Piston Force Calculator
Find the force a hydraulic or pneumatic cylinder delivers from pressure and bore, size a bore for a required force, and see how fast the piston moves.
🔧 What is Piston Force?
Piston force is the push a pressurised fluid exerts on a piston, and it is the working output of every hydraulic and pneumatic cylinder. The basic law is that pressure is force per unit area, so the force on the piston is F = P × A, the gauge pressure times the area the pressure acts on. Because pressure acts equally in every direction inside the fluid, a small pump pressure over a large piston area makes a large force, which is why hydraulic cylinders lift excavator booms, press metal and move machine tools with modest pumps.
The area is not the same in both directions. A double acting cylinder has a rod on one side of the piston. When the cylinder extends, fluid enters the cap side and pushes on the full bore area, A = π D² / 4. When it retracts, fluid enters the rod side and pushes on the annulus left after the rod takes its share, A = π (D² − d²) / 4. The retract force is therefore lower than the extend force by the ratio of the rod area to the bore area, while the retract speed is higher for the same flow. In practice a seal friction loss, often 5 to 10 percent in hydraulics, reduces the force, and back pressure on the exhaust side reduces it again.
The calculation is used by designers sizing a cylinder for a press, clamp, lift or door, by maintenance staff checking what a known cylinder can deliver, and by students learning fluid power. It applies to both liquids and gases. Pneumatic cylinders run at a few bar and are used for clamping, sorting and light automation, while hydraulic cylinders run at 100 to 350 bar and move heavy loads. Always use gauge pressure, the pressure above the surrounding atmosphere, because atmospheric pressure acts on both sides of the piston and cancels in a double acting cylinder.
This calculator has three modes. Force finds the extend and retract force from the pressure, bore, rod, efficiency and optional back pressure, with the areas and the theoretical values. Size bore turns the question around and finds the bore for a required force, with the next common bore size. Speed and flow gives the extend and retract speeds, stroke times, oil volumes and hydraulic power from a flow rate. It is not the same as the Piston Speed Calculator, which finds the mean piston speed of a crank engine from the stroke and rpm. The force it reports is what the fluid produces at the piston, so the load, friction in the guides and a safety factor must be handled separately, for instance with the Linear Actuator Force Calculator.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Hydraulic Cylinder at 100 bar
P = 100 bar, bore 63 mm, rod 25 mm, efficiency 95 %
Example 2 — Pneumatic Cylinder at 6 bar
P = 6 bar gauge, bore 50 mm, rod 20 mm, efficiency 90 %
Example 3 — Imperial Units, 3000 psi and a 4 in Bore
P = 3000 psi, bore 4 in, rod 1.5 in, efficiency 95 %
Example 4 — Back Pressure on the Exhaust Side
P = 100 bar, bore 63 mm, rod 25 mm, efficiency 100 %, back pressure 10 bar
Example 5 — Bore for a 50 kN Press
Required 50 kN extending at 160 bar, rod 36 mm, efficiency 95 %
Example 6 — Bore for a Retracting Pneumatic Cylinder
Required 1500 N retracting at 6 bar, rod 16 mm, efficiency 90 %
Example 7 — Cylinder Speed from Flow
20 L/min into a 63 mm bore, 25 mm rod, stroke 300 mm, 100 bar, efficiency 95 %
❓ Frequently Asked Questions
🔗 Related Calculators
What is the formula for piston force?
Piston force is F = P x A, the gauge pressure times the area the pressure acts on. With a seal efficiency eta it becomes F = P A eta. For 100 bar on a 63 mm bore, A = 31.17 cm2, so the theoretical force is 31,170 N and 29,610 N at 95 percent efficiency.
How do I calculate hydraulic cylinder force?
Convert the pressure to pascals, find the area A = pi D squared over 4 for the bore D, then multiply. For 100 bar (1e7 Pa) and a 63 mm bore the force is 1e7 x 0.003117 = 31,170 N before friction losses. Retraction uses the smaller rod-side area.
Why is the retract force lower than the extend force?
On retraction the pressure acts on the annulus between the bore and the rod, A = pi (D squared minus d squared) over 4, which is smaller than the full bore. With a 63 mm bore and a 25 mm rod the area is 26.26 cm2 against 31.17 cm2, so the force is about 16 percent lower.
What is the rod-side area of a cylinder?
It is the annular area pi (D squared minus d squared) over 4, where D is the bore diameter and d the rod diameter. It is the piston area minus the rod cross-section. Pressure on that area gives the pulling force.
How do I find the pneumatic cylinder force at 6 bar?
Use the same formula with 6 bar gauge (6e5 Pa). A 50 mm bore has A = 19.63 cm2, so F = 6e5 x 0.001963 = 1178 N, or about 1060 N at 90 percent efficiency. Rod-side force for a 20 mm rod is about 890.6 N.
How do I choose the bore size for a required force?
Divide the force by the pressure and the efficiency to get the area, then D = sqrt(4 A / pi). For 50 kN at 160 bar and 95 percent that is 32.89 cm2 and a 64.72 mm bore, so the next common size, 80 mm, is chosen. For retraction add the rod area back in.
Should I use gauge or absolute pressure?
Use gauge pressure for force, because atmospheric pressure acts on both sides of the piston and cancels in a double acting cylinder. Absolute pressure matters for gas volume and compression calculations, not for the net force.
How does back pressure change the force?
Back pressure on the exhaust side pushes against the piston. The extending force becomes P A cap minus Pb A rod, and the retracting force becomes P A rod minus Pb A cap. With 100 bar and 10 bar of back pressure on the 63 mm cylinder the extend force drops from 31,170 N to 28,550 N.
How fast does a hydraulic cylinder move?
Speed is flow divided by area, v = Q / A. A 20 L/min flow into a 63 mm bore gives 106.9 mm/s extending, and 126.9 mm/s retracting into the smaller rod-side area. The flow mode also gives the stroke time and the oil volume.
How is this different from the Piston Speed Calculator?
The Piston Speed Calculator finds the mean piston speed of an engine from stroke and rpm. This calculator finds the force of a pressurised cylinder from pressure and area, sizes its bore, and gives the linear speed from fluid flow. They answer different questions.
Does the calculator include the weight of the load or friction of the guides?
No. It gives the force the fluid produces at the piston. To find what the load actually needs, add gravity, friction and acceleration, for example with the Linear Actuator Force Calculator. Keep the actuator force above the load force with a safety factor.