Linear Actuator Force - Pressure, Bore, Rod, Thrust Solver

The linear actuator force calculator turns a supply pressure, a bore diameter, and an optional rod diameter into the extend and retract thrust a pneumatic or hydraulic cylinder can deliver. It applies Pascal's law F = P * A on the cap side and the same product on the annular rod side, then scales by a seal efficiency factor. The same panel reports force in newtons and pounds force, the effective piston areas, and an approximate vertical lift so one calculation covers sizing, safety checks, and datasheet verification.

• • Sizing a new cylinder: Match a load to a stock bore by reading the rated pressure and entering the bore on the actuator datasheet.
• • Verifying an existing cylinder against a load: Cross-check a published force rating against F = P*A at the actual operating pressure and seal efficiency.
• • Comparing extend vs retract force: Enter the rod diameter to see how much thrust is lost on the retract stroke, critical for clamping, lifting, and pressing.
• • Converting shop-floor readings to thrust: Read psi from a regulator, the bore from a tape measure, and convert directly into newtons and pounds force.

Most linear actuator force problems have three ingredients: a supply pressure, a piston area set by the bore, and a friction loss captured as efficiency. The calculator exposes the resulting forces and areas together so the F = P*A relationship stays visible.

The retract output reflects the smaller annular area between the bore and the rod, which is why a double-acting cylinder always pulls less than it pushes. Setting the rod diameter to zero makes the two outputs match for a single-acting or extend-only calculation.

For problems where the load is the displaced fluid around a piston rather than the piston itself, the buoyant force calculator solves the same F = P*A type product for fluid pressure and submerged volume.

The linear actuator force calculator evaluates Pascal's law on each side of the piston. The cap-side force uses the full bore area, the rod-side force uses the annular area, and both are scaled by the same efficiency factor before unit conversion.

• P: Supply pressure in pascals, converted from psi, bar, kPa, or MPa.
• D_bore: Inner diameter of the cylinder body in metres, from mm, cm, or inches.
• D_rod: Outer diameter of the rod in metres; zero gives a single-acting or extend-only calculation.
• eta: Seal efficiency in 0.5 to 1.0. Use 0.85 for pneumatic, 0.9 for hydraulic, 1.0 for an upper bound.
• F_extend: Force pushing the rod outward, equal to pressure times bore area times efficiency.
• F_retract: Force pulling the rod inward, equal to pressure times annular area times efficiency.

The arithmetic is the same product on both sides: pressure times area times efficiency. The only difference is the area used. On extend, the full bore area sees supply pressure; on retract, the rod subtracts its own cross-section. The ratio F_retract / F_extend = 1 - (D_rod / D_bore)^2 holds for any double-acting cylinder when pressure and efficiency are equal.

The output panel reports force in newtons and pounds force so the same calculation answers an SI lab question and a shop-floor question. The effective areas are shown in cm^2 next to the linear actuator force outputs so the F = P*A product can be back-solved by hand.

According to Wikipedia - Pascal's law, the pressure applied to a confined fluid is transmitted undiminished in every direction and acts perpendicular to every surface, so the force on a piston equals pressure times piston area

After sizing the cylinder, push the resulting thrust and the load mass into the forces and Newton's laws calculator to read the resulting acceleration from F = ma.

Four ideas explain why the same cylinder produces different force at different pressures and strokes. Keep them in mind whenever you set the inputs.

These four ideas together explain why thrust grows with pressure, shrinks with the rod area on retract, never quite reaches P*A because of seal losses, and is the upper bound for what the cylinder can hold rather than what it can swing into motion.

If the load is compressible rather than rigid, the same force flows through the spring constant and deflection calculator to convert thrust into the deflection the spring stores.

Use the tool in five steps. The default values reproduce a stock 50 mm bore pneumatic cylinder at 100 psi so you can verify the workflow before plugging in your own numbers.

1. 1 Read the supply pressure: Use the regulator gauge or the pump datasheet. Enter the number in the Pressure field and pick the unit your gauge uses.
2. 2 Measure the bore diameter: Read it from the actuator datasheet or measure across the inside of the cylinder body. Enter it in the Bore Diameter field with the matching unit.
3. 3 Enter the rod diameter for double-acting cylinders: Set the rod to zero for a single-acting cylinder or an extend-only calculation.
4. 4 Set the seal efficiency: Use 0.85 for pneumatic, 0.9 for hydraulic, 1.0 for a no-friction upper bound. Drop below 0.7 if the cylinder leaks.
5. 5 Read extend and retract force: The results show thrust in newtons and pounds force, plus the effective areas and the usable lift rating for a quick safety check.

A 50 mm bore pneumatic cylinder at 100 psi with a 20 mm rod and 0.85 efficiency returns about 1150 N of extend force (258 lbf) and 966 N of retract force (217 lbf), enough to hold roughly 117 kg vertically with a comfortable margin.

When the actuator drives a four-post lift or scissor jack, run the load through the car lift capacity calculator to verify the structure and not just the cylinder before lifting a vehicle.

Reasons to reach for the linear actuator force calculator instead of working F = P*A by hand.

• • One panel for the full calculation: Pressure, bore, rod, and efficiency share an input panel with extend and retract outputs and effective areas.
• • Mixed units without conversion: Pressure in psi, bar, kPa, or MPa and bore or rod in mm, cm, or inches convert internally.
• • Rod-side loss visible: The retract output uses the annular area, so the F_retract / F_extend = 1 - (D_rod / D_bore)^2 ratio is visible in the result.
• • Auditable for lab and datasheet checks: Every output is a closed-form evaluation of Pascal's law that can be repeated on paper field by field.
• • Pairs with the mechanical physics set: The thrust value flows into the forces and Newton's laws calculator for acceleration and the buoyant force calculator for fluid-immersed pistons.
• • Edge cases handled: Zero pressure gives zero force, rod equal to bore gives zero retract, efficiency outside 0-1 is rejected.

The tool is intentionally narrow: it solves one cylinder-force problem well. It does not model flow or valve timing, which would obscure the simple F = P*A product the page is designed to teach.

If your regulator or pump datasheet uses a unit the dropdown does not support, run the value through the pressure converter first and pick the matching SI or imperial unit on this page.

What changes the linear actuator force result and what the model cannot capture.

• • It assumes supplied pressure equals working pressure at the cylinder port; long hoses and restrictive fittings can drop the working pressure below the regulator reading.
• • It uses a single efficiency factor on both strokes; real cylinders usually lose more force on retract than extend because of the larger seal area on the rod side.

Use the tool as the backbone of a cylinder-force calculation. The F = P*A product is exact, so the answer is usually within the noise of a hand-measured bore. For cycling life, use the datasheet.

According to Wikipedia - Pressure measurement, one bar equals exactly 100000 pascals and one psi equals exactly 6894.757293168 pascals, which are the conversion factors used to read supply pressure in mixed units

When the same hydraulic loop also serves a fluid-handling tank, the hydraulic retention time calculator checks that the pump flow keeps the residence time on target alongside the cylinder force.