Enter the pressure, piston diameter, and (for retraction) rod diameter to calculate the extension (push) or retraction (pull) force of a hydraulic cylinder.

Hydraulic Force Calculator

Select extension (push) or retraction (pull). Enter the known values and leave one field blank to calculate it.







Hydraulic Force Formula

The following formulas are used to calculate the extension (push/cap-side) and retraction (pull/rod-side) forces of a hydraulic cylinder. 

\begin{aligned}
F_{\text{push}} &= P\cdot \frac{\pi D_p^{2}}{4}\\
F_{\text{pull}} &= P\cdot \frac{\pi\left(D_p^{2}-D_r^{2}\right)}{4}
\end{aligned}
  • where F is force (lbf, N)
  • P is pressure (psi, kPa)
  • Dp is piston diameter (in, cm, mm)
  • Dr is rod diameter (in, cm, mm) (used for retraction/pull only)

To calculate the retraction (pull) force, multiply the pressure by the annulus area: π times the difference between the piston diameter squared and the rod diameter squared, divided by 4. To calculate the extension (push) force, use the full piston area: π·Dp2/4.

Hydraulic Force Definition

Hydraulic force is the linear force a hydraulic cylinder can produce, equal to the applied fluid pressure multiplied by the cylinder’s effective piston area (full bore area for extension, and annulus area for retraction).

Example Problem

How to calculate hydraulic force?

  1. First, determine the pressure acting on the rod side of the cylinder.

    For this example problem, the pressure is measured to be 100 psi.

  2. Next, determine the rod diameter.

    The rod is measured to have a diameter of 5 in.

  3. Next, determine the piston diameter.

    The piston is measured to have a diameter of 12 in.

  4. Finally, calculate the hydraulic force.

    The hydraulic (retraction/pull) force is calculated using the formula F = P * (π*(Dp2 - Dr2)/4) = 100 * (π*(122 - 52)/4) = 9346.23 lb-f.

FAQ

What is the significance of rod diameter in calculating hydraulic force?

The rod diameter is crucial in calculating hydraulic retraction (pull) force because it directly influences the effective annulus area on the rod side of the cylinder. A larger rod diameter reduces the effective area available for the pressure to act upon on the rod side, thereby reducing the retraction force generated by the hydraulic cylinder.

Can hydraulic force be negative?

Hydraulic force itself is typically reported as a positive magnitude (push or pull). However, the direction of the force can be considered negative if it opposes a chosen reference direction in a physical system or mathematical model.

How does pressure affect the hydraulic force?

Pressure is directly proportional to the hydraulic force generated by a cylinder. According to the hydraulic force formula, an increase in pressure will result in a proportional increase in force. This relationship allows for the control of the force output by adjusting the hydraulic system's pressure.

hydraulic force calculator