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, including hydraulic and pneumatic cylinders, turn fluid pressure into straight-line force. The output depends on pressure and effective piston area, which is different on extend and retract because the rod takes up part of the area on the return stroke.
This calculator computes extend and retract force, accounts for seal friction, and adds work-per-stroke, fluid volume, and area-ratio outputs. Presets and standard bore tables make it easier to compare a rough sizing estimate with common cylinder sizes.
It is useful for presses, lifts, automation equipment, and other systems where pressure, bore size, and stroke length all affect the usable force.
Cylinder sizing is one of those tasks where the formulas are simple but the bookkeeping is easy to get wrong. Bore area, rod area, pressure, friction, and stroke all affect the result differently.
Keeping the extend and retract cases side by side makes it easier to verify whether a cylinder has enough force in both directions before you pick a part.
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.
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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, which help keep sizes consistent across manufacturers.