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Hydraulic Cylinder Force Calculator

Calculate the push force, pull force, and flow requirements for any hydraulic cylinder. Enter bore, rod diameter, pressure, and stroke to see results update instantly.

Inputs

Results

Extend Force (Push)
0 lbs
Retract Force (Pull) 0 lbs
Bore Area 0 in²
Annular Area 0 in²
Cylinder Volume (extend) 0 gal
Flow for Target Speed (extend) 0 gpm
Force Ratio (Push/Pull) 0
Formulas used:
Bore Area = πd²/4   •   Annular = Abore − Arod
F = P × A   •   Q = A × v

Uses Lame's thick-wall cylinder equations. Verify critical designs with FEA.

How Hydraulic Cylinders Work

A hydraulic cylinder is a piston in a sealed tube. Pressurized oil pushes on the piston. The piston pushes on the rod. The rod moves loads. How much force the cylinder puts out depends on three things: pressure, bore size, and which way it is moving.

Extend vs Retract Force

The extend side is the full bore area. The retract side has the rod taking up space, so the working area is smaller. This makes extend force bigger than retract force. A 3 inch bore with a 1.5 inch rod has about 25 percent less retract force than extend force.

Flow and Speed

Cylinder speed comes from oil flow. The faster the oil flows in, the faster the cylinder extends. For a given flow, a bigger bore moves slower because the oil has to fill more space. This calculator gives you the flow rate needed for your target speed.

Pro tip: If you need equal extend and retract speeds, use a double-rod cylinder. Both sides have the same working area so speeds and forces match.

Picking the Right Cylinder

Start with the load. Divide the load by the operating pressure to get the required area. Pick a bore that gives at least that area. Add a safety factor of 1.25 to 2.0 for real applications. Then pick a rod that handles any tension load without buckling.

Common Applications

Hydraulic cylinders power presses, lifts, excavators, and automation. In machine tools they clamp parts. In robots they move arms. In cars they press brake pads. Any job that needs high force in a small package often uses hydraulics.

Frequently Asked Questions

Extend force equals pressure times the full bore area. Retract force equals pressure times the annular area (bore area minus rod area). The rod takes up space on the retract side, so retract force is always less than extend force.
Annular area is the bore area minus the rod area. It is the area pushed on during retract. A thick rod reduces the annular area and cuts retract force. For example, a 2 inch bore with a 1 inch rod has a retract area of 2.36 square inches versus a 3.14 square inch bore area.
Cylinder speed equals flow rate divided by piston area. To extend a cylinder fast you need high flow. To retract the same speed needs less flow because the annular area is smaller. This calculator gives you the required flow for any speed.
Most hydraulic systems run at 2000 to 3000 psi. High-pressure systems can reach 5000 psi. Mobile hydraulics often use 2500 psi. This calculator accepts any pressure so you can match your system.
Common bores are 1.5, 2, 2.5, 3, 3.5, 4, 5, and 6 inches for inch systems. Metric uses 40, 50, 63, 80, 100, 125, and 160 mm. Rod diameters are usually 50 to 67 percent of the bore.
Match rod diameter to bore based on load. For tension loads, a 5:3 bore-to-rod ratio is standard. For compression loads with long stroke, check for buckling. A thicker rod adds safety margin but cuts retract force.
Operating pressure is what the cylinder sees at steady state. Pressure drop is the loss in the fluid lines from the pump to the cylinder. This calculator uses operating pressure directly. Add about 10 percent to the pump rating to account for line losses.
Yes, the same formulas work for pneumatic cylinders. Just use air pressure (typically 80 to 100 psi) instead of hydraulic pressure. Pneumatic flow is in cubic feet per minute (CFM) which this calculator can convert to gallons per minute equivalent.
Efficiency includes volumetric losses (internal leakage) and mechanical losses (friction). Piston cylinders are typically 90 to 95 percent efficient. For critical designs reduce the calculated force by 5 to 10 percent to account for losses.
Hydraulic cylinder power equals force times velocity. Force comes from pressure and area. Velocity comes from flow and area. Power is easier to measure as flow times pressure divided by 1714 for HP in gallons per minute and psi.

Common Hydraulic Cylinder Bore Sizes

Bore (inch) Bore (mm) Typical Rod Dia Force at 2000 psi
1.5"40 mm5/8" (16 mm)3,530 lbs
2.0"50 mm1" (25 mm)6,280 lbs
2.5"63 mm1-1/4" (32 mm)9,820 lbs
3.0"80 mm1-1/2" (40 mm)14,130 lbs
4.0"100 mm2" (50 mm)25,130 lbs
5.0"125 mm2-1/2" (63 mm)39,270 lbs
6.0"160 mm3" (80 mm)56,550 lbs

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