Hydraulic Cylinder Calculator & Simulator

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🚀 Hydraulic Cylinder Calculator & Simulator

HYDRAULIC CYLINDER

Hydraulic Cylinder Thrust & Differential Flow Rate Calculator
ACTUATOR PHYSICAL ENGINE

Actuator Design Specifications

Range: 20 to 200 mm
mm
Range: 10 to 140 mm
mm
Range: 50 to 1,000 mm
mm
Range: 10 to 350 bar
bar
Range: 1 to 150 LPM
L/min (LPM)

Standard Industrial Cylinder Presets

Double-Acting Stroke Real-Time Simulator

Stroke Status: Standby
Piston Extension Speed 66.3 mm/s
Piston Retraction Speed 95.4 mm/s
Extension/Retraction Area Ratio 1.44x
THEORETICAL EXTEND FORCE 70.37 kN (7.18 Ton) Retraction Force: 48.09 kN (4.90 Ton)
Extend Area (Cap Area) 50.27 cm²
Retract Area (Rod End Area) 34.36 cm²
Extension Stroke Time (Extend Time) 4.52 s
Retraction Stroke Time (Retract Time) 3.14 s

Piston Thrust Calculation Formula

F = P × A

* Net static thrust calculated using the pressure unit conversion 1 bar = 100,000 Pa (N/m²).

Disclaimer: The calculations provided by this simulator are for educational and reference purposes only. For actual product design or manufacturing, please verify with the latest engineering standards and official design codes. The integrity of the calculated values is not guaranteed, and the developer and this blog assume no liability for any direct or indirect damages arising from their use.
💡 💡 Quick User Guide
  1. Set Cylinder Bore (D) and Rod Diameter (d): Use the sliders to input the piston’s bore diameter and the shaft’s rod diameter. (The rod diameter must always be smaller than the bore diameter.)
  2. Input Hydraulic System Supply Variables: Set the rated hydraulic pressure (bar) generated by the pump and the system flow rate (LPM).
  3. Observe Real-Time Cycle Operation and Switching: Use the physics engine animation to observe the slow, powerful thrust during piston extension, and the faster but weaker retraction movement caused by the smaller volume of fluid required due to the rod area.
  4. Analyze Thrust and Velocity Data: Determine the optimal hydraulic actuator specifications based on the extension and retraction forces (kN, Ton) and velocity (mm/s) results displayed on the instrument panel.
📚 Theoretical Formulas for Hydraulic Cylinder Thrust and Extension/Retraction Differential Flow Velocity ▼

1. Cylinder Piston Effective Area and Extension/Retraction Geometric Formulas

In a double-acting hydraulic cylinder, the effective cross-sectional areas in contact with the fluid differ between the **Cap End / Head End**, which is pressurized during extension, and the **Rod End / Annulus End**, which is pressurized during retraction. This geometric asymmetry in area leads to a **differential effect**, causing the force and velocity to differ between extension and retraction even under the same pressure and flow rate.

① Pressurized Area during Extension (Cap End Area, A_push): Pressure acts on the entire bore area.

A_push = π × D² / 4  [mm²]

② Pressurized Area during Retraction (Annulus / Rod End Area, A_pull): The area occupied by the rod is subtracted from the total piston area.

A_pull = π × (D² – d²) / 4  [mm²]

2. Theoretical Extension/Retraction Thrust Force Formulas Based on Operating Pressure

The pushing and pulling force of a cylinder is calculated by multiplying the pressurized effective area by the operating hydraulic pressure (P). Since practical engineering designs typically use bar and mm units, the following unit conversion formulas are used to calculate force in kN and the metric engineering unit tonf (ton-force).

F_extend = (P_bar × 10&sup5; × A_push_m²) / 1,000  [kN]

F_extend [tonf] ≈ F_extend [kN] / 9.80665

F_retract = (P_bar × 10&sup5; × A_pull_m²) / 1,000  [kN]

3. Operating Velocity and Travel Time Formulas Based on Flow Rate

The piston travel velocity resulting from the supply flow rate (Q_LPM) is defined as the flow rate divided by the effective cross-sectional area of the cylinder.

v_extend = Q / A_push  ,   v_retract = Q / A_pull

The formula for deriving the actual travel velocity (mm/s), including unit conversions, is as follows:

v_extend [mm/s] = (Q_LPM × 10&sup6;) / (60 × A_push_mm²) = (16,666.7 × Q_LPM) / A_push_mm²

Since the retraction pressurized area A_pull is always smaller than A_push, the retraction velocity (v_retract) is faster than the extension velocity (v_extend), with the speed ratio changing dynamically based on the ratio of the bore and rod diameters.

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