Hydraulics Calculators

Get to know the math and engineering calculation of hydraulics.

Basic Formulas

Pressure, Force and Horsepower Relationships :

Pressure (psi)  =  force (lbs)  /  area (in²)

Force (lbs)  =  area (in²)  x  pressure (psi)  

Area (in²)  =  force (lbs)  /  pressure (psi)

Fluid Power Horsepower:

Fluid Power Horsepower (hp)  =  pressure (psi)  x  pump flow (gpm)  /  1,714 

Torque and Horsepower Relationships::

Torque (ft lbs)  =  horsepower (hp) x 5,252  /  speed (rpm)

Horsepower (hp)  =  torque (ft lbs) x speed (rpm)  /  5,252

Speed (rpm)  =  horsepower (hp) x  5,252  /  torque (ft lbs)  

Basic Cylinder Calculations:
Piston Cylinder Area (in²) = diameter squared x .7854

(Can also use 3.1416 x radius squared (ins) ) 

Piston Rod End (annulus end) Area (in²)  =  piston cylinder area (in²)  –  rod area (in²)

Cylinder Force (lbs)  =  pressure (psi) x area (in²)

Cylinder Speed (ft/min)  =  19.25 x flow rate (gpm)  /  area (in²)    

(Divide by 60 to convert speed to ft/sec)

Cylinder Speed (in/min)  =  flow rate (cu ins/min)  /  area (in²) 

(Note that 1 US gallon  =  231 cu ins) 

Cylinder Time (secs)  =  area (in²) x cylinder stroke (ins) x .26  /  flow rate (gpm)

Cylinder Flow Rate (gpm)  =  12 x 60 x cylinder speed (ft/sec) x area (in²)  /  231

Cylinder Volume Capacity (gals)  =  cylinder area (in²) x cylinder stroke (ins)  /  231

Basic Pump Calculations:

Pump Outlet Flow (gpm)  =  pump speed (rpm) x pump displacement (cu ins/rev)  /  231

Pump Speed (rpm)  =  231 x pump flow rate (gpm)  /  pump displacement (cu ins/rev)

Pump Horsepower (hp)  =  flow rate (gpm) x pressure (psi)  / 1,714 x pump efficiency factor

(Can also use horsepower (hp)  =  torque (in lbs) x pump speed (rpm)  /  63,025)

Pump Torque (in lbs)  =  pressure (psi) x pump displacement (cu ins/rev)  /  6.28

(Can also use horsepower (hp) x 63,025  /  pump displacement (cu ins/rev)  

Commonly Used Fluid Power Equivalents:

One US gallon equals:

  • 231 cubic inches
  • 3.785 liters  (1 liter = .2642 US gals)
  • 4 quarts or 8 pints
  • 128 ounces liquid  /  133.37 ounces weight
  • 8.3356 pounds weight

On psi equals:

  • .0689 bar  (1 bar = 14.504 psi)
  • 6.895 kilopascal
  • 2.0416 hg (inches of mercury)
  • 27.71” water

One atmosphere equals:

  • 14.696 psi
  • 1.013 bar
  • 29.921 hg (inches of mercury)

Note: This information is provided as a quick reference resource and is not intended to serve as a substitute for qualified engineering assistance. While every effort has been made to ensure the accuracy of this information, errors can occur.