Hydraulic Cylinder Force Calculator (Push, Pull & Speed)
A hydraulic cylinder pushes with the pressure acting on the full bore and pulls with the same pressure acting on the bore minus the rod, which is why every cylinder is weaker retracting than extending. Enter the bore, the rod diameter and the working pressure to get both forces, the rod speed for a given flow, and the oil volume each stroke takes.
Push force (extending)
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Results are estimates for planning purposes. Verify with your supplier, engineer, or a qualified professional before ordering material or performing work.
How much the rod costs you on the pull
The pull force is the push force multiplied by 1 − (rod ÷ bore)². It depends only on that ratio, not on the pressure, so the table below is true for any cylinder at any pressure.
| Rod ÷ bore | Pull force, as a share of push | What it means in practice |
|---|---|---|
| 0.4 | 84 % | Light-duty rod. Most pull force kept, slowest return. |
| 0.5 | 75 % | The most common proportion on general-purpose cylinders. |
| 0.6 | 64 % | Heavier rod for column strength on a long stroke. |
| 0.7 | 51 % | The cylinder pulls with about half of what it pushes. |
The same ratio works the other way round on speed: the rod that costs you pull force gives you a quicker return, because the same flow fills a smaller annulus.
Why the cylinder never quite delivers the calculated force
- Pressure drop on the way in. Hoses, fittings, the directional valve and any flow control all take pressure. What matters is the pressure at the port with the cylinder working, not the reading at the pump.
- Back-pressure on the way out. Oil leaving the other side has to get through the return line and the filter, and whatever pressure that takes acts against the piston on its own area.
- Seal friction. Real cylinders lose a few percent to the rod and piston seals, more when they are new, cold or worn.
- Side load and misalignment. A cylinder pushing at an angle puts part of its force into the bearing and the rod rather than into the work.
- The rating on the nameplate is the ceiling. More pressure always gives more force on paper; the cylinder, the mounting and the pins are what decide whether that is allowed.
Using this to size a cylinder
Working backwards from a load is the common job, and the arithmetic is the same in reverse: the area you need is the force divided by the pressure you can count on. Two habits keep that honest.
- Size on the pull, not on the push, whenever the hard part of the job is retracting. It is the weaker direction, and it is the one people forget.
- Leave margin on pressure. Sizing at the relief valve setting means the cylinder only just makes the load on a good day. Sizing so the job is done well below the relief leaves room for cold oil, a worn pump and a load that turns out heavier than the drawing said.
- Check the speed you get, not only the force. A big bore makes force cheap and speed expensive: the same pump fills a larger area more slowly, and cycle time is often what the production line actually cares about.
- Rod buckling and mounting style are the manufacturer's calculation, and a long stroke in compression is exactly where they matter. Nothing on this page covers them.
Before anyone works on the machine
A cylinder holding a load stores that energy whether the pump is running or not, and a hose or a fitting will release it in an instant when it is cracked open.
- Lower the load to the ground or block it mechanically. A closed valve is not a block.
- After the lockout devices are applied, relieve the stored pressure — 29 CFR 1910.147(d)(5)(i) requires all potentially hazardous stored or residual energy to be relieved, disconnected, restrained or otherwise rendered safe.
- Verify at a gauge that the pressure is actually gone before breaking a connection, and expect trapped oil in the lines even then.
- Never look for a pinhole leak with your hand. High-pressure oil injects through skin and the wound looks minor for the first few hours.
- Guard the moving parts the cylinder drives — 29 CFR 1910.212(a)(1) requires methods that protect employees from point-of-operation and ingoing nip point hazards.
Writing the sequence down for a particular machine is what the lockout/tagout procedure builder is for.
How it's calculated
- Full bore area (cap end)
A₁ = π / 4 × bore²- Annulus area (rod end)
A₂ = π / 4 × (bore² − rod²)The rod takes up part of the piston face, so the effective area on the rod side is the bore area minus the rod area — the differential-area case worked through in NAVEDTRA 14105 chapter 2.- Extend force (push)
F₁ = pressure × A₁Pounds from psi × in². In metric, kN = bar × mm² × 10⁻⁴.- Retract force (pull)
F₂ = pressure × A₂- Rod speed
v = flow ÷ areaIn imperial, gpm × 231 in³/gal gives in³/min, divided by the area in in² to get in/min. Extending uses A₁, retracting uses A₂ — the rod always comes back faster than it goes out, at the same flow.- Oil per stroke
V = area × strokeExtending fills A₁ × stroke; retracting fills A₂ × stroke and pushes A₁ × stroke back to tank. A US gallon is 231 in³ exactly.- Time for one stroke
t = V ÷ flow
Frequently asked questions
Multiply the pressure by the area the pressure acts on. Extending, that area is the full bore: π/4 × bore². A 4 in bore at 2,000 psi gives 12.57 in² × 2,000 = 25,130 lb, about 12.6 short tons. Retracting, subtract the rod area first.
Because the rod occupies part of the piston face on that side. The effective area is the bore area minus the rod area, so a 4 in bore with a 2 in rod pulls on 9.42 in² instead of 12.57 in² — 75 % of the push force at the same pressure. A bigger rod means a bigger difference.
Divide the flow by the area. Ten gallons per minute is 2,310 cubic inches per minute; against a 12.57 in² bore that is 184 in/min, or about 3 in per second. Retracting on the smaller annulus area, the same flow gives a faster rod — which is why cylinders usually come back quicker than they go out.
It is the theoretical force from the pressure that actually reaches the port. Real output is lower: pressure drops through hoses and valves, seals add friction, and back-pressure on the return side pushes against the piston. Treat the calculated figure as the ceiling and design with margin — and never above the cylinder's rated working pressure.
The pressure the system will really see at the cylinder port under load, which is normally the relief valve setting. Using the pump's maximum catalog rating overstates the force; using the gauge reading at no load understates it. If you want the worst case for a structural check, use the relief setting.
Extending, the cap end fills with the bore area times the stroke. A 4 in bore with a 24 in stroke takes 301.6 in³, or 1.31 gallons. Retracting takes less — the annulus area times the stroke — and sends the larger cap-end volume back to tank, which is what sizes the return line and the reservoir.
Yes, and not only for buckling. A larger rod reduces the annulus area, so retracting is faster at the same flow and the return volume is smaller. What you give up is pull force. Rod sizing is a manufacturer's calculation that also covers column buckling at full extension and side loading — it is not something to settle from this page.
Lower or block the load and bleed the pressure. A cylinder holding a load stores energy whether the pump runs or not, and 29 CFR 1910.147(d)(5)(i) requires all potentially hazardous stored or residual energy to be relieved, disconnected, restrained or otherwise rendered safe once lockout devices are on. Blocking the load mechanically is not optional just because a valve is closed.
Sources & references
- U.S. Navy — Fluid Power, NAVEDTRA 14105 (Nonresident Training Course, approved for public release): Pascal's law, "the force acting on each piston is directly proportional to its area, and the magnitude of each force is the product of the pressure and the area", the differential-area case, and the flow equation Q = vA — Public-domain U.S. Navy training course. The PDF is hosted by the San Francisco Maritime National Park Association.
- NIST Special Publication 811 — Guide for the Use of the International System of Units: US gallon = 3.785 411 784 × 10⁻³ m³ exactly, 1 in = 25.4 mm exactly, 1 bar = 100 kPa
- 29 CFR 1910.147(d)(5)(i) — after lockout or tagout devices are applied, all potentially hazardous stored or residual energy must be relieved, disconnected, restrained or otherwise rendered safe
- 29 CFR 1910.212(a)(1) — machine guarding: one or more methods must be provided to protect operators from hazards such as points of operation, ingoing nip points and rotating parts
Content checked against these sources — last reviewed September 1, 2026.