mm² / 10 gives newtons; in US units, psi × in² gives pounds-force.
Why does a hydraulic cylinder retract faster than it extends?
The rod takes up part of the area on the rod side, so the same flow fills a smaller volume per millimetre of stroke. With a 100 mm bore and 56 mm rod the annulus is 69% of the piston area, so retraction is 1.46 times faster.
How do I calculate cylinder speed from gpm?
Speed in inches per second = 231 × gpm / (60 × area in in²), since one US gallon is 231 cubic inches. A 3 in bore (7.07 in²) fed with 10 gpm extends at 231 × 10 / 60 / 7.07 = 5.45 in/s.
How much flow does a hydraulic cylinder need?
Flow = area × speed. In metric, L/min = area in cm² × speed in m/min / 10. A 100 mm bore (78.5 cm²) moving at 6 m/min (100 mm/s) needs 47 L/min on the extend stroke.
What is a regenerative hydraulic circuit?
A circuit that sends the oil leaving the rod side back into the cap side during extension. The net area doing work is the rod area, so the cylinder extends faster for the same pump flow but with only rod-area force. It suits fast, light approach strokes.
How do you calculate hydraulic horsepower?
Hydraulic hp = psi × gpm / 1714. In metric, kW = bar × L/min / 600. Divide by pump efficiency, often 85 to 90% overall, to size the motor or engine that drives the pump.
What bore size do I need for a given force?
Rearrange F = p × π D² / 4 to D = √(4F / (π p)). For 50 kN at 160 bar (16 N/mm²), D = √(4 × 50,000 / (π × 16)) = 63.1 mm, so a 63 mm bore is marginal and an 80 mm bore gives headroom.
Is there an in-depth guide to the Hydraulic Cylinder Calculator?
Yes. “Hydraulic Cylinder Force, Speed and Flow: The Sizing Maths” covers the background, how it works, common pitfalls and worked examples. Read the full guide.
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