Hydraulic Cylinder Calculator
Work out a hydraulic cylinder's push and pull force from bore, rod and pressure, the speed from flow, the volume per stroke and the bore needed for a load. Imperial or metric, with the formulas shown.
Your numbers
The inside diameter of the barrel, the number on the cylinder's data plate.
Leave empty for a ram with no rod side; the pull force needs it.
The relief valve setting or the working pressure at the cylinder.
For the rod speeds. Use the flow reaching this cylinder.
For the oil volume and the time per stroke.
Push force (extend)
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- Pull force (retract)
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- Push force, other units
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- Bore (piston) area
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- Rod area
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- Annulus (rod side) area
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- Area ratio, bore to annulus
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- Extend speed
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- Retract speed
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- Time to extend
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- Time to retract
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- Oil to extend
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- Oil to retract
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Theoretical figures. Seal friction and back pressure on the other side of the piston take a little off the real force, so leave a margin. Check the cylinder's rated pressure, and the rod's buckling limit on a long stroke, in the maker's data.
The calculation runs in your browser and ParrotNotes does not store your numbers. They sit in the page address so you can bookmark or share the result.
How the hydraulic cylinder calculator works
A hydraulic cylinder turns pressure into force over the piston's area: F = p × A. In US units psi × sq in gives pounds-force directly; in metric, bar × cm² gives decanewtons (1 daN = 10 N), which is why European catalogs often quote both. The page works in the system you pick and shows the force in the other one too.
Choose Force and speed to start from a cylinder's bore, rod and pressure, or Bore for a load to start from the force you need. Flow and stroke are optional: add them for rod speeds, stroke times and the oil each stroke takes.
Push force by bore and pressure
Theoretical push force (full bore), worked out with the same formulas as the calculator. The bores are examples, not a list of standard sizes.
| Bore | 1,000 psi | 2,000 psi | 2,500 psi | 3,000 psi |
|---|---|---|---|---|
| 1.5 in | 1,767 | 3,534 | 4,418 | 5,301 |
| 2 in | 3,142 | 6,283 | 7,854 | 9,425 |
| 2.5 in | 4,909 | 9,817 | 12,272 | 14,726 |
| 3 in | 7,069 | 14,137 | 17,671 | 21,206 |
| 3.5 in | 9,621 | 19,242 | 24,053 | 28,863 |
| 4 in | 12,566 | 25,133 | 31,416 | 37,699 |
| 5 in | 19,635 | 39,270 | 49,087 | 58,905 |
| 6 in | 28,274 | 56,549 | 70,686 | 84,823 |
| 8 in | 50,265 | 100,531 | 125,664 | 150,796 |
| Bore | 100 bar | 160 bar | 200 bar | 250 bar |
|---|---|---|---|---|
| 40 mm | 12.6 | 20.1 | 25.1 | 31.4 |
| 50 mm | 19.6 | 31.4 | 39.3 | 49.1 |
| 63 mm | 31.2 | 49.9 | 62.3 | 77.9 |
| 80 mm | 50.3 | 80.4 | 100.5 | 125.7 |
| 100 mm | 78.5 | 125.7 | 157.1 | 196.3 |
| 125 mm | 122.7 | 196.3 | 245.4 | 306.8 |
| 160 mm | 201.1 | 321.7 | 402.1 | 502.7 |
| 200 mm | 314.2 | 502.7 | 628.3 | 785.4 |
Push, pull and the area ratio
Extending, pressure acts on the full bore. Retracting, it acts on the annulus, the bore area minus the rod area, so a double-acting cylinder always pulls with less force than it pushes and, at the same flow, retracts faster. The area ratio (bore area ÷ annulus area) tells you by how much; it also means the oil coming out of the bore side on retract is that much more than the pump flow, which matters for return lines and valves.
Speed, stroke time and oil volume
Rod speed is the flow divided by the area being filled. One US gallon is 231 cubic inches (3.785 L in NIST SP 811), so GPM × 231 ÷ 60 is the flow in cubic inches per second. Divide the stroke by the speed for the stroke time, and multiply the area by the stroke for the oil volume. Use the flow that actually reaches the cylinder: with a fixed pump and a relief valve, flow lost over the relief or through a flow control slows it down.
For hydraulics distributors and industrial sales
When a customer asks for "a cylinder that does 20 tons", ask the pressure the power unit runs at, whether the load is a push or a pull, the stroke and the cycle time they need. The bore follows from the force and pressure, the pump from the speed. Note the units each time: a European spec sheet in bar and mm and a US power unit in psi and GPM can be on the same job.
Unit factors from NIST SP 811, read on 2026-11-01: 1 lbf = 4.448 222 N, 1 US ton-force (2,000 lbf) = 8.896 443 kN, 1 kgf = 9.806 65 N, 1 psi = 6,894.757 Pa, 1 bar = 100,000 Pa, 1 gal = 3.785 412 L. Force = pressure × area is basic physics; the results are theoretical, before friction:
Related: the pressure conversion calculator to turn bar, MPa or kgf/cm² into psi (it only converts; this page works out force), and the flow rate calculator for GPM, L/min and pipe velocity.
More for industrial and distributor sales: Industrial distributor, Sales engineer, Manufacturers' rep.
Cylinder specs come up in conversation
On a site visit the customer gives you the load, the pressure the power unit runs at, the stroke and the cycle time, often in mixed units. Record the visit in ParrotNotes and you get a transcript and a summary, so every figure is in writing when you size and quote the cylinder.
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