Hydraulic Cylinder Calculator
Calculate the output force of a hydraulic cylinder during extension or retraction from bore diameter, rod diameter, and system pressure. Used by hydraulic system designers to verify actuator force capacity for machinery and presses.
About this calculator
A hydraulic cylinder converts fluid pressure into linear force. On the extension stroke, pressure acts on the full bore area: F_extend = π × (D_bore / 2)² × P, where D_bore is the bore diameter in metres and P is pressure in Pascals. On the retraction stroke, the piston rod occupies part of the piston face, so the effective area is annular: F_retract = π × ((D_bore / 2)² − (D_rod / 2)²) × P. In this calculator, diameters are entered in mm (divided by 2000 to convert to radius in metres) and pressure in bar (multiplied by 100,000 to convert to Pa), giving force in Newtons. The difference between extension and retraction forces is significant in asymmetric cylinders — retraction force is always less than extension force for the same pressure. This must be accounted for in circuit design to ensure adequate clamping or pulling force.
How to use
A cylinder has a bore diameter of 100 mm, a rod diameter of 50 mm, and operates at 200 bar. Extension force: Step 1 — radius = 100 / 2000 = 0.05 m. Step 2 — F = π × 0.05² × (200 × 100,000) = π × 0.0025 × 20,000,000 = 157,080 N ≈ 157.1 kN. Retraction force: Step 1 — bore radius² = 0.0025 m²; rod radius = 50 / 2000 = 0.025 m; rod radius² = 0.000625 m². Step 2 — F = π × (0.0025 − 0.000625) × 20,000,000 = π × 0.001875 × 20,000,000 ≈ 117.8 kN.
Frequently asked questions
Why is the retraction force of a hydraulic cylinder less than its extension force at the same pressure?
During retraction, the hydraulic fluid pushes on the annular area of the piston — the full bore area minus the cross-sectional area of the piston rod. Since the rod reduces the effective pressure area, the resulting force is proportionally smaller than on the full bore face during extension. A larger rod diameter means a greater reduction in retraction force. This asymmetry is important in applications like clamping presses or pulling operations where both stroke directions must meet minimum force requirements.
How do I convert hydraulic pressure in bar to force in kilonewtons for a cylinder?
First convert bar to Pascals by multiplying by 100,000 (1 bar = 100,000 Pa). Then calculate the piston area in square metres using A = π × r², where r is the bore radius in metres. Finally, multiply pressure by area: F (N) = P (Pa) × A (m²). Divide by 1000 to get kilonewtons. For example, 150 bar on a 80 mm bore gives P = 15,000,000 Pa, A = π × 0.04² = 0.005027 m², F = 75,398 N ≈ 75.4 kN.
What factors should I consider when selecting a hydraulic cylinder for an application?
Key factors include the required extension and retraction forces, stroke length, operating pressure rating, mounting style, and duty cycle. Ensure the system pressure is within the cylinder's rated working pressure with an appropriate safety factor (typically 1.5–2×). Check that the rod diameter is sufficient to resist buckling under the expected compressive load using Euler's column buckling formula. Also consider seal type for temperature and fluid compatibility, cushioning at end-of-stroke to prevent impact damage, and whether a double-acting or single-acting cylinder suits the application.