How to Calculate Cylinder Force: Formula, Examples, and Practical Tips

A hydraulic cylinder is a force multiplier in the simplest possible sense: a small pump and a modest bore can shift a load that no crew of people could move by hand. The arithmetic behind that multiplication is short — one formula, one area calculation, and a couple of unit conversions — but it is also exactly where most sizing mistakes hide. Whether you are checking a crane boom cylinder, a scissor lift, or a jacking cylinder for a pipe installation, the same handful of steps gets you a trustworthy answer.

The Core Relationship in One Line

Force equals pressure multiplied by the area that pressure acts on: F = P × A. Pressure is the hydraulic fluid's push per unit of surface, and the piston area is how much surface it has to push against. Double one and you double the force; double both and you get four times as much.

In metric practice, the cleanest pairing is megapascals and square millimetres. Because one megapascal is one newton per square millimetre, the result lands directly in newtons — divide by 1,000 and you have kilonewtons. In imperial practice, pounds per square inch multiplied by square inches gives pounds of force with no conversion at all.

The values you will meet most often when converting between systems:

• 1 bar = 0.1 MPa = 100 kPa, roughly 14.5 psi
• 1 MPa = 10 bar, roughly 145 psi
• 1 square inch = 645.16 square millimetres
• 1 kilonewton is roughly 224.8 pounds of force
• 1 tonne-force is roughly 9.81 kilonewtons

Write the units down before you start. Most wrong answers we see are not wrong formulas; they are bars fed into an equation expecting megapascals, or millimetres fed into one expecting centimetres.

Push and Pull Rarely Match

On the extend stroke, full pump pressure acts on the whole bore area, so the area is π/4 × D², where D is the bore diameter. On the retract stroke the fluid only sees the ring-shaped area around the rod, so the effective area is π/4 × (D² − d²), with d being the rod diameter. The rod occupies metal that pressure cannot reach.

Take a 100 mm bore cylinder with a 70 mm rod running at 20 MPa. The full bore area is about 7,854 mm², giving roughly 157 kN of thrust. The annulus area is about 4,006 mm², giving roughly 80 kN of pull — barely half. A cylinder that lifts a load with authority may be quite tame when it has to pull the same load back.

This matters whenever the working load reverses direction during a cycle: a folding arm that pulls as well as pushes, a leveling cylinder that has to hold a platform down as well as up, or a stabilizer leg that must retract against resistance. Size on the weaker side, not the stronger one.

A Worked Example You Can Follow

Suppose a machine needs to raise 8 tonnes steadily, and the pump relief is set at 20 MPa. Here is the sequence we would walk through with a customer.

1. Convert the load: 8 tonnes × 9.81 = about 78.5 kN.
2. Add a working margin. A factor of 1.5 covers seal friction, back pressure, and the small pressure losses in hoses and fittings, giving about 118 kN.
3. Divide by pressure to find the required area: 118,000 N ÷ 20 N/mm² = 5,900 mm².
4. Back out the bore: the square root of (4 × 5,900 ÷ π) is about 86.7 mm, so the next standard size up is 90 mm, which gives 6,362 mm² and roughly 127 kN at full pressure.
5. Check the rod end and the stroke. If the load pulls during retraction, verify the annulus area. If the stroke is long and the load is compressive, check rod buckling before you accept the bore — a slender rod can fail well below the cylinder's theoretical thrust.

That last step is where theory meets practice. A cylinder can be strong enough and still be the wrong cylinder, because the rod behaves like a column under compression and its safe load falls sharply as stroke length grows.

From Theory to the Force You Actually Get

The number from F = P × A is theoretical. Real output is a little lower, and it is worth knowing why. Seal friction, guide friction, and the pressure needed to push oil back to tank all take a bite. For most mobile machinery, an efficiency of 0.85 to 0.95 applied to the theoretical figure gets you close to reality, with larger cylinders and higher pressures sitting toward the lower end of that range.

A useful form of the equation is: net force = (extend pressure × bore area) − (return-line pressure × annulus area) − friction. The middle term is easy to forget, and it can be significant on circuits with restricted return flow or counterbalance valves.

Pressure also needs care. The relief valve setting is a ceiling, not a promise. During fast extension, flow demand can outrun the pump and system pressure sags, so the force available at the moment you need it may be lower than the catalogue calculation suggests. Systems that hold a load for long periods, such as outrigger cylinders, should be checked for holding capability as well as moving capability.

Bore Size and Theoretical Thrust at a Glance

The table below is a quick sanity check for common bore sizes. Values assume the full bore area on the extend stroke and ignore friction, so treat them as an upper bound rather than a working capacity.

How These Numbers Play Out in Real Machines

The formula is universal, but the inputs are not. On a truck-mounted crane, the luffing cylinder's job is to hold the boom at a working radius, and the force it feels depends on the angle of the boom as much as on the load hanging from the hook. As the boom rises, the cylinder's moment arm changes, so the same lift can demand very different pressures. That is why luffing cylinders are specified by geometry and mounting as carefully as by bore.

Truck-Mounted Crane Hydraulic Luffing CylinderFunction: Adjusting the Boom Angle: Through the extension and retraction of the luffing cylinder, the boom can tilt up and down to meet lifting needs at various height...View Product →

Scissor lifts sit at the other end of the spectrum. The lifting cylinder works through a linkage whose mechanical advantage shifts continuously as the platform rises, so the highest rod force often appears near the fully collapsed position rather than at full height. Large bore, modest pressure, and a short stroke are typical, and the calculation has to be repeated at several points in the lift curve.

Scissor Lift Aerial Platform Hydraulic Lifting CylinderDetails single-acting lifting cylinders with damping holes for smooth ascent and descent, plus bore, rod and stroke ranges suited to scissor lift platform calculations.View Product →

Pipe jacking pushes the calculation to its limit. Main jacking cylinders drive pipe through the ground against soil resistance and wall friction, often at several hundred tonnes of thrust over a long stroke. Here the force budget is set by the ground conditions first and the hydraulics second, and the cylinder has to deliver that thrust repeatedly without buckling. You can see how these requirements differ across the range of hydraulic cylinders for piling machinery.

Pipe Jacking Machine Hydraulic Main Jacking CylinderCore power source for pipe jacking, delivering strong thrust, stable propulsion and precise extension control, with high-pressure resistance and sealing for harsh continuous operation.View Product →

Mistakes Worth Avoiding

• Using bore area for a retract stroke, which overstates pull force by 30 to 50 percent on typical rod ratios.
• Treating relief valve pressure as continuously available working pressure.
• Forgetting return-line pressure on circuits with counterbalance or metering valves.
• Sizing for the load alone and ignoring rod buckling on long-stroke, compressive applications.
• Mixing bar, megapascal, and psi inside one calculation.
• Leaving no margin for seal friction, temperature-driven viscosity changes, or wear over the service life.

Questions We Hear From Designers

What is the shortest version of the formula?

Force in newtons equals pressure in megapascals multiplied by area in square millimetres. Everything else is conversion and correction.

Why does my measured force differ from the calculated one?

Usually friction, back pressure, or a gauge reading taken downstream of a restriction. Check pressure at the cylinder port under load rather than at the pump.

How much margin should I add?

For steady industrial loads, 1.25 to 1.5 is a sensible starting point. For shock loads, outdoor duty, or safety-critical holding functions, go higher and confirm with testing.

We have been building hydraulic cylinders in Zhejiang since 2004, and most of the force questions we answer come from engineers midway through a design rather than at the start. If you would like a second pair of eyes on the numbers, send us the load, the stroke, the pressure you expect, and how the cylinder is mounted — that is usually enough for us to tell you whether the bore you have chosen is comfortable or marginal. For more background on matching a cylinder to an application, our notes on key design considerations when selecting a hydraulic cylinder are a good place to continue.