Cylinder Force Calculator

Q: Does this calculator work for air (pneumatic) cylinders too?

Yes. The math is the same for oil and air: Force = Pressure × Area . Just enter your air pressure, bore, and rod size. Air cylinders lose a bit more force to seal friction, so expect the real push to be around 10% lower than the number shown.

Updated Aug 27, 2026 By Jehan Wadia

Introduction

This Cylinder Force Calculator tells you how hard a hydraulic or pneumatic cylinder can push and pull. Just type in the pressure, the bore diameter, and the rod diameter. The tool shows the extend (push) force, the retract (pull) force, the piston areas, and the full math behind each answer.

A cylinder pushes harder than it pulls. When it extends, the fluid presses on the whole face of the piston. When it retracts, the rod takes up part of that face, so there is less area for the fluid to press on. Less area means less force. The calculator shows this gap as a retract efficiency percent, so you can see how much pull force you really have.

You can work in imperial units (psi, inches, lbf) or metric units (bar, mm, kN), and switch between them with one click. Charts and a drag-and-drop visualizer let you see how a bigger bore, a thicker rod, or higher pressure changes the force. Use it to size a cylinder, check a design, or match a cylinder to the load you need to move. For related jobs, try our Force Calculator for basic F = ma problems or the PSI Calculator for pressure conversions.

How to use our Cylinder Force Calculator

Enter your cylinder pressure, bore size, and rod size. The calculator shows the push force, the pull force, the retract efficiency, and the bore, annulus, and rod areas.

Unit System: Pick Imperial (psi, in, lbf) or Metric (bar, mm, kN). This sets the units on every box at once. Your numbers stay the same. If you need to swap other units by hand, the Unit Converter Calculator and Metric Conversion Calculator can help.

Operating Pressure: Type the fluid pressure sent to the cylinder port. Then pick the unit, like psi, bar, kPa, or MPa.

Bore Diameter: Type the inside width of the cylinder tube. This is the full face of the piston. Pick the unit, like inches or millimeters. Need the diameter in another unit? Use the Mm to Inches Calculator.

Rod Diameter: Type the outside width of the piston rod. It must be smaller than the bore. Pick the unit, like inches or millimeters.

Force output unit: Choose how you want the push and pull force shown, such as lbf, N, kN, or kgf.

Area output unit: Choose how you want the bore, annulus, and rod areas shown, such as in², mm², or cm². Our Circle Area Calculator and Area Converter Calculator are handy if you want to check a piston face by hand.

Buttons: Click Calculate to see your answer and the step-by-step math. Click Load Example for a 4 in bore, 1.5 in rod, 2000 psi sample. Click Clear to start over.

Interactive Visualizer: Drag the bore, rod, and pressure sliders to see the cylinder cross-section change and watch the force numbers update. This tool always uses inches and psi.

What Is Cylinder Force?

Cylinder force is the push or pull that a hydraulic or pneumatic cylinder can make. A cylinder is a metal tube with a piston inside and a rod attached to that piston. When fluid (oil) or air is pumped in under pressure, the pressure presses on the piston face. That press turns into force, and the rod moves in or out.

The Formula

Force equals pressure times area:

Force = Pressure × Area

So a cylinder only needs two things to make force: pressure from the pump or compressor, and piston area from the bore size. Double the pressure and you double the force. Double the area and you double the force too. The same pressure-times-area idea drives our Hydrostatic Pressure Calculator and Buoyancy Calculator.

Push Force vs. Pull Force

A cylinder is stronger when it pushes than when it pulls. Here is why:

Extend (push): Fluid presses on the whole flat piston face. The area is a full circle, found with π/4 × bore².
Retract (pull): Fluid presses on the other side, but the rod takes up space in the middle. That leaves a ring shape called the annulus. Its area is π/4 × (bore² − rod²).

Since the ring is smaller than the full circle, the pull force is always less. A thick rod means a bigger gap between push and pull. A thin rod means the two forces are closer. This gap is called retract efficiency — the pull force shown as a percent of the push force. To see how that percent is worked out, look at our Percentage Calculator.

A Quick Example

Take a cylinder with a 4 in bore, a 1.5 in rod, and 2,000 psi of oil pressure.

Bore area = π/4 × 4² = 12.57 in² → Push force = 12.57 × 2,000 = 25,133 lbf
Annulus area = π/4 × (4² − 1.5²) = 10.80 in² → Pull force = 10.80 × 2,000 = 21,598 lbf

The pull is about 86% of the push. The rod "steals" the rest.

Units to Watch

Mixing units is the biggest cause of wrong answers. Pressure in psi with area in in² gives force in pounds (lbf). Pressure in bar or MPa with area in mm² gives force in newtons (N) or kilonewtons (kN). Remember that 1 bar ≈ 14.5 psi, and 1 MPa = 10 bar. If you also track cylinder mass or load weight, the Pounds to Kilograms Calculator keeps those figures straight.

Things to Keep in Mind

Real force is a bit lower. Seal drag and friction eat up roughly 5–10% of the math answer. Air cylinders lose more than oil ones.
Back pressure cuts force. If the return line is small or clogged, the trapped fluid pushes back on the piston. Check line sizing with the Pipe Flow Calculator and the Friction Loss Calculator.
Pull strokes are faster. The annulus holds less fluid, so the same pump flow moves the rod quicker on the way in. Use the Flow Rate Calculator and the Cylinder Volume Calculator to work out stroke speed and oil volume.
Long rods can bend. A rod under a heavy push can buckle. Check rod size and stroke length, not just force — our Beam Deflection Calculator and Section Modulus Calculator cover the bending side of the job.
Design with a safety margin. Pick a cylinder that makes more force than your load needs, often 1.25 to 2 times more.
Size the pump and motor too. Pressure plus flow sets the power draw, so pair this tool with the Pump Power Calculator or the Horsepower Calculator.
Mounts matter. Pins, clevises, and bolted flanges must hold the same load — see the Bolt Torque Calculator before you tighten anything.

Where This Is Used

Cylinder force math shows up in excavators, log splitters, dump truck lifts, presses, forklifts, car jacks, factory clamps, and robot arms. Anywhere a rod pushes or pulls a load, these numbers decide if the job gets done or the machine stalls. When a cylinder drives a lever or arm, pair this tool with the Torque Calculator to turn linear force into a moment, and use the Pulley Calculator or Gear Ratio Calculator when the motion passes through a cable or gear train. For steel frames and cylinder mounts, the Steel Weight Calculator helps you tally up the structure that carries all that force.

Formulas used

Bore Area (full piston face)

A_{bore} = \frac{\pi}{4} D^2

Annulus Area (rod side)

A_{ann} = \frac{\pi}{4}\left(D^2 - d^2\right)

Rod Cross-Section Area

A_{rod} = A_{bore} - A_{ann} = \frac{\pi}{4} d^2

Extend (Push) Force

F_{ext} = A_{bore} \times p

Retract (Pull) Force

F_{ret} = A_{ann} \times p

Retract Efficiency

\eta = \frac{F_{ret}}{F_{ext}} \times 100\%

Unit conversion to SI (generic)

X_{SI} = X_{input} \times k_{unit}, \qquad X_{output} = \frac{X_{SI}}{k_{unit}}

Frequently asked questions

Does this calculator work for air (pneumatic) cylinders too?

Yes. The math is the same for oil and air: Force = Pressure × Area. Just enter your air pressure, bore, and rod size. Air cylinders lose a bit more force to seal friction, so expect the real push to be around 10% lower than the number shown.

Why do I get an error that says the rod must be smaller than the bore?

The rod slides inside the tube, so it has to be thinner than the bore. If you type a rod size equal to or bigger than the bore, the ring (annulus) area would be zero or negative, and the pull force would make no sense. Check that both numbers use the same unit — 25 mm and 25 in are very different.

What is the annulus area?

The annulus is the ring-shaped part of the piston on the rod side. The rod blocks the middle, so fluid can only press on the ring around it. Its area is π/4 × (bore² − rod²). This ring sets your pull force.

Does the calculator subtract friction and back pressure?

No. It gives the pure theoretical force. Real cylinders lose about 5–10% to seal drag, and more if the return line has back pressure. Take the answer and plan for a little less in the real world.

Should I enter the maximum pressure or the working pressure?

Use the working pressure your pump or regulator actually sets, since that is the force you get every day. You can also run the max relief valve setting to check the worst case load on your mounts and pins.

Does stroke length change the force?

No. Force only depends on pressure and piston area. A 6 inch stroke and a 60 inch stroke with the same bore make the same push force. Stroke length does affect speed, oil volume, and the risk of the rod buckling.

How do I pick a bore size if I know the load?

Divide your load by your pressure to get the area you need, then try bore sizes in the calculator until the push force is bigger than the load. Add a safety margin of 1.25 to 2 times the load, and always check the retract force if the cylinder pulls.

What is a good retract efficiency?

Most standard cylinders land near 80–90%. A thin rod gives a higher percent and a stronger pull. A thick rod drops it, sometimes near 50% on 2:1 rod cylinders, but a thick rod resists bending better. Pick based on which stroke does the hard work.

Why does the result also show newtons and pound-force under the big number?

Those two lines are a quick cross-check. No matter which output unit you pick, you always see the same force in N and lbf. This helps you spot a unit mistake fast.

Can I get the answer in tons?

Yes. Open the force output list and pick ton-force (US short), tonne-force (metric), or ton-force (UK long). This is handy for rating a hydraulic press or a shop jack.

Is bore the same as the outside size of the cylinder tube?

No. Bore is the inside diameter of the tube, where the piston rides. The outside is bigger because of the wall thickness. Using the outside size will give a force that is too high.

Should I use gauge pressure or absolute pressure?

Use gauge pressure, which is what your gauge reads. That is the pressure difference that pushes the piston. Absolute pressure adds about 14.7 psi of air pressure that already presses on both sides.

Does this work for a single-acting cylinder?

Yes for the push side. A single-acting cylinder is only fed on the bore side, so use the extend force. It returns by spring or by the load's own weight, so the retract number does not apply.

What about a double-rod (through-rod) cylinder?

A double-rod cylinder has a rod on both ends, so both sides are ring shaped. Push and pull forces are equal. Use the retract (pull) force from this tool for both directions.

Why is my force showing a dash or zero?

One of the three boxes is empty, holds a negative number, or the rod is not smaller than the bore. Fill all three boxes with positive numbers. Zero pressure also gives zero force.

Can the visualizer use metric units?

No. The slider view always works in inches and psi to keep it simple. The main calculator above it handles metric, and both use the same formula.

Why is the pie chart split into annulus and rod areas?

Together they add up to the full bore area. The orange slice is the ring that makes your pull force. The purple slice is the area the rod takes away. A bigger rod slice means a weaker pull.

Does oil type or temperature change the force?

Not directly. Force comes from pressure and area only. Thick, cold oil can raise back pressure and slow the cylinder, which lowers the useful force a little, but the formula stays the same.

Interactive Visualizer

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