Hydraulic Formulas & Calculator — Learn Fittings
Common hydraulic formulas plus an interactive calculator for cylinder area, force, volume, flow rate, pump and motor horsepower, torque, and displacement.
This page offers calculators for the most common hydraulic formulas — cylinder area, force, volume and flow rate, plus pump and motor horsepower, torque, and displacement. Enter your known values into the interactive calculator below to solve for the unknown, or work backwards to size a cylinder, pump, or motor. The formulas each calculator uses are listed for reference below.
Formulas
Cylinder Area (Sq.In.)
(Bore Diameter)/2)2 × π(3.14) = Piston Surface Area
Use this to find the area in working square inches on the barrel side of the piston in square inches.
Cylinder Rod End Area (Sq.In.)
((Bore Diameter / 2)2 - (Rod Diameter / 2)2) × 3.14 = Rod Side Piston Surface Area
Use this to find the working surface area on the rod side of the piston in square inches.
Cylinder Volume
Piston Surface Area × Stroke / 231 = Gallons (Volume)
Use this to determine volume of oil to fill a cylinder.
Cylinder Force
(Cyl. Area) in2 × PSI = (Pounds of Force) LBF.
Determine how much force will be applied with a certain cylinder and psi. You can also work backwards to find out what psi you would need to run to achieve a specific amount of force.
Cylinder Flow Rate (and Velocity)
CYLINDER AREA IN2 × CYLINDER STROKE × 60 ÷ TIME IN SECONDS × 231 = GPM
Use this to find the rate of flow based on cylinder speed or use to calculate the speed your cylinder will travel based on your GPM.
Pump Input Horsepower
PSI × GPM ÷ 1714 × PUMP EFFICIENCY = HP
Determine your required engine horsepower using your PSI and GPM.
Motor Horsepower (Fluid Motor)
TORQUE × RPM ÷ 63025 = MOTOR HP
Determine your horsepower using your torque and rpm. Work backwards using your rpm and hp to determine your torque.
Motor Torque
PSI × MOTOR DISPLACEMENT ÷ 6.28 = MOTOR TORQUE
Determine your motor torque using the psi and motor displacement.
Pump Flow or Displacement
RPM × DISPLACEMENT ÷ 231 = GPM
Determine your pumps gpm or work backwards to figure out your displacement.
Tip
Most of these formulas can be rearranged to solve for any single variable. Use the calculator below to fill in what you know and let it solve for the rest.
Inputs
Push/pull force from pressure acting on the piston area.
Result