The hydraulic cylinder force calculator above works out what a linear actuator will actually do at a given supply pressure. It gives you the extend force from the full piston area, the retract force from the reduced annulus area on the rod side, the rod speed in each direction from your pump flow, and the oil volume one extend stroke consumes. Together they determine whether a cylinder suits a job; any one read in isolation will mislead you.
Arb Digital builds free engineering calculators that keep the geometry visible rather than collapsing it into a single output. The point of separating push from pull on this page is that the difference is not a small correction. With a common bore-to-rod ratio the retract force is around two thirds of the push force while the retract speed is around fifty per cent higher, and a mechanism designed around the push figure alone will be undersized in one direction and overspeed in the other.
What This Hydraulic Cylinder Calculator Does
It converts pressure and geometry into force, and flow and geometry into speed. Force comes from pressure multiplied by the area the pressure acts on. On the extend stroke that is the full circular face of the piston. On the retract stroke the rod passes through the middle of the pressurised chamber, so the effective area is the piston area minus the rod cross-section — an annulus rather than a full circle.
Speed comes from the same areas used the other way round. A pump delivers a volume per unit time, and that volume must fill the space the piston vacates, so dividing flow by the area being filled gives the rod velocity. Because the annulus is smaller than the full bore, the same pump drives the rod back faster than it drives it out. The oil volume figure is the swept volume of one extend stroke, which sizes a reservoir and sets how many cycles a fixed-displacement system delivers per minute.
The efficiency field applies to force only, not speed. Seal friction and side loading consume pressure without producing useful output, so the force reaching the workpiece is lower than the ideal figure. Volumetric losses in a healthy cylinder are negligible by comparison, so the speed calculation uses raw flow. If a cylinder leaks internally enough to matter, only a flow test will characterise it.
How to Use It
- Set the unit system first. Switching converts the values already entered, so you can type a bore in millimetres, flip to imperial and read the force in pounds without re-entering anything.
- Enter the bore, not the tube outside diameter. The bore is the internal diameter the piston seals against. Using the outside of the barrel typically overstates the area by twenty to thirty per cent, which is a very large error in a force figure.
- Use the relief valve setting for pressure. The pressure that matters is the highest the circuit will actually reach under load, which is what the relief valve caps. A pump rated to 250 bar in a circuit relieving at 160 bar delivers 160 bar of force.
- Enter the pump flow reaching this cylinder. If a single pump feeds several actuators simultaneously, only its share drives this rod, and the speed figures will be optimistic otherwise.
- Read the push and pull bars together. Check that the weaker retract direction still clears your load requirement before you commit to a bore size.
The Formula: How Cylinder Force Is Calculated
Force is pressure times area, which is Pascal's principle applied to a piston: pressure applied to a confined fluid is transmitted undiminished throughout it, so the pressure at the piston face equals the pressure the pump delivers, less line losses. OpenStax University Physics Volume 1, section 14.3 on Pascal's principle and hydraulics, derives this and shows why a hydraulic system multiplies force in proportion to the ratio of the two piston areas.
The extend force is Fpush = p × πD2/4, and the retract force is Fpull = p × π(D2 − d2)/4, where D is the bore and d is the rod diameter. Work the defaults through. A bore of 80 mm gives a piston area of π × 802 ÷ 4 = 5,026.5 mm2. A pressure of 160 bar is 16 N/mm2, so the ideal push force is 5,026.5 × 16 = 80,425 N, or 80.4 kN. At 95 per cent efficiency that becomes 76.4 kN, roughly 7.8 tonnes of thrust.
Now the rod side. A 45 mm rod has a cross-section of 1,590.4 mm2, leaving an annulus of 5,026.5 − 1,590.4 = 3,436.1 mm2. The ideal pull force is 3,436.1 × 16 = 54,978 N, or 55.0 kN, which is 52.2 kN after efficiency — just under 68 per cent of the push figure. For speed, 30 L/min is 500,000 mm3/s, so the extend velocity is 500,000 ÷ 5,026.5 = 99.5 mm/s and the retract velocity is 500,000 ÷ 3,436.1 = 145.5 mm/s. A 500 mm stroke therefore takes 5.03 seconds out and 3.44 seconds back, and consumes 2.51 litres of oil on the way out.
Why the Rod Side Is Always Weaker and Always Faster
This is the single most useful thing to internalise about a differential cylinder, and it follows from one piece of geometry: the rod takes up space on one side of the piston and not the other. The pressurised area on retract is reduced by exactly the rod's cross-section, so force falls in the same proportion that speed rises. The product of force and speed — the power delivered — stays the same in both directions, which is the expected result for a fixed pump flow at fixed pressure.
The ratio matters when the load is not symmetrical. A press pushes hard and returns unloaded, so a large rod is fine and the faster return is a bonus. A cylinder that pulls a stuck component is working in its weak direction, and sizing it on the push figure leaves it short. Check the retract number against the worst case in that direction before deciding the bore.
Rod diameter also carries a second constraint that has nothing to do with force. A long rod in compression can buckle, and buckling depends on rod diameter, extended length and how the cylinder is mounted. That failure mode is not in this calculator and cannot be inferred from the force figures, because a rod can be strong enough in pure compression and still fail as a column. Long-stroke cylinders in compression need a buckling check from the manufacturer's tables or a qualified engineer.
Pressure at the Cylinder Is Not Pressure at the Pump
Every metre of hose, every fitting and every valve costs pressure when oil is flowing. The gauge at the power pack reads higher than the pressure reaching the piston, and the gap grows with flow rate, hose length and oil viscosity. On a short, generously sized circuit the loss may be a few bar; on a long run of undersized hose with cold oil it can be tens of bar, a directly proportional loss of force.
The pressure that appears in this calculation is the pressure at the cylinder port under working flow. If you are checking a real machine, that is what a gauge teed in at the port will read while the cylinder is moving against its load, not what the power pack shows at rest. Note also that hydraulic gauges read gauge pressure, above atmospheric, which is exactly the quantity this calculation needs; OpenStax University Physics Volume 1, section 14.2 on measuring pressure, sets out the difference between gauge and absolute pressure and why instruments report the former. Our pipe flow calculator and flow rate calculator cover the velocity and pressure-drop side of the plumbing, and the pressure converter moves cleanly between bar, psi, MPa and the other units that appear on hydraulic datasheets.
What This Page Does Not Cover
A force figure is not a design. This calculator tells you the thrust available from a given bore and pressure; it says nothing about whether the barrel wall, the rod end, the mounting pins, the pin brackets or the structure behind them can carry that thrust. Those are strength calculations against material properties and safety factors, and this page publishes no allowable-stress data of any kind and deliberately offers none.
The same boundary applies to the fluid side. Hose burst ratings, cylinder pressure ratings, relief settings and the load-holding valves required on anything that could fall are safety-critical selections governed by standards and by the manufacturer's limits. Treat the numbers here as the physics input to a design that a qualified engineer signs off, and follow the manufacturer's ratings wherever they differ. That is the same rule we state on the breaker size calculator, where a calculated figure is a starting point and the governing document is the code and the person qualified to apply it.
Regeneration, Intensification and Two Circuit Surprises
Two circuit arrangements produce results this simple model will not predict, and both surprise people the first time they meet them. The first is regeneration, where the rod-side oil is routed back to join the pump flow on the bore side instead of returning to tank. The cylinder then extends at a speed set by the rod area rather than the bore area, which is much faster, but the effective pressurised area drops to the rod cross-section alone, so the available force collapses to roughly what the rod area gives. It is a fast-approach trick, not a working stroke.
The second is intensification. If an external load drives the cylinder in the extend direction while the rod-side return is restricted, pressure on the small annulus can rise well above supply pressure, in the ratio of bore area to annulus area. A cylinder fed at 160 bar can develop several hundred bar on the rod side. This is a known cause of seal and port failures on overhauling loads, and one reason counterbalance valves exist.
Choosing a Bore From a Load
Most real problems run backwards from the one this tool solves directly: you know the force you need and want the bore. Work it by hand in one step. Required area equals required force divided by working pressure, then diameter equals the square root of four times that area divided by π. For 50 kN at 160 bar, the area is 50,000 ÷ 16 = 3,125 mm2, giving a diameter of 63.1 mm — so you would specify the standard 63 mm bore and confirm it here with the efficiency applied.
Then check what the first pass hides. Does the retract force still clear the load in that direction? Does the pump flow give a workable rod speed at the larger bore? Does the swept volume per cycle fit the reservoir and cooling capacity? The cylinder volume calculator is useful for the reservoir side, and the force converter translates between newtons, kilonewtons, tonnes-force and pounds-force when a specification and a datasheet disagree on units.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Using the barrel outside diameter as the bore — force scales with the square of diameter, so a 10 per cent error in diameter is a 21 per cent error in thrust.
- Sizing on push force when the load pulls — the retract stroke is typically 60 to 75 per cent as strong, and that direction is the one that fails.
- Taking the pump's rated pressure as the working pressure — the relief valve setting caps what the circuit reaches, and line losses reduce it further at the port.
- Ignoring rod buckling on long strokes — a rod can be perfectly strong in compression and still fail as a slender column, which no force calculation reveals.
- Assuming the return stroke takes the same time — the same pump flow into a smaller annulus moves the rod substantially faster, which changes cycle time and shock loading.
Related Free Tools From Arb Digital
For pressure produced by a column of fluid rather than by a pump, the hydrostatic pressure calculator handles depth, density and gravity, while the general pressure calculator solves pressure, force and area for any flat surface. On the plumbing side, the pipe flow calculator and flow rate calculator relate pipe size to velocity and volumetric flow. For rotary rather than linear actuation, the motor torque calculator covers the equivalent problem on a shaft, and the mechanical advantage calculator handles the lever and linkage that usually sits between a cylinder and its load. Everything Arb Digital publishes is on the free online tools hub.
Frequently Asked Questions
Because the rod occupies part of the piston face on the retract side. The pressurised area becomes an annulus equal to the piston area minus the rod cross-section, so the force falls in exactly that proportion while the rod speed rises by the same factor.
The pressure at the cylinder port while it is moving under load, which is normally set by the relief valve rather than by the pump's maximum rating. Hose, fittings and valves all drop pressure at working flow, so the reading at the power pack overstates what reaches the piston.
No. On the extend stroke the pressure acts on the full circular face of the piston, so only the bore matters. The rod diameter affects the retract force, the retract speed and the oil volume returning to tank.
Divide the required force by the working pressure to get the area needed, then take the square root of four times that area divided by pi to get the diameter. Round up to the next standard bore and re-check the retract direction and the resulting rod speed.
Ninety to ninety-five per cent is typical for a cylinder in good condition with correctly aligned mounting. Side loading, worn seals and misalignment push it lower, and no calculator can tell you where a particular cylinder sits — that requires measuring it under load.
No. It computes the force available from bore, rod and pressure only. Barrel wall stress, rod buckling, mounting and pin strength, and the pressure ratings of the components are separate design checks that a qualified engineer must carry out against the manufacturer's data.
That tool computes the pressure a column of static fluid produces at a given depth, which depends on density and gravity. This page starts from a pressure a pump supplies and converts it into actuator force and rod speed. One is fluid statics; the other is power transmission.
This tool is provided for educational and estimating use. It models ideal piston areas with a user-supplied efficiency factor and performs no strength, buckling, pressure-rating or safety assessment. Hydraulic equipment selection must follow the manufacturer's ratings and be signed off by a qualified engineer.
