SizingKitMechanical · Hydraulic actuators
Hydraulic cylinder force, speed and flow
Enter a bore, a rod diameter and the gauge pressure at the port and this gives push and pull in tons, kilonewtons and pounds-force. Enter the pump flow as well and it gives the half that decides the machine: travel speed in each direction, the time each stroke takes, the oil the tank turns over per cycle, and the return flow — which on the retract stroke comes back larger than the pump ever sent, in the ratio of the two piston areas. Free, no signup, and both the standard and the regenerative connection are worked.
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- Speed and cycle time
- Return-flow multiplier
- Regen circuit
The cylinder and the power unit
Pressure and area give the force. Flow and area give the speed, the cycle time and the size of every line on the drawing — including the one that carries more oil than the pump ever sent.
Tube inside diameter. Doubling it quadruples the force and quarters the speed at the same pump flow.
Gives an area ratio of 1.333:1. A rod at 0.707 of the bore is the catalog 2:1.
Sets the cycle time and the oil per cycle, and nothing about the force.
The pressure available at the cylinder port, which is the relief setting less what the valve and hoses take. Gauge, not absolute — the atmosphere is on both sides of the piston and cancels.
Delivered at working pressure, not displacement times shaft speed — a worn gear pump slips several percent of its theoretical output back to tank.
Default 85% — ISO 4409 defines how a hydraulic pump's overall, volumetric and hydro-mechanical efficiencies are measured, and the number itself is published per model on the manufacturer's own performance curve. 0.85 is this page's starting figure, not a table on this site.
EXTEND FORCE
7.07 tons
14,137 lbf · 62.9 kN
TIME OUT AND BACK
7.71 s
4.41 s out, 3.3 s back
PEAK RETURN FLOW
13.3 GPM
50.5 L/min through the filter
| Cap-end area | 7.0686 in² 4560 mm² |
|---|---|
| Rod-end area | 5.3014 in² 3420 mm² |
| Area ratio, cap to rod end | 1.333:1 rod is 0.5× the bore |
| Extend force | 14,137 lbf 62.9 kN · 7.07 tons |
| Retract force | 10,603 lbf 47.2 kN · 5.3 tons |
| Extend speed | 5.45 in/s 0.14 m/s |
| Retract speed | 7.26 in/s 0.18 m/s |
| Stroke time, out then back | 4.41 s / 3.3 s 7.71 s per cycle, valve shift excluded |
| Return flow while retracting | 13.3 GPM 50.5 L/min |
| Return flow while extending | 7.5 GPM 28.4 L/min |
| Oil the pump delivers per cycle | 1.285 gal 4.86 L · 296.9 in³ |
| Fluid power, and at the pump shaft | 11.7 hp 8.7 kW · 13.7 hp in at 85% |
The binding number on this drawing is not the force. Retracting, the cap end empties at 13.3 GPM while the pump is only sending 10 GPM — the area ratio multiplies it, and every hose, port, directional valve and return filter downstream of the cap end has to carry that larger figure, not the pump’s. Sizing the return line to the pump rating is the standard way a system ends up with a blown filter element, a cracked case drain and a cylinder that will not come back under load.
Retraction is the weaker and faster direction, and by exactly the same factor: 1.333:1 less force, 1.333:1 more speed, because the pump is filling a smaller area. A cylinder chosen for its push is therefore sized on the cap end and timed on the rod end, and a machine that has to pull hard wants the rod on the working side — which is why a press has the rod down and a log splitter does not.
Everything above is the ideal cylinder: gauge pressure acting on machined areas, with no allowance for seal friction, for the pressure drop across the directional valve and hoses, or for the load the cylinder is pushing against being anything but resistive. Rod speed is reported without judgement because the limit belongs to the seal, not to the arithmetic — seal manufacturers publish a maximum surface speed per material and this site carries no such table, so take it from the catalog for the seal actually fitted. Fluid power is pressure times flow; the shaft figure divides it by an efficiency that belongs to your pump’s own curve rather than to a class of pump. Roughly 80–85% for an external gear pump, 80–88% for a vane pump and 88–93% for an axial piston pump, falling with wear, with low shaft speed and with thin hot oil. Read it off the pump curve at your working pressure and speed before quoting an input horsepower to anyone.
Turning that shaft power into a motor is a separate step — torque and speed against horsepower — and it has to be done at the peak of the duty cycle rather than the average, because a hydraulic pump against a relief valve draws full power while achieving nothing. The compressed-air version of this cylinder answers a different question again: air is compressible, so there the piston sits on a spring and the interesting figure is consumption rather than cycle time. None of this is a stamped design — burst rating, rod buckling, mounting and the relief setting that protects all three are the manufacturer’s and a qualified engineer’s.
How to work a cylinder for force and cycle time at once
Pressure buys the force. Flow buys the speed, and decides the size of every line on the drawing.
Give it the two diameters and the pressure at the port
Bore and rod set the two working areas and the ratio between them, which is the single number that governs how differently the cylinder behaves in each direction. Use the pressure actually available at the cylinder, which is the relief setting less whatever the directional valve, the hoses and the fittings take on the way — a long 1/2 in hose at 15 GPM can be worth a couple of hundred psi on its own. The field is gauge because the atmosphere presses on both sides of the piston and cancels out of the force entirely.
Enter the pump's delivered flow, not its displacement
Flow is what makes the rod move, and the figure that matters is what the pump delivers at working pressure rather than displacement times shaft speed. A gear pump slips a few percent back through its own clearances and more as it wears, so the catalog theoretical flow is optimistic exactly when the machine is under load. With flow entered the page gives extend and retract speed, the time each stroke takes and the volume the tank has to turn over every cycle.
Read the return-flow row before you size anything
Retracting, the cap end has to empty at the pump flow multiplied by the area ratio — 13.3 GPM out of a cylinder fed by a 10 GPM pump on a 1.33:1 rod, and 20 GPM on a 2:1. That larger figure is what the return hose, the tank port, the directional valve's T passage and the return filter all have to pass. Switch the circuit selector to regenerative and the same arithmetic runs the other way: the cap-end port then carries pump flow plus the recycled rod-end oil, which on the worked example is four times the pump's rating.
Technical specifications
| Force model | Extend = p·(π/4)·D², retract = p·(π/4)·(D² − d²), with p the gauge pressure at the cylinder port. Seal friction, valve and hose pressure drop and any load-induced back pressure on the opposite side are excluded and all subtract |
|---|---|
| Speed and time | Piston velocity is delivered pump flow divided by the area being filled, so extend speed uses the full bore and retract speed the annulus. Stroke time excludes valve shift, acceleration and deceleration ramps, which on a fast short stroke are a real fraction of the cycle |
| Return flow | Pump flow × area ratio while retracting, pump flow ÷ area ratio while extending. This is the row that sizes the return hose, the tank port, the valve T passage and the filter — none of which see the pump's rating |
| Regenerative connection | Net area is the rod cross-section, so force falls and speed rises by the area ratio, and the cap-end port carries pump flow × (bore area ÷ rod area). Modeled with both faces at system pressure and no allowance for the drop across the regeneration path |
| Power | Fluid power is pressure × flow, worked in pascals and m³/s and reported in hp and kW. Shaft power divides by an editable overall efficiency, default 85%; ISO 4409 defines how a pump's efficiencies are measured and the value belongs to the individual pump curve |
| Input ranges | Gauge pressure 0–10,000 psi, pump flow 0–500 GPM, rod strictly smaller than the bore. A rod diameter of zero is refused rather than treated as a ram, because a ram has no return stroke to time |
| Worked example | 3 in bore, 1.5 in rod, 24 in stroke, 2,000 psi, 10 GPM: 7.07 tons out and 5.30 tons back, 5.45 in/s out and 7.26 in/s back, 4.41 s and 3.30 s, 13.3 GPM back through the return line, 1.285 gal of oil per cycle, 11.7 hp of fluid power and 13.7 hp at the shaft |
| Not carried here | The maximum rod surface speed, which belongs to the seal material and is published per compound by the seal manufacturer; rod buckling on a long stroke; and burst ratings. This page reports the speed and leaves the limit to the catalog for the parts actually fitted |
Frequently asked questions
Why does my return filter blow its bypass on the way back?
Because the cap end empties faster than the pump fills anything. On the retract stroke the pump is filling the small rod-side area, so the piston travels quicker, and the large cap-side area has to discharge at that speed — the flow leaving is the pump flow multiplied by the area ratio. A 4 in bore with a 2 in rod is 1.33:1, a 4 in bore with a 2.83 in rod is 2:1, and on the second one a 20 GPM pump produces 40 GPM through the return line. Filters, tank ports and valve return passages are routinely sized to the pump nameplate, and that is the mistake.
Is the cylinder faster or stronger with a bigger rod?
Faster in retract, weaker in retract, and completely unchanged in extend. The rod does not touch the cap-end area, so the push is the same whatever rod is fitted; it eats into the annulus, so pull force falls and pull speed rises in the same proportion. That proportion is the whole design decision: a 2:1 cylinder retracts at twice the speed and half the force of its own extend stroke, which suits a press returning to the top, while a 1.5:1 rod suits a machine that has to work in both directions. A rod also has to be sized for buckling on a long stroke, which is a column problem and not an area one.
How do I work out the motor for the power unit?
Fluid power is pressure times flow and nothing else — 2,000 psi at 10 GPM is 11.7 hp, or 8.7 kW — and the shaft needs that divided by the pump's overall efficiency, giving about 13.7 hp at 85%. Two things then decide the motor. It has to be sized on the worst moment of the duty cycle rather than the average, because a pump held against the relief valve draws full power and produces only heat. And if the peak is brief and the duty is light, a smaller motor with an accumulator or a variable-displacement pump does the same job, which is where the real energy saving on a power unit lives.
What happens if I set the relief valve higher to get more force?
Force rises in proportion and so does every stress in the circuit, which is why the setting is not yours to choose alone. The cylinder has a rated working pressure stamped on it, the hoses carry a working pressure and a burst pressure, and the pump has a maximum continuous rating that is often lower than its intermittent one. Raising the relief also raises the power the motor draws at stall and the heat the system rejects, and heat is what kills hydraulic oil and seals. The correct move when a machine is short of force is nearly always a larger bore, because force goes with the square of it.
Why does my cylinder creep down under load with the valve closed?
Oil is close to incompressible, so the movement you are seeing is leakage rather than compliance — past the piston seal, through the directional valve spool clearance, or through a worn check. A spool-type directional valve is not a seal and never was; every one of them leaks a small measured flow across the land, which is why a load that must be held is held on a pilot-operated check valve or a counterbalance valve mounted at the cylinder port rather than at the valve bank. The remaining compliance is the trapped oil itself plus the hoses swelling, and it is small enough to feel solid.
Does a regenerative circuit really make the cylinder faster for free?
It is faster and it is not free — the speed is bought with force in exactly the area ratio. Returning the rod-end oil to the cap end puts system pressure on both faces, so the net area doing work is the rod cross-section alone: on a 3 in bore with a 1.5 in rod, 2,000 psi gives 3,534 lbf regenerating against 14,137 lbf in the normal connection, while the speed goes from 5.5 in/s to 21.8 in/s. It is a rapid-approach circuit and has to be switched out the moment the tool touches the work.
Do I use the bore or the rod-end area to size the tank?
Neither on its own — a reservoir is sized on the flow the pump turns over and on the heat the circuit has to shed, not on the cylinder's swept volume, because its job is to give the oil dwell time to release air and lose heat rather than to hold a stroke. The multiple of pump flow that gets quoted for that dwell time is shop convention rather than a standard, it varies by a factor of three between a stationary power unit and a mobile machine with a cooler, and this page does not supply one. What the cylinder does contribute is the differential volume: an unequal-area cylinder sends back more oil than it took on the retract stroke and less on the extend, so the tank level moves by the rod volume every cycle and the sight glass has to cover both ends of that swing.
About the area ratio, and why it decides everything
Hydraulic oil is close enough to incompressible that a cylinder behaves as a solid link between the pump and the load, and that one property is what the whole discipline is built on. It means force is pressure times area with nothing else in it, and it means velocity is flow divided by area with nothing else in it either. The two share the same denominator, which is why they cannot be chosen independently: at a fixed pump, a cylinder twice the bore gives four times the force at a quarter of the speed, and no arrangement of valves changes that trade. Everything interesting about a real cylinder comes from the fact that its two ends do not have the same area, because the rod occupies part of one of them.
That asymmetry is quoted as the area ratio, and catalog cylinders are built to nominal values of it — 1.5:1, 2:1 — by choosing the rod against the bore. A 2:1 cylinder needs a rod at 0.707 of the bore, which is where that odd-looking number on a data sheet comes from: the rod removes exactly half the area when its diameter is the bore over the square root of two. The ratio then multiplies and divides everything in sight. Retract force is the extend force divided by it; retract speed is the extend speed multiplied by it; and the flow leaving the cap end while the cylinder comes back is the pump flow multiplied by it, which is the number this page exists to put in front of you. Sizing a return line, a tank port or a filter to the pump’s nameplate rating is the commonest expensive error in a hydraulic schematic, and the machine tells you about it by bypassing the filter under return flow, so the oil goes back to tank unfiltered exactly when it is dirtiest.
The last thing worth separating out is power, because two different powers get confused. Fluid power is pressure times flow and it is the useful output — 2,000 psi at 10 GPM is 11.7 hp. Shaft power is that divided by the pump’s own overall efficiency, and the difference between them becomes heat in the oil. What a beginner underestimates is that a pump held against its relief valve delivers zero useful power and draws the full shaft figure anyway, all of it into the tank, which is why a power unit that idles at pressure needs a cooler that a continuously working one does not. Sizing the motor from that shaft figure is a torque-and-speed question, and it is worth noting that the head-and-flow arithmetic used for a centrifugal water pump does not transfer here: a positive-displacement pump makes whatever pressure the circuit demands of it until something gives, which is precisely why a relief valve is not optional. Nothing on this page is a stamped design — working pressure, rod buckling, mounting style and the relief setting that protects all three belong to the manufacturer’s catalog and to a qualified engineer.
What happens to the circuit you type in
Every number on this page is worked out by JavaScript running in the tab you are reading it in. Nothing you type — loads, lengths, nameplate ratings, the rates your utility charges you — is uploaded, logged or kept, which is also why the calculators carry on working in a mechanical room with no signal.
Bores, rods, relief settings and pump ratings live in this tab only and vanish with it — there is nothing to sign into and no saved machine history, so a customer’s press specification does not end up on somebody else’s server.