Fluid Power Formulas | Magister Hydraulics
Fluid Power Formulas | Magister Hydraulics
Extend Area (in²) = π * Bore Diameter (in)²


Extend Volume (in³) = π * Bore Diameter (in)² * Stroke (in)


Extend Time (sec) = Extend Volume (in³) * 60

Flow (gpm) * 231

Extend Rate (in/sec) = Flow (gpm) * 231

Extend Area (in²) * 60

Extend Force (lbs) = Extend Area (in²) * Pressure (psi)
Retract Area (in²) = π * (Bore Diameter (in)² – Rod Diameter (in)²)


Retract Volume (in³) = π * (Bore Diameter (in)² ‐ Rod Diameter (in)²) * Stroke (in)


Retract Time (sec) = Retract Volume (in³) * 60

Flow (gpm) * 231

Retract Force (lbs) = Retract Area (in²) * Pressure (psi)
Retract Rate (in/sec) = Flow (gpm) * 231

Retract Area (in²) * 60

Retract Rod Area (in²) = Rod Diameter (in)² * 0.7854
Cylinder Ratio = Extend Area (in²)

Retract Area (in²)

Flow out rod (gpm) = Flow in base (gpm)

Cylinder Ratio

Flow out base (gpm) = Flow in rod (gpm) * Cylinder Ratio
Cycle Time (sec) = Extend time (sec) + Retract Time (sec)
Hydraulic Power (HP) = Pressure (psi) * Flow (gpm)




Sample of Calculation – Force of Hydraulic Cylinder




The force produced on the rod side of a double-acting hydraulic piston – can be expressed as

F1 = P1 (π (d22 – d12) / 4)

F1 = rod force (lb, N)

d1 = rod diameter (in, mm)

d2 = piston diameter (in, mm)

P1 = pressure in the cylinder on the rod side (psi, N/mm2)

1 bar = 105 N/m2 = 0.1 Nm/mm2

The force produced on the opposite of rod side – can be expressed as

F2 = P2 (π d22 / 4)

F2 = rod force (lb, N)

P2 = pressure in the cylinder (opposite rod) (psi, N/mm2)

Hydraulic systems leverage the power of liquid mechanics to generate force and motion. At the heart of these systems is the hydraulic cylinder that converts hydraulic energy into useful mechanical energy. The force exerted by the cylinder is a function of the cylinder pressure applied and the size of the piston and rod.

Two primary scenarios dictate the force calculation:

  1. Rod Side Force (F1): This is the force produced on the rod side of a double-acting hydraulic piston. It takes into account the diameters of both the rod and the piston, as well as the pressure on the rod side.
  2. Opposite Rod Side Force (F2): This force is produced on the side opposite to the rod in the hydraulic cylinder. It’s calculated using the piston diameter (cylinder bore diameter) and the pressure on the opposite side.

Both these forces play a key role in determining the overall efficiency, power, and longevity of a hydraulic system. By understanding and optimizing these forces, you can ensure that the hydraulic system operates at its peak potential, reducing wear and tear and ensuring longer operational life.

Plus, for those in industries like construction, manufacturing, or any field that relies on hydraulic machinery, having a clear grasp of these forces can aid in system design, troubleshooting, and regular maintenance.


Hydraulics and hydraulic power are a blend of science and engineering, where precision and knowledge drive performance. By understanding the forces at play in your hydraulic system, you can ensure its longevity, efficiency, and reliability. And remember, while our piston cylinder force calculator is a valuable tool, nothing beats the expertise of seasoned professionals. If you find yourself in need of hydraulic cylinder repairs, advice, or any related services, don’t hesitate to contact Cylinders, Inc. We’re here to ensure your hydraulic systems run smoothly, efficiently, and effectively.


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