Hydraulic cylinders generate tremendous force from relatively compact packages. Proper sizing ensures your system has enough force for the application without being overbuilt. This guide covers force calculations and cylinder selection fundamentals.
The Hydraulic Force Formula
Force equals pressure times area:
F = P × A
For a circular piston:
F = P × (π × D²/4)
Where F is force in pounds, P is pressure in PSI, and D is bore diameter in inches.
Extend vs. Retract Force
Extension (Push Stroke)
Full piston area is used:
F_extend = P × (π × Bore²/4)
Retraction (Pull Stroke)
Rod area must be subtracted:
F_retract = P × π/4 × (Bore² - Rod²)
Retract force is always less than extend force due to the rod occupying part of the piston area.
Calculate Hydraulic Cylinder Force
Enter bore, rod, and pressure to get extend and retract forces instantly.
Quick Reference Table
Force in pounds at common pressures (standard rod sizes):
| Bore | Rod | @ 1000 PSI | @ 3000 PSI |
|---|---|---|---|
| 2" | 1" | 3,140 ext / 2,356 ret | 9,420 / 7,068 |
| 3" | 1.5" | 7,069 ext / 5,301 ret | 21,207 / 15,903 |
| 4" | 2" | 12,566 ext / 9,425 ret | 37,698 / 28,275 |
| 5" | 2.5" | 19,635 ext / 14,726 ret | 58,905 / 44,178 |
| 6" | 3" | 28,274 ext / 21,206 ret | 84,822 / 63,618 |
Sizing for Your Application
Step 1: Determine Required Force
- Calculate or measure the load to be moved
- Add friction forces (guides, seals, etc.)
- Consider acceleration forces if speed matters
Step 2: Apply Safety Factor
- 1.25: Known, consistent loads
- 1.5: Variable loads, moderate shock
- 2.0: Unknown conditions, heavy shock
Step 3: Select System Pressure
- 1000-1500 PSI: Light industrial
- 2000-3000 PSI: Standard industrial/mobile
- 3000-5000 PSI: Heavy-duty, compact packages
Step 4: Calculate Required Bore
Bore = √(4 × F / (π × P))
Then select the next standard bore size up.
Rod Sizing
Rod diameter affects:
- Buckling: Long strokes with push loads need larger rods
- Retract force: Larger rod = less retract area
- Speed: Larger rod = faster extend (less volume to fill)
Standard rod-to-bore ratios: 2:1 is common (4" bore with 2" rod). Higher ratios for long strokes.
Speed Calculations
Cylinder speed depends on oil flow rate:
Speed (in/sec) = Flow (GPM) × 231 / Area (sq.in.) / 60
Or simplified:
Speed = GPM × 3.85 / Area
Common Applications
Press Applications
Size for maximum expected force plus safety factor. Consider dwell time and cycle rate.
Lifting/Clamping
Account for holding force vs. moving force. Pilot-operated check valves for load holding.
Mobile Equipment
Higher pressures (3000+ PSI) for compact packages. Extreme temperature considerations.
Common Mistakes
- Forgetting retract force: If you need force in both directions, check both
- Ignoring friction: Seals and guides add significant resistance
- Undersizing rod: Long strokes with push loads can buckle
- Pressure drop: Line losses reduce effective pressure at cylinder
System Considerations
- Pump must supply adequate flow for desired speed
- Valves must handle flow and pressure
- Reservoir sized for heat rejection
- Cylinder mounting style for load alignment
Hydraulic force is straightforward mathematics. The challenge is capturing all the real-world factors—friction, acceleration, shock loads, and system losses—that determine the actual force requirement at the cylinder.
