Basic
Fluid Power Formulas / Hydraulics
/ Pneumatics

Variable

Word Formula
w/ Units

Simplified Formula

Fluid
Pressure  P 
(PSI)
= Force (Pounds) / Area ( Sq. In.) 
P
= F / A 
Fluid
Flow Rate  Q 
GPM=
Flow (Gallons) / Unit Time (Minutes) 
Q
= V / T 
Fluid
Power in Horsepower  HP 
Horsepower
= Pressure (PSIG) × Flow (GPM)/ 1714 
HP
= PQ / 1714 
Actuator
Formulas

Variable

Word Formula
w/ Units

Simplified Formula

Cylinder
Area  A 
(
Sq. In.) = π × Radius (inch)^{2} 
A
= π × R^{2} 
(Sq.
In.) = π × Diameter (inch)^{2}
/ 4 
A
= π × D^{2} / 4 
Cylinder
Force  F 
(Pounds)
= Pressure (psi) × Area (sq.
in.) 
F
= P × A 
Cylinder
Speed  v 
(Feet
/ sec.) = (231 × Flow Rate (gpm)) /
(12 × 60 × Area) 
v
= (0.3208 × gpm) / A 
Cylinder
Volume Capacity  V 
Volume
= π × Radius^{2} × Stroke
(In.) / 231 
V = π × R^{2}
× L / 231
(L = length of stroke)

Cylinder
Flow Rate  Q 
Volume
= 12 × 60 × Velocity (Ft./Sec.) × Net
Area(In.)^{2} / 231 
Q
= 3.11688 × v × A 
Fluid
Motor Torque  T 
Torque
(in. lbs.) = Pressure (psi) × disp.
(in.^{3} / rev.) / 6.2822 
T
= P × d / 6.2822

Torque
= HP × 63025 / RPM 
T
= HP × 63025 / n 
Torque
= Flow Rate (GPM) × Pressure × 36.77
/ RPM 
T
= 36.77 × Q × P / n 
Fluid
Motor Speed  n 
Speed
(RPM) = (231 × GPM) / Disp.
(in.)^{3} 
n
= (231 × GPM) / d 
Fluid
Motor Horsepower  HP 
HP = Torque (in. lbs.) × rpm / 63025 
HP
= T × n / 63025 
Pump
Formulas

Variable

Word Formula
w/ Units

Simplified Formula

Pump
Output Flow  GPM 
GPM
= (Speed (rpm) × disp. (cu. in.)) /
231 
GPM
= (n ×d) / 231 
Pump
Input Horsepower  HP 
HP
= GPM × Pressure (psi) / 1714
× Efficiency 
HP
= (Q ×P) / 1714 × E 
Pump
Efficiency  E 
Overall
Efficiency = Output HP / Input HP 
E_{Overall}
= HP_{Out} / HP_{In X 100} 
Overall
Efficiency = Volumetric Eff. × Mechanical
Eff. 
E_{Overall}
= Eff_{Vol.} × Eff_{Mech.}

Pump
Volumetric Efficiency  E 
Volumetric
Efficiency = Actual Flow Rate Output
(GPM) / Theoretical Flow Rate Output
(GPM) × 100 
Eff_{Vol.}
= Q_{Act.} / Q_{Theo.}
X 100 
Pump
Mechanical Efficiency  E 
Mechanical
Efficiency = Theoretical Torque to Drive
/ Actual Torque to Drive × 100 
Eff_{Mech}
= T_{Theo.} / T_{Act.}
× 100 
Pump
Displacement  CIPR 
Displacement
(In._{3} / rev.) = Flow Rate
(GPM) × 231 / Pump RPM 
CIPR
= GPM × 231 / RPM 
Pump
Torque  T 
Torque
= Horsepower × 63025 / RPM 
T
= 63025 × HP / RPM 
Torque
= Pressure (PSIG) × Pump Displacement
(CIPR) / 2π 
T
= P × CIPR / 6.28 