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) x Flow (GPM)/ 1714 
HP = PQ / 1714 
Actuator Formulas 
Variable 
Word Formula w/ Units 
Simplified Formula 
Cylinder Area  A 
( Sq. In.) = pi x Radius (inch)^{2} 
A = pi x R^{2} 
(Sq. In.) = pi x Diameter (inch)^{2} / 4 
A = pi x D^{2} / 4 
Cylinder Force  F 
(Pounds) = Pressure (psi) x Area (sq. in.) 
F = P x A 
Cylinder Speed  v 
(Feet / sec.) = (231 x Flow Rate (gpm)) / (12 x 60 x Area) 
v = (0.3208 x gpm) / A 
Cylinder Volume Capacity  V 
Volume = pi x Radius^{2} x Stroke (In.) / 231 
V = pi x R^{2} x L / 231
(L = length of stroke) 
Cylinder Flow Rate  Q 
Volume = 12 x 60 x Velocity (Ft./Sec.) x Net Area(In.)^{2} / 231 
Q = 3.11688 x v x A 
Fluid Motor Torque  T 
Torque (in. lbs.) = Pressure (psi) x disp. (in.^{3} / rev.) / 6.2822 
T = P x d / 6.2822

Torque = HP x 63025 / RPM 
T = HP x 63025 / n 
Torque = Flow Rate (GPM) x Pressure x 36.77 / RPM 
T = 36.77 x Q x P / n 
Fluid Motor Speed  n 
Speed (RPM) = (231 x GPM) / Disp. (in.)^{3} 
n = (231 x GPM) / d 
Fluid Motor Horsepower  HP 
HP = Torque (in. lbs.) x rpm / 63025 
HP = T x n / 63025 
Pump Formulas 
Variable 
Word Formula w/ Units 
Simplified Formula 
Pump Output Flow  GPM 
GPM = (Speed (rpm) x disp. (cu. in.)) / 231 
GPM = (n x d) / 231 
Pump Input Horsepower  HP 
HP = GPM x Pressure (psi) / 1714 x Efficiency 
HP = (Q x P) / 1714 x E 
Pump Efficiency  E 
Overall Efficiency = Output HP / Input HP 
E_{Overall} = HP_{Out} / HP_{In X 100} 
Overall Efficiency = Volumetric Eff. x Mechanical Eff. 
E_{Overall} = Eff_{Vol.} x Eff_{Mech.} 
Pump Volumetric Efficiency  E 
Volumetric Efficiency = Actual Flow Rate Output (GPM) / Theoretical Flow Rate Output (GPM) x 100 
Eff_{Vol.} = Q_{Act.} / Q_{Theo.} x 100 
Pump Mechanical Efficiency  E 
Mechanical Efficiency = Theoretical Torque to Drive / Actual Torque to Drive x 100 
Eff_{Mech} = T_{Theo.} / T_{Act.} x 100 
Pump Displacement  CIPR 
Displacement (In._{3} / rev.) = Flow Rate (GPM) x 231 / Pump RPM 
CIPR = GPM x 231 / RPM 
Pump Torque  T 
Torque = Horsepower x 63025 / RPM 
T = 63025 x HP / RPM 
Torque = Pressure (PSIG) x Pump Displacement (CIPR) / 2 pi 
T = P x CIPR / 6.28 