Hydraulics & Fluid Power Reference Library · Wall Charts

Fluid Power Formulas Chart

The basic formulas for cylinder force and area, cylinder speed, pump flow, motor speed and torque, and hydraulic horsepower, in US units with metric equivalents.

Ref HY-0053

Draft, open for review. Check every value against the governing standard and the manufacturer’s data before use.

What it is

A short set of formulas for checking hydraulic circuits. They give theoretical values. Real systems lose some force, flow and power to friction, leakage and heat. Use the manufacturer's efficiency data for final figures. Units must match the formula. One US gallon is 231 cubic inches.

How to use it

Pick the formula for the value you need.
Convert all inputs to the units shown.
For a cylinder, use the full bore area when extending and the annulus area (bore minus rod) when retracting.
Apply efficiency at the end. Divide by efficiency for input power. Multiply by efficiency for output force or torque.

Formula chart (US units)

To find	Formula	Units
Area of a circle	A = 0.7854 x D²	in², D in inches
Annulus (rod side) area	A = 0.7854 x (D² − d²)	in², D = bore, d = rod
Cylinder force	F = P x A	lbf, P in psi, A in in²
Cylinder speed	v = (231 x Q) / (60 x A)	in/s, Q in gpm, A in in²
Cylinder volume	V = A x stroke / 231	gallons, stroke in inches
Pump flow	Q = (displacement x rpm) / 231	gpm, displacement in in³/rev
Motor speed	rpm = (231 x Q) / displacement	Q in gpm, displacement in in³/rev
Motor torque	T = (P x displacement) / 6.283	lb-in, P in psi
Hydraulic horsepower	HP = (Q x P) / 1714	Q in gpm, P in psi
Fluid velocity in a line	v = (0.3208 x Q) / A	ft/s, A = line inside area in in²

Metric equivalents

To find	Formula	Units
Cylinder force	F = 10 x P x A	N, P in bar, A in cm²
Hydraulic power	kW = (Q x P) / 600	Q in L/min, P in bar
Pump flow	Q = (displacement x rpm) / 1000	L/min, displacement in cm³/rev

Key points

Pressure is set by the load. Flow sets the speed.
Retracting is faster but weaker than extending at the same flow and pressure.
Input horsepower to the pump is hydraulic horsepower divided by overall pump efficiency.
Line velocity checks help size suction, pressure and return lines. Use the component maker's recommended velocity limits.

Common mistakes

Using bore area for the retract stroke.
Mixing units, such as psi with cm².
Treating theoretical pump flow as actual flow at full pressure.

Governing standards: Unit conversions per NIST SP 811; component manufacturer efficiency and rating data.

Reference only. Verify against the current governing code or standard, the manufacturer's data and the project documents before use. Apps for Distributors disclaims liability arising from reliance on this reference.

More in Wall Charts

← All Hydraulics & Fluid Power sheets