Hydraulic Cylinder Calculator
A hydraulic cylinder calculator finds force as pressure times piston area: a 3 in bore at 2,000 psi pushes 14,137 lb and fills 0.306 gal on a 10 in stroke.
Hydraulic cylinder calculator
A hydraulic cylinder calculator multiplies system pressure by the area of the piston. A 3 inch bore at 2,000 psi pushes about 14,137 lb. On a 10 inch stroke it takes 0.306 gallons of oil to fill. Enter bore, pressure and stroke, and the force and volume update.
The formulas in plain words
- Piston area (sq in) = π × (bore ÷ 2)².
- Force (lb) = area × pressure in psi.
- Volume per stroke (cu in) = area × stroke in inches.
- Gallons = cubic inches ÷ 231.
Pressure acts on every square inch of the piston face at once. Force is that pressure added up over the whole face.
Worked examples
Defaults, 3 in bore, 2,000 psi, 10 in stroke:
- Area: π × 1.5² = 7.0686 sq in
- Force: 7.0686 × 2,000 = 14,137 lb
- Volume: 7.0686 × 10 = 70.686 cu in, ÷ 231 = 0.306 gal
A log splitter ram, 4 in bore, 2,500 psi, 24 in stroke:
- Area: π × 2² = 12.566 sq in
- Force: 12.566 × 2,500 = 31,416 lb, which is about 15.7 tons
- Volume: 12.566 × 24 = 301.6 cu in, ÷ 231 = 1.306 gal
A small jack, 2 in bore, 1,500 psi, 12 in stroke:
- Area: π × 1² = 3.1416 sq in
- Force: 3.1416 × 1,500 = 4,712 lb
- Volume: 3.1416 × 12 = 37.7 cu in, ÷ 231 = 0.163 gal
Force by bore size at 2,000 psi
| Bore | Piston area | Extend force |
|---|---|---|
| 2 in | 3.14 sq in | 6,283 lb |
| 2.5 in | 4.91 sq in | 9,817 lb |
| 3 in | 7.07 sq in | 14,137 lb |
| 4 in | 12.57 sq in | 25,133 lb |
| 5 in | 19.63 sq in | 39,270 lb |
Force grows with the square of the bore. Going from a 2 in to a 4 in bore doubles the diameter and quadruples the push.
Speed is a separate question
The calculator does not take a pump flow, but speed follows from the same area. Speed in inches per minute = gpm × 231 ÷ piston area. At 5 gpm into a 3 in bore, that is 5 × 231 ÷ 7.0686, about 163 in per minute, or 2.7 in per second.
If the ram is too slow, you need more flow, a smaller bore, or both. A smaller bore at the same pressure gives less force, which is the usual trade.
Extend versus retract
The numbers here describe the cap end, where oil pushes on the full piston face. On the way back the rod blocks part of that face. A 3 in bore with a 1.5 in rod has 7.0686 − 1.7671 = 5.3014 sq in left, and 5.3014 × 2,000 = 10,603 lb. The rod side also uses less oil per stroke, which is why a retracting cylinder is quicker than an extending one at the same flow.
Common mistakes
- Typing the rod diameter into the bore field.
- Using the pump’s maximum pressure when the relief valve is set lower.
- Forgetting that hose length and fittings add fluid volume to the reservoir calculation.
- Sizing a cylinder at its exact required force. Leave margin for friction, side loads and pressure spikes.
- Ignoring rod buckling on a long stroke. A long, thin rod loaded in compression can bend well below its force rating, so check the manufacturer’s rod chart.
Safety
Hydraulic systems store energy and a failed hose can inject oil under skin. Follow the cylinder’s rated pressure, use hoses and fittings rated above your relief setting, and have a qualified hydraulics technician check any system that lifts loads over people.
Related tools
The pump head calculator and flow rate calculator cover the water-system side of fluid power, and the tank volume calculator helps with reservoir sizing.
Frequently asked questions
How do you calculate hydraulic cylinder force?
Find the piston area from the bore, π × (bore ÷ 2)², then multiply by pressure in psi. A 3 in bore has 7.0686 sq in of area, and at 2,000 psi that gives 14,137 lb. Doubling the bore quadruples the area, so a 6 in bore at the same pressure pushes about 56,549 lb.
Why is retract force lower than extend force?
On the retract stroke, the rod takes up part of the piston face, so oil pushes on a smaller ring-shaped area. With a 3 in bore and a 1.5 in rod, that area is 5.30 sq in, which gives about 10,603 lb at 2,000 psi. This calculator reports the extend force, from the full bore.
How much fluid does a cylinder use per stroke?
Piston area times stroke length gives cubic inches, and dividing by 231 converts to US gallons. A 3 in bore with a 10 in stroke is 70.69 cubic inches, or 0.306 gal. Add the volume of hoses if you are sizing a reservoir.
What decides how fast the cylinder moves?
Pump flow divided by piston area. At 5 gpm into a 3 in bore, speed is 5 × 231 ÷ 7.0686, or about 163 inches per minute. More flow or a smaller bore makes it faster, but the same pressure then gives less force.
Is the pressure I enter the pump rating or the working pressure?
Enter the pressure the cylinder will actually see during the push, which is limited by the relief valve setting. Never enter more than the cylinder's rated pressure. Check the rating on the cylinder and have a qualified hydraulics technician review any system that lifts people or loads overhead.
Estimates only. Verify quantities with your supplier before purchasing.