Hydraulic Cylinder Force Calculator
Find force, pressure, or bore size for hydraulic systems.
Calculate
Formulas
F = P × A = P × π(d/2)²1 bar = 100,000 Pa. A 50mm cylinder at 200 bar produces ~39.3 kN.
Hydraulic Systems
Pascal's law: pressure applied to a confined fluid is transmitted equally in all directions. Hydraulic advantage: small cylinder pushes big cylinder with multiplied force. Used in excavators, presses, brakes, jacks.
How Hydraulic Cylinder Force Works
A hydraulic cylinder converts fluid pressure into linear force. The force it produces is the pressure multiplied by the piston area:
F = P × A = P × π(d/2)²F is the output force in newtons, P is the hydraulic pressure in pascals, and d is the piston (bore) diameter.
Because force scales with the square of the diameter, a modest increase in bore size produces a large gain in force. This is the basis of the hydraulic press and lift.
Worked Example
A 100 mm (0.1 m) bore cylinder at 150 bar (15×10⁶ Pa):
A = π(0.05)² = 0.00785 m²
F = 15000000 × 0.00785 = 117800 N ≈ 11.8 tonnes
Bore Size vs Force
| Bore diameter | Area | Force at 150 bar |
|---|---|---|
| 50 mm | 0.00196 m² | ~29 kN |
| 100 mm | 0.00785 m² | ~118 kN |
| 200 mm | 0.0314 m² | ~471 kN |
Doubling the bore quadruples the force, because area grows with the square of diameter.
Frequently Asked Questions
Does the rod side produce the same force?
No. On the rod side, the rod's area is subtracted from the piston area, so the retracting force is lower than the extending force at the same pressure.
How do I convert bar to pascals?
Multiply bar by 100000. For example, 150 bar = 15,000,000 Pa = 15 MPa.
Why are hydraulics so powerful?
Fluids transmit pressure undiminished, and force equals pressure times area. A large piston area turns moderate pressure into enormous force.