About Hydraulic Cylinder Calculator — Push/Pull Force & Speed
The hydraulic cylinder calculator turns bore, rod, pressure, and pump flow into the four numbers that size a cylinder: push (extend) force, pull (retract) force, extend speed, and retract speed. Force is pressure times area — the full piston circle π/4·B² when extending, the annulus π/4·(B²−R²) when retracting, because the rod occupies part of the piston face on the rod side. Speed is flow divided by the same two areas.
The rod-side asymmetry is the useful intuition: the same cylinder always pulls weaker but retracts faster, in exactly the ratio of annulus to bore area. A 100 mm bore with a 56 mm rod at 200 bar pushes 157 kN but pulls only 108 kN, and on 40 L/min it extends at 0.085 m/s but retracts at 0.124 m/s. Work in mm/bar/L·min or in/psi/gpm — the toggle converts your entries and keeps them valid.
How It Works
- Enter the bore (piston) diameter and rod diameter — from the cylinder's spec plate or catalog listing. The rod must be smaller than the bore; the calculator rejects impossible geometry outright.
- Enter the working pressure (the relief-valve or system setting, not the pump's catalog maximum) and the pump flow reaching the cylinder.
- Push force is P × π/4 × B²: pressure acting on the whole piston circle during extension. Pull force is P × π/4 × (B² − R²): on retraction the fluid only presses on the annulus around the rod.
- Extend speed is Q ÷ bore area and retract speed is Q ÷ annulus area — continuity, so the smaller rod-side area makes retraction proportionally faster at the same flow. The tool reports m/s (with in/s in imperial mode) for both directions.
- Toggle between metric (mm, bar, L/min) and imperial (in, psi, gpm) at any time: entries are converted, rounded to the field's step, and clamped to the valid range so a working setup never turns into an error.
Worked Example
A 100 mm bore cylinder with a 56 mm rod runs at 200 bar (20 MPa) on 40 L/min. Bore area: π/4 × 0.100² = 7.854×10⁻³ m², so push force = 20×10⁶ × 7.854×10⁻³ = 157.08 kN. Annulus area: π/4 × (0.100² − 0.056²) = 5.391×10⁻³ m², so pull force = 107.82 kN — about 69% of the push, the price of the rod. Speeds from the same areas: extend = (40/60000) ÷ 7.854×10⁻³ = 0.0849 m/s, retract = 0.1237 m/s. The chart below runs the same 200 bar across the standard 40–125 mm bores with the common rod ≈ bore/2 proportion.
Hydraulic cylinder force chart at 200 bar
Push and pull force for the common ISO bore sizes at 200 bar working pressure, with the rod at the frequent bore/2 proportion (40 mm bore → 20 mm rod, and so on — every value enterable in the tool at its 0.5 mm step). Pull is always 75% of push at this rod ratio because the rod removes a quarter of the piston area.
| Bore (rod = bore/2) | Push force (kN) | Pull force (kN) |
|---|---|---|
| 40 mm bore, 20 mm rod | 25.13 | 18.85 |
| 50 mm bore, 25 mm rod | 39.27 | 29.45 |
| 63 mm bore, 31.5 mm rod | 62.34 | 46.76 |
| 80 mm bore, 40 mm rod | 100.53 | 75.40 |
| 100 mm bore, 50 mm rod | 157.08 | 117.81 |
| 125 mm bore, 62.5 mm rod | 245.44 | 184.08 |
Formulas
- Push (extend) force
F_push = P × (π/4) × B²- Pull (retract) force
F_pull = P × (π/4) × (B² − R²)- Extend and retract speed
v_extend = Q / (π/4 · B²); v_retract = Q / (π/4 · (B² − R²))
Standards & References
- Force and speed relations from fluid-power fundamentals: F = P·A and continuity Q = A·v (any hydraulics text, e.g. Esposito, Fluid Power with Applications)
- Unit conversions per NIST SP 811 Appendix B: 1 bar = 100 kPa and 1 in = 25.4 mm (exact), 1 psi = 6.894757 kPa, 1 US gal = 3.785411784 L (exact)
- Bore/rod sizes in the chart follow the common ISO 3320 bore series (40, 50, 63, 80, 100, 125 mm); actual rod options vary by cylinder series — use your catalog's rod diameter
Frequently Asked Questions
How do I calculate hydraulic cylinder force?
Multiply pressure by piston area: F = P × π/4 × B². A 100 mm (0.1 m) bore at 200 bar (20 MPa) gives 20×10⁶ × π/4 × 0.01 = 157 kN — about 16 tonnes of push. In imperial units the same arithmetic reads directly in pounds: a 4 in bore at 3,000 psi pushes 3,000 × 12.57 = 37,700 lbf.
Why does a cylinder pull less than it pushes?
Because on retraction the hydraulic fluid can only press on the ring of piston face around the rod: area π/4 × (B² − R²). With the common rod ≈ half-bore proportion the annulus is 75% of the bore area, so pull force is 75% of push — 107.8 kN versus 157.1 kN in the worked example. The larger the rod (for buckling resistance on long strokes), the bigger the gap.
How fast will my cylinder move?
Divide the flow by the area the fluid fills: extend speed = Q ÷ (π/4·B²), retract speed = Q ÷ (π/4·(B²−R²)). 40 L/min into a 100 mm bore extends at 0.085 m/s; the same flow retracts at 0.124 m/s because the rod-side volume is smaller. Note the flip side: the same asymmetry that speeds retraction also returns more flow to tank than the pump delivers during retract — plumbing and valves must handle it.
What pressure should I use in the calculation?
The actual working pressure at the cylinder — normally the system relief-valve setting minus line losses, not the pump's catalog maximum. Mobile equipment commonly runs 200–350 bar (3,000–5,000 psi); industrial systems often 100–210 bar. If you need a specific force, run the calculation backwards: required P = F ÷ (π/4·B²), then confirm the cylinder's rated pressure covers it with margin.
Does this calculator account for efficiency and seal friction?
No — it returns theoretical (ideal) force and speed. Real cylinders lose a few percent to seal friction (typical force efficiency 90–97%) and speed follows the actual flow reaching the cylinder after valve and line losses. Size with margin: pick the bore so the theoretical force exceeds the load by 10–25%, more for fast or shock-loaded circuits.
What do bore and rod diameter mean on a cylinder spec?
The bore is the inside diameter of the cylinder tube — the piston's diameter and the number that sets force. The rod is the polished shaft that extends; its diameter is chosen for stroke length and buckling, commonly around half the bore. A "100/56 × 400" catalog designation is a 100 mm bore, 56 mm rod, 400 mm stroke cylinder — exactly the worked example's geometry.