Hydraulic Cylinder Force Calculator
The Hydraulic Cylinder Force Calculator computes push force (F = P × πD²/4), pull force with rod deduction, cylinder speed from pump flow rate, and hydraulic power (HP = P×Q/1714). It features an interactive SVG cross-section diagram with force arrows and covers bore sizes from 1" to 12" — free, no signup required.
Cylinder Specifications
Cylinder Size Reference
| Size | Bore (in) | Rod (in) | Bore (mm) | Rod (mm) |
|---|---|---|---|---|
| 1" bore / 5/8" rod | 1 | 0.625 | 25.4 | 15.9 |
| 1-1/2" bore / 5/8" rod | 1.5 | 0.625 | 38.1 | 15.9 |
| 1-1/2" bore / 1" rod | 1.5 | 1 | 38.1 | 25.4 |
| 2" bore / 1" rod | 2 | 1 | 50.8 | 25.4 |
| 2" bore / 1-1/4" rod | 2 | 1.25 | 50.8 | 31.8 |
| 2-1/2" bore / 1-1/4" rod | 2.5 | 1.25 | 63.5 | 31.8 |
| 2-1/2" bore / 1-1/2" rod | 2.5 | 1.5 | 63.5 | 38.1 |
| 3" bore / 1-1/2" rod | 3 | 1.5 | 76.2 | 38.1 |
| 3" bore / 2" rod | 3 | 2 | 76.2 | 50.8 |
| 3-1/4" bore / 2" rod | 3.25 | 2 | 82.5 | 50.8 |
| 4" bore / 2" rod | 4 | 2 | 101.6 | 50.8 |
| 4" bore / 2-1/2" rod | 4 | 2.5 | 101.6 | 63.5 |
| 5" bore / 2-1/2" rod | 5 | 2.5 | 127.0 | 63.5 |
| 5" bore / 3" rod | 5 | 3 | 127.0 | 76.2 |
| 6" bore / 3" rod | 6 | 3 | 152.4 | 76.2 |
| 6" bore / 4" rod | 6 | 4 | 152.4 | 101.6 |
| 7" bore / 3-1/2" rod | 7 | 3.5 | 177.8 | 88.9 |
| 8" bore / 4" rod | 8 | 4 | 203.2 | 101.6 |
| 8" bore / 5" rod | 8 | 5 | 203.2 | 127.0 |
| 10" bore / 5" rod | 10 | 5 | 254.0 | 127.0 |
| 12" bore / 6" rod | 12 | 6 | 304.8 | 152.4 |
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What is Hydraulic Cylinder Force?
Hydraulic cylinder force is the linear force produced by pressurized oil acting on the piston area inside a cylinder. Extension (push) force equals pressure × bore area: F = P × π × D²/4. Retraction (pull) force is reduced because the rod displaces part of the piston area: F = P × π × (D² − d²)/4, where d is the rod diameter. A 4" bore cylinder at 3,000 psi produces 37,699 lbs of push force. Cylinder speed depends on oil flow rate: v = Q / A, where Q is the volumetric flow rate and A is the effective piston area.
How to Use This Calculator
- Enter the cylinder bore diameter and rod diameter in inches
- Enter the system hydraulic pressure in PSI
- Enter the stroke length for volume and timing calculations
- Enter the pump flow rate (GPM) for speed calculations
- Click Calculate to see push/pull forces, extend/retract speeds, and hydraulic power
Frequently Asked Questions
Why is retraction force less than extension force?
During retraction (pull), oil pushes on the rod-side annular area, which is the bore area minus the rod cross-section area. The rod takes up space, reducing the effective area. For example, a 4" bore with 2" rod has a bore area of 12.57 in² but an annular area of only 9.42 in² — about 25% less. This means the pull force is 25% less than the push force at the same pressure.
How do I calculate cylinder speed?
Cylinder speed = Flow Rate / Area. For extension: speed (in/min) = (GPM × 231) / bore area (in²). For retraction: speed = (GPM × 231) / annular area. Since the annular area is smaller, the retract speed is faster than extend speed for the same flow rate. The factor 231 converts gallons to cubic inches.
What is the standard hydraulic pressure for mobile equipment?
Most mobile hydraulic systems operate at 2,000–3,000 psi. Agricultural equipment typically uses 2,000–2,500 psi. Construction equipment (excavators, loaders) operates at 3,000–5,000 psi. Industrial presses can reach 5,000–10,000 psi. The system pressure is limited by the pump capacity and the weakest component rating.
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