Hoop Stress Calculator
Calculate hoop stress, axial stress, and Von Mises stress in thin-walled pressure vessels. Supports cylinders and spheres with safety factor analysis.
Linear Actuator Force Calculator
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.
Pa
m
m
m
%
Active Force⧉
74,612.8 N
Push with friction
Extend Force (ideal)⧉
78,539.8 N
8,006.1 kgf
Retract Force (ideal)⧉
65,973.4 N
6,725.1 kgf
Bore Area⧉
78.54 cm²
Ø 100.0 mm
Annulus Area⧉
65.97 cm²
Bore area − rod area
Area Ratio⧉
1.19
Bore / Annulus — extend-to-retract force ratio
Work per Stroke⧉
22,383.8 J
Over 0.300 m stroke
Pressure⧉
100.0 bar
1,450 psi
Extend vs Retract Force
Extend (effective)
74,613 N
Retract (effective)
62,675 N
Standard Bore / Rod Sizes (ISO 6020)
| Bore (mm) | Rod (mm) | Bore Area (cm²) |
|---|---|---|
| 25 | 10 | 4.91 |
| 32 | 12 | 8.04 |
| 40 | 16 | 12.57 |
| 50 | 20 | 19.63 |
| 63 | 25 | 31.17 |
| 80 | 32 | 50.27 |
| 100 | 40 | 78.54 |
| 125 | 50 | 122.72 |
| 160 | 63 | 201.06 |
| 200 | 80 | 314.16 |
Planning notes, formulas, and examples
About the Linear Actuator Force Calculator
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.
When This Page Helps
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.
How to Use the Inputs
- Choose a preset or enter system pressure, bore diameter, and rod diameter.
- Select extend or retract direction to highlight the active force.
- Enter stroke length to compute work per stroke and fluid volume.
- Adjust friction loss percentage for seal drag (typically 3–8%).
- Compare extend and retract forces in the bar chart.
- Reference the ISO standard bore table for nearest standard size.
Formula used
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)Example Calculation
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.
Tips & Best Practices
- Always select the next standard bore size above your required force to provide a safety margin.
- Retract speed is faster than extend speed (same flow rate, smaller area) — important for cycle time calculations.
- Pneumatic cylinders operate at much lower pressures (~6 bar) than hydraulic (~200 bar), so they produce less force per bore size.
- Include a 15–25% force margin for acceleration, friction, and system losses in real applications.
- The rod diameter must be checked for buckling (Euler column) on long-stroke, high-force applications.
Hydraulic vs Pneumatic Actuators
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.
Cylinder Sizing Workflow
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.
Regenerative Circuits
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.
Sources & Methodology
Last updated:
Frequently Asked Questions
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.
More in this topic
Mechanical Advantage Calculator
Calculate ideal and actual mechanical advantage for all six simple machines: lever, pulley, wedge, screw, wheel & axle, and inclined plane. Includes efficiency and work analysis.
Impact Energy Calculator
Calculate impact energy from mass and drop height or velocity. Includes impact force, deceleration in g, dynamic load factor, and Charpy test reference data.