Hydraulic Cylinder & Pump Calculator
Work out a hydraulic cylinder’s push and pull force, the pressure or bore a load needs, its speed and stroke time, and the power a hydraulic or water pump takes, in psi, bar, MPa, gpm or L/min.
How to Use
- Choose what to work out: the cylinder’s Force, the Pressure a load needs, the Bore a load needs, Speed & time, a hydraulic Pump’s power, or a Water pump’s power from its head.
- For a cylinder, pick Extend (oil on the full bore) or Retract (oil on the rod side), then enter the bore, the rod diameter and the pressure or load, each with its unit.
- Add the pump flow and the stroke length to get the speed and the time for one stroke each way; leave them blank if you only need the force.
- For a pump, enter the flow, the pressure (or the head for a water pump) and the efficiency; the shaft power is the hydraulic power divided by the efficiency.
- The answer appears in the highlighted field and the first readout; the table under the drawing gives both directions and other units.
- Press a preset to load a log splitter, an excavator boom cylinder, a car lift or a garden water pump.
Worked Example
A log splitter. A 4 in bore has A = π × 4² ÷ 4 = 12.566 in². At 2,500 psi it pushes F = 2,500 × 12.566 = 31,416 lbf, about 15.7 short tons. An 11 gpm pump delivers 11 × 231 = 2,541 in³/min, so the rod moves at 2,541 ÷ 12.566 = 202.2 in/min (3.37 in/s) and a 24 in stroke takes 7.12 s.
A garden water pump. 2 m³/h is 0.000556 m³/s. Lifting it through 30 m of head takes ρgQH = 998.2 × 9.80665 × 0.000556 × 30 = 163.2 W of water power. With a pump that is 50% efficient the motor must deliver 326.3 W, and the 30 m of head is a pressure rise of 2.937 bar (42.59 psi).
The common mistake: using the full bore area for the pull. The same splitter cylinder has a 1.75 in rod, so on the return stroke the oil only acts on the annulus π(4² − 1.75²) ÷ 4 = 10.161 in². The pull is 2,500 × 10.161 = 25,403 lbf, not 31,416 lbf; taking the full bore overstates it by 23.7%. The same area difference makes the return faster: 5.76 s for the 24 in stroke instead of 7.12 s.
Show Work
Formulas
From Pascal’s Law to the Hydraulic Press
A hydraulic cylinder is Pascal’s law put to work: pressure applied to a confined liquid acts equally in every direction, so a small force on a small piston becomes a large force on a large one. Blaise Pascal set the principle out in his treatise on the equilibrium of liquids, published in 1663, the year after his death, and the SI unit of pressure carries his name.
Joseph Bramah, the London locksmith and inventor, patented the hydraulic press in 1795. Its leather cup seal, which the pressure itself pressed tighter against the cylinder wall, is the ancestor of the seals in every cylinder today. In the 1840s William Armstrong built water-powered hydraulic cranes on the Newcastle quayside, and hydraulic machinery driven from pumped accumulators went on to work dock cranes, lifts and the bascules of Tower Bridge, opened in 1894.
Modern machines use oil instead of water and pressures of 200 to 350 bar, but the sums have not changed: force is pressure times area, speed is flow divided by area, and power is flow times pressure.
About This Tool
This calculator solves F = p × A for the force, the pressure or the bore, on the extend side (full bore) or the retract side (bore minus rod), and with a flow and a stroke it gives the speed and the time for each direction, the oil volume per stroke and the hydraulic power. The pump modes give the power to drive a hydraulic pump from flow and pressure, or a water pump from flow and head, with the head converted to pressure and back using the liquid’s density (998.2 kg/m³ for water at 20 °C, from the CRC Handbook).
The results are ideal: real cylinders lose a few percent to seal friction, and a relief valve setting is the most a system can give, not what it always gives. Everything runs in your browser; nothing you enter is sent anywhere.
Related tools: Fluid Flow Calculator, Force Calculator, and Moment of Inertia & Centroid Calculator.
Frequently Asked Questions
How do you calculate hydraulic cylinder force?
Multiply the pressure by the piston area: F = p × A, with A = πD²/4. A 4 in bore has 12.566 in², so at 2,500 psi it pushes 2,500 × 12.566 = 31,416 lbf, which is 15.7 short tons or 139.7 kN.
Why does a cylinder pull with less force than it pushes?
On the way back the oil acts on the ring around the rod, not the whole piston. With a 1.75 in rod in a 4 in bore the annulus is π(4² − 1.75²)/4 = 10.161 in², so at 2,500 psi it pulls 25,403 lbf, and with the same flow it retracts 1.24 times faster.
How fast will a hydraulic cylinder move?
Speed is flow divided by area, v = Q ÷ A. 11 gpm is 2,541 in³/min; into a 4 in bore (12.566 in²) that is 202.2 in/min or 3.37 in/s, so a 24 in stroke takes 7.12 s out and 5.76 s back with a 1.75 in rod.
How much horsepower does a hydraulic pump need?
Hydraulic horsepower is gpm × psi ÷ 1,714. 20 gpm at 2,500 psi is 29.17 hp; divide by the pump efficiency for the motor, so at 85% it needs 34.3 hp. In metric, kW = L/min × bar ÷ 600: 40 L/min at 200 bar is 13.33 kW, or 15.69 kW at the shaft.
How do I convert pump head to pressure?
Use Δp = ρgH. For water at 20 °C (998.2 kg/m³) each 10 m of head is 0.979 bar (97.9 kPa), and 1 psi lifts water 2.311 ft. A pump delivering 30 m of head raises the pressure by 2.937 bar, or 42.59 psi.
How do I use the Hydraulic Cylinder & Pump Calculator?
Just type your numbers. The answer shows up right away — there is no button to press. Change anything and it updates by itself.
Is it free? Does it work without internet?
Yes to both. It is free with no sign-up, and once the page has loaded it keeps working even with no internet.
Where does my data go?
Nowhere — every calculation runs on your own device. Nothing you enter is uploaded, logged, or stored.
Common Use Cases
Log splitters
A 4 in cylinder at 2,500 psi pushes 31,416 lbf (15.7 tons). Running 11 gpm at that pressure would take 16.04 hydraulic hp, which is why splitters use two-stage pumps that drop the flow when the pressure rises.
Excavators and loaders
A 125 mm bore, 90 mm rod cylinder at 250 bar pushes 306.8 kN and pulls 147.8 kN; 120 L/min moves it 1.2 m in 7.36 s out and 3.55 s back.
Lifts and presses
Raising 3,000 kg on a 100 mm ram needs 37.46 bar (543.3 psi), plus whatever friction and the ram’s own weight add.
Sizing a cylinder
50 kN at 200 bar needs at least a 56.42 mm bore; the next ISO 3320 size up is 63 mm.
Water pumps
Lifting 2 m³/h through 30 m of head is 163.2 W of water power; a pump that is 50% efficient needs 326.3 W at the shaft.
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