Hydraulic cylinders convert fluid pressure into linear force and motion. Sizing a cylinder correctly requires matching bore diameter to the required force, rod diameter to structural loading, and flow rate to the required speed. Getting any of these wrong results in a cylinder that cannot do the job, fails prematurely, or wastes energy.
The fundamental equation is simple: Force = Pressure × Area. A 4-inch bore cylinder at 3,000 PSI produces 37,700 pounds of force on the extend stroke. But real-world sizing involves retract force (reduced by the rod area), speed calculations from flow rate, intensification ratio on the retract stroke, and column buckling analysis for long-stroke cylinders.
This guide covers the core calculations, rod sizing for buckling resistance, mount style selection, and the practical considerations that separate a cylinder that works on paper from one that works in the field.
Force, Pressure, and Area: The Core Equation
Extend force = System pressure (PSI) × Bore area (in²). Bore area = π ÷ 4 × Bore diameter². A 3-inch bore cylinder: area = 0.7854 × 9 = 7.069 in². At 3,000 PSI: force = 3,000 × 7.069 = 21,206 lbs.
Retract force is always less than extend force because the rod displaces part of the piston area. Retract area = Bore area − Rod area. A 3-inch bore with a 1.75-inch rod: retract area = 7.069 − 2.405 = 4.664 in². Retract force at 3,000 PSI = 13,992 lbs — only 66% of extend force.
Always size the cylinder for the stroke direction that needs the force. If the working stroke is retract (pulling), you need a larger bore than if the working stroke is extend. Many applications use the extend stroke for the power stroke and retract under light load, but not always.
System pressure is not pump pressure. Account for line losses, valve drops, and filter pressure drop. A pump delivering 3,000 PSI may only provide 2,700 PSI at the cylinder. Size for the pressure available at the cylinder port, not at the pump outlet.
Extend Force = P × (π/4 × Bore²)
Retract Force = P × (π/4 × (Bore² − Rod²))
Common bore areas:
2" bore = 3.142 in² | 3" bore = 7.069 in²
4" bore = 12.566 in² | 5" bore = 19.635 in²
6" bore = 28.274 in² | 8" bore = 50.265 in²
Hydraulic Cylinder Force & Speed Calculator
Calculate hydraulic cylinder extend and retract force, speed, GPM requirements, and Euler rod buckling safety factor for any bore, rod, pressure, and flow combination.
Cylinder Speed from Flow Rate
Cylinder speed (inches per second) = Flow rate (in³/sec) ÷ Piston area (in²). Convert GPM to in³/sec: GPM × 231 ÷ 60 = in³/sec. So 10 GPM = 38.5 in³/sec.
Extend speed with a 4-inch bore at 10 GPM: 38.5 ÷ 12.566 = 3.06 in/sec (15.3 ft/min). Retract speed is faster because the annular area is smaller. With a 2.5-inch rod: retract area = 12.566 − 4.909 = 7.657 in². Retract speed = 38.5 ÷ 7.657 = 5.03 in/sec.
The faster retract speed means more flow exits the rod-end port during extend than enters the cap-end port. During retract, the cap-end port dumps more oil than the rod-end port receives. This flow imbalance matters for regenerative circuits and meter-out flow control sizing.
For precise speed control, use a flow control valve sized for the required flow at the expected pressure drop. Meter-out control (restricting exhaust flow) provides better load stability than meter-in for resistive loads.
Intensification Ratio and Back-Pressure
The intensification ratio is the bore area divided by the annular area (bore area minus rod area). For a 4-inch bore with a 2.5-inch rod: 12.566 ÷ 7.657 = 1.64:1. This ratio tells you how pressure intensifies when oil is trapped on the rod side during extension.
If the system is at 3,000 PSI extending against a load, and the rod-side port is blocked, pressure on the rod side can reach 3,000 × 1.64 = 4,920 PSI. This can exceed the rating of rod-side components, hoses, and fittings. A 2:1 ratio cylinder at 3,000 PSI generates 6,000 PSI on the rod side.
Always ensure rod-side hoses, fittings, and valves are rated for the intensified pressure, not just the system pressure. This is the number one cause of unexpected hose failures on hydraulic equipment. A pressure relief valve on the rod-side circuit prevents damage.
Rod-side pressure = System pressure × (Bore area ÷ Annular area)
Example: 3,000 PSI system, 4" bore, 2.5" rod:
Ratio = 12.566 ÷ 7.657 = 1.64:1
Rod-side pressure = 3,000 × 1.64 = 4,920 PSI
All rod-side components must be rated for this pressure.
Euler Column Buckling and Rod Sizing
Long-stroke cylinders pushing compressive loads can buckle like a column. Euler's formula determines the critical buckling load: F_cr = π² × E × I ÷ (n × L)². E is the modulus of elasticity for steel (30 × 10⁶ PSI). I is the moment of inertia of the rod. L is the stroke length. n is the end condition factor.
End condition factors depend on mounting: n = 2.0 for fixed-free (worst case, clevis mount with no guided load), n = 1.0 for pinned-pinned (both ends pivoting), n = 0.707 for fixed-pinned, n = 0.5 for fixed-fixed (best case, rigid mount with guided load).
A 2-inch rod with 36-inch stroke in a fixed-free mount: I = π × 2⁴ ÷ 64 = 0.785 in⁴. F_cr = π² × 30×10⁶ × 0.785 ÷ (2.0 × 36)² = 44,850 lbs. Apply a safety factor of 3:1 minimum: allowable load = 14,950 lbs.
If the cylinder can produce more force than the rod can safely resist in buckling, upsize the rod or change the mount style. Going from a clevis (fixed-free) to a trunnion with guided load (fixed-fixed) quadruples the allowable load.
F_cr = π² × E × I ÷ (n × L)²
End condition factors (n):
Fixed-free (clevis/trunnion, unguided): 2.0
Pinned-pinned (both pivot): 1.0
Fixed-pinned (one rigid, one pivot): 0.707
Fixed-fixed (rigid mount, guided load): 0.5
Apply safety factor of 3:1 minimum to F_cr.
Pump Flow and Horsepower Requirements
Required GPM = Piston area (in²) × Speed (in/sec) × 60 ÷ 231. For a 4-inch bore at 6 in/sec: 12.566 × 6 × 60 ÷ 231 = 19.6 GPM. Add 5% to 10% for internal leakage in the pump and valves.
Hydraulic horsepower = GPM × PSI ÷ 1,714. For 20 GPM at 3,000 PSI: HP = 20 × 3,000 ÷ 1,714 = 35 HP. The electric motor must be at least this size, plus allowance for pump efficiency (typically 85% to 90%).
Input horsepower = Hydraulic HP ÷ Pump efficiency. At 87% efficiency: 35 ÷ 0.87 = 40.2 HP. Select a 40 HP or 50 HP motor. Starting torque of the pump must not exceed the motor's locked-rotor torque capability.