You need extend and retract force for a hydraulic cylinder at a known system pressure before you pick a bore or check a press load. This pad takes port pressure, bore, rod, optional friction loss, and optional stroke plus oil flow, then returns theoretical and practical forces, bore/rod areas, retract/extend ratio, oil volumes when stroke is set, and velocity/time when stroke and flow are both set.
Defaults open on a common industrial path: 160 bar, 80 mm bore, 40 mm rod, 0% friction, 500 mm stroke, 20 L/min. That force path gives about 80.42 kN extend (≈ 8,201 kgf) and 60.32 kN retract (≈ 6,151 kgf), ratio 0.75. With the default stroke and flow you also get about 66.3 mm/s extend and 7.54 s stroke time. Switch Metric or Imperial first. Math stays in your browser.
It lives under Fluid Power Calculators. For shop air use the pneumatic cylinder force calculator. For oil-pump flow, displacement, and drive power use the hydraulic pump selector.
Formula
- Extend: F = P × (π/4) × D² on the full bore (cap) face.
- Retract: F = P × (π/4) × (D² − d²) on the annulus (rod side).
- Practical force = theoretical × (1 − friction%/100).
- Oil volume = area × stroke. Velocity v = Q / A. Time t = stroke / v.
- Rod-side outflow on extend ≈ Q × (A_annulus / A_bore).
- P in pascals (bar × 10⁵ or psi converted). Outputs prefer kN (Metric) or lbf (Imperial).
Reproduce the default Metric path (force + kinematics):
| Check | Value on this pad |
|---|---|
| Inputs | 160 bar, bore 80 mm, rod 40 mm, stroke 500 mm, 20 L/min |
| Extend / retract | ≈ 80.42 kN / 60.32 kN (ratio 0.75) |
| Areas | ≈ 50.27 cm² bore · 37.70 cm² annulus |
| Extend velocity / time | ≈ 66.3 mm/s · ≈ 7.54 s |
| Retract velocity / time | ≈ 88.4 mm/s · ≈ 5.65 s |
How it works
Pick Metric or Imperial. Enter port pressure, bore, and rod. Extend force uses full piston area; retract uses the annulus. Optional friction loss scales theoretical force to a practical estimate. Stroke above zero adds oil volumes; stroke and oil flow together add velocity, time, and rod-side outflow. CALCULATE animates the cutaway. RESET restores the 160 bar / 80 mm defaults.
Pick Metric (bar, mm, kN, L/min) or Imperial (psi, in, lbf, gpm). Enter port pressure, bore, and rod. Friction loss defaults to 0%. Stroke above zero unlocks oil volumes. Stroke and oil flow together unlock velocity, time, and rod-side outflow. Set stroke to 0 for a force-only check. CALCULATE fills the cards and animates the oil cutaway. RESET restores 160 bar / 80 mm / 40 mm / 500 mm / 20 L/min.
Bore side, rod side, and the 0.75 ratio
Hydraulic force is still Pascal's law: pressure times the area the oil can push. On extend that is the full bore (cap) face. On retract the rod takes area away, so pull force drops.
On the default 80 mm / 40 mm path the annulus is 75% of the bore area, which is why the ratio is 0.75. If your clamp or lift needs pull force, size on retract, not the extend headline.
Cap / bore side uses full piston area. Rod side uses the annulus. Same pressure still gives different forces.
Default CALCULATE: 160 bar · Ø80 · rod 40 → ≈80.42 kN extend / ≈60.32 kN retract (ratio 0.75).
Optional stroke, flow, velocity, and time
Enter stroke alone to see cap-side and rod-side oil volumes. Add oil flow to unlock extend and retract velocity, stroke time, and rod-side outflow on extend. Force needs only pressure and areas — leave stroke at zero for a pure force check.
With Q = 20 L/min into an 80 mm bore, extend speed is about 66.3 mm/s and a 500 mm stroke takes about 7.54 s. Retract is faster on the smaller annulus (≈ 88.4 mm/s, ≈ 5.65 s). Rod-side outflow on extend is 15 L/min on the default path (75% of pump flow).
- v = Q / A with consistent SI units (this pad converts for you)
- t = stroke / v for each direction at constant flow
- Force does not need stroke or flow; set stroke to 0 for a pure force check
Force from P×A. Speed from Q/A. Time from stroke/speed. Stroke 0 keeps a force-only check.
Default path: 20 L/min · Ø80 · L 500 mm → ≈66.3 mm/s · ≈7.54 s extend.
Friction loss and shop pressure
Catalog theory ignores seal drag, packing friction, and return-line back-pressure. A 5–15% friction loss is a common first-pass derate for industrial cylinders. Enter it here to see practical extend and retract in kN.
Use regulated pressure at the cylinder port, not pump relief alone. Hose drop and valve pressure drop can cut available force even when the nameplate relief looks fine.
Default 160 bar / 80 / 40 path with friction examples:
| Friction | Extend practical | Retract practical |
|---|---|---|
| 0% | 80.42 kN | 60.32 kN |
| 10% | 72.38 kN | 54.29 kN |
| 15% | 68.36 kN | 51.27 kN |
What this pad covers, and what we skip
Hydraulic cylinder sizing often aligns bore and rod series with hydraulic cylinder standards in the ISO 3320 / 3321 family. This pad is a first-pass force and stroke-speed check, not a catalog picker or quote workflow.
This pad stays a first-pass force and stroke-speed check: dual units, friction percent, areas, ratio, and optional kinematics. Pump HP, motor torque, piping Reynolds, rod buckling, and cushion design stay out of scope. Confirm critical loads with the manufacturer chart after you pick a bore.
- No pump power or heat-load model
- No rod buckling or mount strength check
- Not a substitute for ISO catalog certification or sealing-system design software
Worked example
160 bar, 80 mm bore, 40 mm rod, stroke 500 mm, 20 L/min, friction 0%. Reproduce on CALCULATE.
- Keep Metric. Pressure 160, bore 80, rod 40, stroke 500, flow 20, friction 0.
- A_bore = π/4 × 0.08² ≈ 0.005027 m² → F_extend = 160×10⁵ × A ≈ 80.42 kN.
- A_annulus = π/4 × (0.08² − 0.04²) ≈ 0.003770 m² → F_retract ≈ 60.32 kN (ratio 0.75).
- Q = 20/60000 m³/s → v_extend ≈ 66.3 mm/s → t_extend ≈ 7.54 s for 500 mm.
Result: Extend ≈ 80.42 kN, retract ≈ 60.32 kN, ratio 0.75. With defaults, extend ≈ 66 mm/s and ≈ 7.5 s. Set friction to 10% for practical 72.38 / 54.29 kN.
When to use
- Checking hydraulic push/pull force at a known port pressure and bore
- Comparing retract vs extend on a double-acting cylinder
- Estimating stroke time from pump flow before you pick valve Cv
- Applying a friction percent before you lock a press or clamp design
- Cross-checking Metric kN/kgf against Imperial psi/in/lbf
Limitations
- Static force at the pressure you enter; no hose drop, valve Cv, or cushion effects
- Velocity assumes constant pump flow and full-area fill (no compressibility or cavitation model)
- Friction percent is a lumped estimate, not a seal friction model
- No rod buckling, mount strength, or pump horsepower
- Not a substitute for manufacturer force charts or certified selection software
FAQ
- Why is retract force lower than extend force?
- On extend, pressure acts on the full piston area. On retract, the rod occupies part of the bore, so the annulus is smaller. On the default 80/40 mm path the ratio is 0.75.
- Do I need stroke and oil flow?
- No for force. Force uses pressure and areas only. Enter stroke above zero for bore/rod oil volumes. Enter stroke and oil flow together for velocity, stroke time, and rod-side outflow.
- How is this different from the pneumatic calculator?
- Same area physics, different typical pressures and units. Hydraulics often run 100 to 350 bar and show kN. Pneumatics run about 4 to 10 bar and show N/kgf. This pad also adds optional oil volumes and flow kinematics.
- What friction loss should I enter?
- Use 0% for a clean theoretical check. For shop estimates, 5–15% is common on industrial cylinders. Practical force cards appear when friction is above 0%.
- Can I use Imperial units?
- Yes. Use the Imperial tab. Pressure becomes psi, lengths inches, force lbf, and flow gpm. Areas, ratio, and the cutaway animation stay the same.
- Can rod diameter equal bore diameter?
- No. Rod must be smaller than bore. As rod approaches bore size, retract force approaches zero and the pad rejects rod ≥ bore.
- Does this include pressure drop in hoses?
- No. Use the pressure measured or expected at the cylinder port, not pump relief setting alone.
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