Calculate extend and retract forces for hydraulic and pneumatic cylinders from system pressure, bore diameter, and rod diameter. Includes friction loss and ISO bore sizes.
Linear actuators — hydraulic and pneumatic cylinders — convert fluid pressure into linear force and motion. The force output depends on the system pressure and the effective piston area, which differs between the extend (full bore) and retract (annular) strokes. Sizing a cylinder correctly is critical for reliable operation in presses, lifts, robotics, and mobile equipment.
This Linear Actuator Force Calculator computes both extend and retract forces, accounts for seal friction losses, and provides work-per-stroke, fluid volume, and area ratio. Presets cover common applications from small pneumatic cylinders to heavy industrial hydraulic rams, and the reference table lists standard ISO 6020/6022 bore and rod combinations.
Engineers, technicians, and students use this tool for quick sizing checks, verifying catalog data, and understanding the fundamental F = P × A relationship that governs all fluid power actuators. Check the example with realistic values before reporting. Use the steps shown to verify rounding and units. Cross-check this output using a known reference case.
Sizing a cylinder involves looking up bore and rod areas, applying pressure, and accounting for friction and annular-area differences. This calculator automates all of those steps, compares extend vs retract forces visually, and provides ISO standard bore/rod combinations for reference — saving time and reducing sizing errors. Keep these notes focused on your operational context.
Extend Force (full bore): F_ext = P × A_bore A_bore = π(d_bore/2)² Retract Force (annular): F_ret = P × A_annulus A_annulus = A_bore − A_rod = π(d_bore/2)² − π(d_rod/2)² Effective Force (with friction): F_eff = F × (1 − η_friction) Work per Stroke: W = F_eff × stroke Where: P = pressure (Pa) d = diameter (m) η = friction coefficient (decimal)
Result: Extend = 74,613 N, Retract = 62,642 N
At 100 bar (10 MPa), a Ø100 mm bore / Ø40 mm rod cylinder extends with ~74.6 kN and retracts with ~62.6 kN after 5% friction loss. The bore area ratio is 1.19, meaning extend force is 19% greater than retract force.
Hydraulic cylinders use incompressible oil at high pressures (100–350 bar), providing very high force density and precise position control. Pneumatic cylinders use compressible air at low pressures (4–10 bar), offering faster speeds, cleaner operation, and simpler infrastructure but significantly lower force per bore size. The choice between them depends on the force requirement, speed, precision, and environment.
The sizing process starts with the required force and direction (extend or retract), then selects the operating pressure based on the available power unit. The bore diameter is calculated from F = P × A, rounded up to the next standard ISO size. Rod diameter is then selected for buckling resistance, and stroke is set by the application geometry. Finally, flow rate is calculated for the desired cycle time.
In regenerative hydraulic circuits, the fluid from the rod side is routed back to the cap side during extension, increasing extend speed (at reduced force) without additional flow. This is common in press applications where high speed is needed during approach and high force only during the working stroke.
On retract, the rod occupies part of the piston area, so the effective annular area is smaller than the full bore area. This reduces the force for the same pressure.
For well-maintained cylinders with modern seals, 3–5% is typical. Older cylinders or those with heavy-duty seals may lose 5–10%. Breakaway friction (static) is higher than running friction.
The area ratio (bore area / annulus area) determines the extend-to-retract force and speed ratio. A common ratio is 1.3–2.0, set by the rod diameter relative to the bore.
1 bar = 100,000 Pa = 14.5 psi. Hydraulic systems typically operate at 100–350 bar, while pneumatic systems run at 4–10 bar.
No — force depends only on pressure and area. Stroke length affects total work (energy = force × stroke) and the volume of fluid required.
These are international standards for hydraulic cylinder bore and rod diameter combinations, ensuring interchangeability and consistent sizing across manufacturers. Use this as a practical reminder before finalizing the result.