How to Do Basic Hydraulic Cylinder Calculations

Designing with hydraulic cylinders is very common in everything from injection molds to log splitters to Backhoes and more. Here are some of the most basic calculations used in these applications.

This article shows you how to do the three most basic, and common, calculations for designing with hydraulic cylinders. These three would be the forward force of the cylinder, the return force, and flow rate required for the forward portion of the cycle. The return flow rate and force are lower because the volume and area are reduced by the presence of the piston rod, and therefore is not included in these calculations. The working portion of the hydraulic cylinder cycle should be the piston forward movement, for the above-mentioned reasons.

The first choice to be made is the units you wish to work with, inch or metric.

To calculate the forces generated by the piston, you must enter the appropriate diameter or diameters and the pressure supplied to the cylinder, in the appropriate units. In order to calculate the required volumetric flow rate, you must also use the length of stroke and the time is seconds.
The familiar relationships for area are used to calculate these answers:
Piston forward area = (Piston diameter)^2 x Pi / 4

Piston return area = ((Piston diameter)^2 - (Rod diameter)^2) x Pi / 4

Force = Pressure x Area

GPM = (((Pi * (D^2)) / 4) * S) * (60 / 231) / T

where,
GPM = gallons per minute
D = Piston diameter in inches
S = Stroke in inches
T = time in seconds
the 60 factor converts seconds to minutes
If you have a hydraulic cylinder with a 2.000 diameter piston, a 1.000 diameter rod, a 12-inch stroke, and want to extend the rod in .5 seconds, and the system pressure is 1000 p.s.i., the calculations for force and gallons per minute are as follows.
Piston forward area = 2^2 x Pi/4 = 4 x Pi / 4 = Pi = 3.142 inches^2 (rounded)
Piston return area = ((2)^2 - (1)^2) x Pi / 4 = 2.356 inches^2

Forward Force = 1000 x 3.142 = 3142 pounds
Return Force = 1000 x 2.356 = 2356 pounds
Since the time to extend the piston rod is only affected by the diameter of the piston, we can ignore the piston's rod size.

GPM = (((Pi * (D^2)) / 4) * S) * (60 / 231) / T
GPM = ((3.142 x 4)/4) * S) x (60/231) / .5 = 19.58 gallons per minute.
Of course, if you are going to a have a continuously cycling hydraulic cylinder, you must do the flow rate calculations for both the piston side, and the rod side.
Do not exceed the manufacturers recommendation for pressure in your hydraulic cylinder. Make sure that there are pressure and temperature relief valves for safety, and if in doubt, get professional advice.
Picture courtesy Parker Hannafin.