Free · Physics models
Pneumatic Piston Extension and Return Force
Compute ideal piston and annular return forces with the captured friction reduction and cylinder modes.
- Formula & worked example
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
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Formula and method
One square millimeter at one bar produces 0.1 newton with zero friction.
Extension=P×πD²/4×(1−friction); return=P×π(D²−d²)/4×(1−friction).
Worked example
Enter these known values and leave the other values blank.
- Cylinder pressure (P)
- 100000 Pa
- Piston area (Aᵤ)
- 1 mm²
- Piston diameter (D)
- 1.1284 mm
- Outward stroke force (F₁)
- 0.1 N
Assumptions and limitations
- Pressure is the effective pressure difference across the piston. Friction is an entered proportional reduction, not a manufacturer-specific seal-force curve.
- Double-acting return uses piston area minus rod area. The selected single-acting mode hides rod/return controls while retaining captured state.
- Back pressure, acceleration, side load, temperature, seal behavior and mounting strength require separate engineering analysis.
- Clear the unknown numerical field before using a supported inverse; selection controls retain their captured branches.
Common questions
What assumptions matter for this model?
Pressure is the effective pressure difference across the piston. Friction is an entered proportional reduction, not a manufacturer-specific seal-force curve.
What does this model leave out?
Back pressure, acceleration, side load, temperature, seal behavior and mounting strength require separate engineering analysis.
References
- Festo: cylinder force from pressure, piston area and friction
- Calculation definition and unit reference
Model requirements: Pressure difference must be nonnegative. Friction reduction must be between zero and less than one. Piston diameter must be positive. Rod diameter must be nonnegative and smaller than piston diameter. Authored accessible explanations preserve each captured diagram mode and its geometric relationships. Port the exact pinned five-decimal display helper to standalone decimal rounding; preserve all pressure, area, force and friction inverses.