Hydraulic Cylinder Force Calculator.

Cylinder Force, Speed and Flow

A cylinder converts fluid pressure into linear force. The whole calculation rests on one relationship — force equals pressure times area — but the area is different in each direction, and that asymmetry drives most of the design decisions.

The Two Areas

Extend: F₁ = p × π·D²/4
Retract: F₂ = p × π·(D² − d²)/4
Area ratio φ = A₁ / A₂

On extension the full piston face sees pressure. On retraction the rod occupies part of that face, so only the annulus is pressurised — a cylinder always pulls less hard than it pushes. With a bore of 80 mm and a 45 mm rod the annulus is only 68% of the bore area, so retract force is 68% of extend force at the same pressure.

The speeds invert: the same flow into a smaller area moves faster, so the rod retracts about 1.5× faster than it extends. Sizing a valve on extend flow alone is a standard mistake — the return stroke can overrun the valve and cavitate.

Working in Bar and Millimetres

The convenient shortcut for shop use: bar ÷ 10 = MPa = N/mm². Multiply by the area in mm² and the answer is newtons directly.

• Ø80 bore = π × 80² / 4 = 5027 mm²
• 160 bar = 16 N/mm²
• F = 5027 × 16 = 80,430 N ≈ 80 kN before efficiency
• At 92% mechanical efficiency → 74 kN usable

The efficiency term covers seal friction and is not optional. New cylinders with fresh seals can run 5–8% below theoretical; a worn or misaligned unit far worse.

Rod Buckling — the Check People Skip

A long rod in compression is a column. Force capacity is not limited by pressure but by Euler buckling:

F_crit = π²·E·I / (K·L)²  where  I = π·d⁴/64

K is the end-fixity factor: 0.7 for both ends rigidly fixed, 1.0 for both pivoted, 2.0 for one fixed and one pivoted, 4.0 for a cantilever. L is the extended length — the rod is at its most vulnerable fully out, which is exactly when many designs apply peak load. Aim for a buckling safety factor of at least 2.5, and 4 or more if the load is shock or eccentric.

Rod diameter is usually driven by buckling, not by tensile stress. If the buckling factor is short, increase rod diameter before increasing bore — a bigger bore raises force but does nothing for column stability.

Common Bore and Rod Combinations (ISO 6020/6022)

Most standard ranges hold φ near 1.46 (the 2:1 area series), which keeps retract force at roughly 68% of extend and retract speed at roughly 1.46× extend. A 1.25 ratio rod is available where a faster, stronger return is needed.

Pneumatic Cylinders

The same equations apply, but three things change in practice. Working pressure is typically 6 bar rather than 160, so bores are far larger for the same force. Air is compressible, so the rod does not hold position under varying load and speed depends on load as well as flow. And the efficiency term is lower — 0.85 is a realistic starting figure for a standard pneumatic cylinder with the load moving.

For sizing air consumption, remember that flow must be quoted in free air delivered: multiply the swept volume by the absolute pressure ratio (roughly 7 for a 6 bar system) to get FAD per stroke.

Sizing Checklist

1. Establish the worst-case load, including friction and any acceleration term (F = m·a).
2. Apply a design factor — 1.25 for steady loads, 2.0 or more for shock.
3. Pick the bore from extend force at the system's relief valve setting, not its nominal pressure.
4. Check retract force against the return load — it is only ~68% of extend.
5. Check rod buckling at full extension.
6. Size the valve and lines on the faster stroke, which is normally retract.

Related Tools

For the pump driving the circuit, see the Pump Power Calculator. For the motor behind it, see Motor HP / Power. For clamping loads on the mounting, use Bolt Torque, and for the mounting bracket check Beam Deflection.