Hydraulic Cylinder Force Calculator
Extension force, retraction force, cylinder speed, and required flow rate for any bore, rod, and pressure combination. Imperial (psi/in) and metric (bar/mm).
Extension force (push)
—
lb
Retraction force (pull)
—
lb
Flow for ext. speed
—
GPM
Retraction speed
—
in/min
Bore area
—
in²
Annular area
—
in²
Cycle time (full stroke)
—
sec (extend + retract)
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Common cylinder bore / rod combinations
| Bore (in) | Bore area (in²) | Common rod size | Annular area (in²) | Force @ 2000 psi (ext) | Force @ 2000 psi (ret) |
|---|---|---|---|---|---|
| 1.5" | 1.77 | 1" | 0.99 | 3,534 lb | 1,963 lb |
| 2" | 3.14 | 1.25" | 1.91 | 6,283 lb | 3,826 lb |
| 2.5" | 4.91 | 1.5" | 3.14 | 9,817 lb | 6,283 lb |
| 3" | 7.07 | 2" | 3.93 | 14,137 lb | 7,854 lb |
| 4" | 12.57 | 2" | 9.42 | 25,133 lb | 18,850 lb |
| 4" | 12.57 | 2.5" | 7.66 | 25,133 lb | 15,315 lb |
| 5" | 19.64 | 3" | 12.57 | 39,270 lb | 25,133 lb |
| 6" | 28.27 | 3.5" | 18.65 | 56,549 lb | 37,306 lb |
| 8" | 50.27 | 5" | 30.68 | 100,531 lb | 61,359 lb |
Hydraulic cylinder formulas
Bore area (in²) = π/4 × bore²
Annular area (in²) = π/4 × (bore² − rod²)
Extension force (lb) = pressure (psi) × bore area × efficiency
Retraction force (lb) = pressure (psi) × annular area × efficiency
Flow for ext speed (GPM) = bore area × speed (in/min) / 231
Flow for ret speed (GPM) = annular area × speed (in/min) / 231
Retraction speed (in/min) = (flow × 231) / annular area
Speed ratio explained
The extension-to-retraction speed ratio equals bore area divided by annular area. A 4" bore with 2" rod has a ratio of 12.57 / 9.42 = 1.33 — the cylinder retracts 33% faster than it extends at the same GPM. This is important for cycle time calculations and for matching pump flow to application requirements.
Common hydraulic pressure ranges
- Agricultural / low pressure: 500–1000 psi
- Mobile equipment (tractors, excavators): 2,500–3,500 psi
- Industrial hydraulics: 2,000–3,000 psi
- High-pressure systems (presses, tube bending): 5,000–10,000 psi
- Ultra-high (hydraulic torque tools): 10,000+ psi
Frequently asked questions
How do I select the right cylinder bore?
Calculate the required force first (what load are you moving, plus a 1.5–2× safety factor). Then: bore diameter = 2 × √(required force / (π × pressure × efficiency)). Round up to the next standard bore size. Standard bore diameters: 1.5", 2", 2.5", 3", 3.5", 4", 5", 6", 7", 8".
What is the 2:1 ratio rule for rod sizing?
A common rule is to size the rod at approximately half the bore diameter. A 4" bore gets a 2" rod. This gives roughly a 3:1 extension-to-retraction force ratio, which works for most applications. For compression-loaded cylinders (rod pushing from below), use a larger rod for column strength.
How do I figure out GPM needed for a cycle time?
Determine required stroke speed in in/min (stroke length ÷ desired seconds × 60). Multiply by bore area (in²) to get in³/min. Divide by 231 to get GPM. Size your pump to deliver at least that GPM at system pressure.
Why does my cylinder drift under load?
Drift (slow movement with no command) usually means internal seal leakage or external system leakage. A counterbalance valve or pilot-operated check valve can hold the load in position. If drifting just started, inspect seals. If it's a new installation, check for thermal expansion of the fluid and ensure the counterbalance valve is set above load-induced pressure.