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Hydraulic Calculators

Nine interactive calculators for speccing a hydraulic system: cylinder force and speed, piston and rod-end areas, oil volume, pump horsepower and flow, motor torque and horsepower. Enter your numbers — results update as you type.

Cylinder Force Calculator
Cylinder Piston Area
Rod-End (Annulus) Area
Cylinder Oil Volume
Cylinder Speed / Required Flow
Pump Input Horsepower
Hydraulic Motor Torque
Hydraulic Motor Horsepower
Pump Output Flow

Sizing a cylinder for a press, splitter, or loader? The Hydraulic Cylinder Force Calculator guide pairs the force tool with worked examples, safety factors, real-world force losses, and a metric conversion table.

Cylinder Force Calculator

Size a cylinder for the load: enter bore, rod, and system pressure to get extend and retract force in pounds and tons.

Bore + Rod + PSI → Push / Pull force

Bore diameter (in)Rod diameter (in)Pressure (PSI)

Push force (extend): 31,416 lbf · 15.71 tons
Pull force (retract): 23,562 lbf · 11.78 tons

Real-world output runs 10–15% lower after friction and back-pressure. Browse hydraulic cylinders or request a quote with your bore, rod, stroke, and mount.

Cylinder Piston Area

The blank-end area is the basis for every force and speed calculation.

Area = Bore² × 0.7854

Bore diameter (in)

Piston area: 12.57 in²

Rod-End (Annulus) Area

The retract-side area — it sets pull force and retract speed.

Area = (Bore² − Rod²) × 0.7854

Bore diameter (in)Rod diameter (in)

Rod-end area: 9.42 in²

Cylinder Oil Volume

Oil needed to extend the cylinder — use it to sanity-check reservoir size.

Volume = Area × Stroke ÷ 231

Bore diameter (in)Stroke (in)

Oil to extend: 1.31 gal
Volume: 301.6 in³

Cylinder Speed / Required Flow

Pick the pump flow that hits your target cycle time.

GPM = Area × Stroke × 60 ÷ (Time × 231)

Bore diameter (in)Stroke (in)Time to extend (s)

Required flow: 15.67 GPM
Rod speed: 4.8 in/s

Shop hydraulic pumps by GPM.

Pump Input Horsepower

The engine or motor power a pump needs at a given pressure and flow.

HP = PSI × GPM ÷ (1714 × Efficiency)

Pressure (PSI)Flow (GPM)Efficiency (%)

Input power needed: 17.16 HP

Hydraulic Motor Torque

Theoretical output torque from pressure and displacement.

Torque = PSI × Displacement ÷ 6.28

Pressure (PSI)Displacement (in³/rev)

Output torque: 3,583 lb-in (299 lb-ft)

Shop hydraulic motors by displacement.

Hydraulic Motor Horsepower

Shaft power from torque and speed.

HP = Torque × RPM ÷ 63,025

Torque (lb-in)Speed (RPM)

Output power: 14.6 HP

Pump Output Flow

Flow a pump delivers at a given drive speed.

GPM = RPM × Displacement ÷ 231

Drive speed (RPM)Displacement (in³/rev)

Output flow: 11.69 GPM

Need help matching a pump or motor? Request a quote and an NH specialist will confirm displacement, ports, and shaft.

Numbers in hand but not sure which part matches them? Request a quote — send your figures and an NH specialist will spec the pump, motor, or cylinder, including obsolete cross-references.