Hydraulic Cylinder Design & Sizing Calculator
Calculate push/pull forces, required bore sizing, extend/retract velocities, hydraulic pump power, and Euler rod column buckling screening.
Cylinder Parameters
Mathematical Models & Equations
F_{push} = P \cdot A_{bore} \cdot \eta = P \cdot \frac{\pi d_{bore}^2}{4} \cdot \etaF_{pull} = P \cdot A_{annulus} \cdot \eta = P \cdot \frac{\pi (d_{bore}^2 - d_{rod}^2)}{4} \cdot \etaP_{cr} = \frac{\pi^2 E I}{(K \cdot L)^2} \quad \text{where } I = \frac{\pi d_{rod}^4}{64}P_{hyd} = \frac{P \cdot Q}{600} \quad [\text{kW for } P \text{ in bar, } Q \text{ in L/min}]Verification Calculation Log
- 1Calculate Piston & Annulus Area:
- •A_bore = π · (100 mm)² / 4 = 7853.98 mm²
- •A_rod = π · (50 mm)² / 4 = 1963.50 mm²
- •A_annulus = A_bore - A_rod = 5890.49 mm²
- 2Calculate Push and Pull Forces:
- •F_push = P · A_bore · η = 149.23 kN
- •F_pull = P · A_annulus · η = 111.92 kN
- •Push/Pull Force Ratio = 1.33:1
- 3Speed and Velocity:
- •Extend Speed = 53.05 mm/s
- •Retract Speed = 70.74 mm/s
- 4Euler Column Buckling Evaluation (Ideal Column Screening):
- •Effective Length L_eff = 500.0 mm
- •Critical Buckling Load P_cr = 2422.37 kN
- •Buckling Safety Factor SF = 16.23 (Target ≥ 2.0; screening check only — not a standards-certified analysis; ISO/TS 13725:2021 provides a more comprehensive method for evaluating hydraulic-cylinder buckling using cylinder geometry and mounting configuration)
Calculation Results
149.2 kN
111.9 kN
7854.0 mm²
5890.5 mm²
53.1 mm/s
70.7 mm/s
9.42 s
7.07 s
8.33 kW
2422.4 kN
Buckling SF: 16.23
Engineering Application Notes
Pull force is consistently lower than push force due to the rod cross-sectional area reducing active pressurized piston surface (Annulus Area). Retract speed is higher than extend speed at a constant pump flow rate because less fluid volume is required to fill the annulus cavity. Euler Ideal-Column Rod Buckling Screening Estimate: rod buckling is evaluated using Euler's ideal column formulation as a preliminary screening check. This calculator provides a screening estimate only and is not a standards-certified analysis. ISO/TS 13725:2021 provides a more comprehensive method for evaluating hydraulic-cylinder buckling using cylinder geometry and mounting configuration. Industrial standard operating pressures typically range from 160 bar to 210 bar (2,300–3,000 psi) for standard mobile and stationary hydraulics.
Standard Citations & References
- ISO 6020/2 - Fluid power cylinders - Mounting dimensions for single rod cylinders, 160 bar compact series.
- ISO/TS 13725:2021 - Hydraulic fluid power — Method for evaluating the buckling load of an oil-hydraulic cylinder.
- NFPA/T3.6.7 R2 - Fluid power systems - Cylinder dimensions and column strength.