BIZOMAT MAKEOS · Hydraulics
Hydraulic Cylinder Force and Speed
What ideal force and stroke time follow from pressure and flow?
Calculate double-acting cylinder forces with return pressure, plus ideal extension and retraction times.
Open the calculatorRuns in your browser. No account needed.
How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Bore diameter | mm | Cylinder drawing or manufacturer datasheet. |
| Rod diameter | mm | Rod diameter at the working piston. |
| Supply pressure | bar gauge | Pressure at the active cylinder port under load. |
| Return pressure | bar gauge | Opposing-port pressure under the relevant return flow. |
| Inlet flow | L/min | Actual flow delivered to the active chamber. |
| Stroke | mm | Travel between the analysed positions. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Bore diameter
- What it is
- The inside diameter of the cylinder barrel, equal to the piston diameter. It sets the full piston area used on extension.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Extension force rises with the square of bore; extension speed falls with it.
- Get it right
- Use the bore from the cylinder datasheet, not the outside diameter of the tube.
What this means: Rod diameter
- What it is
- The diameter of the piston rod. It reduces the area on the rod side, so the cylinder pulls with less force and retracts faster.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger rod lowers retraction force and raises retraction speed.
- Get it right
- Use the rod diameter at the working piston from the datasheet; it must be smaller than the bore.
What this means: Supply pressure
- What it is
- The gauge pressure at the port of the chamber that is driving the piston, while the load is moving.
- Units and format
- Enter a number in bar gauge: bar gauge. The form accepts 0 bar gauge to 10000 bar gauge. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 bar gauge as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Driving force in each direction rises in direct proportion to supply pressure.
- Get it right
- Use pressure at the cylinder port, not the relief valve or pump setting; line and valve losses reduce it.
What this means: Return pressure
- What it is
- The gauge pressure in the opposite chamber that resists the motion, from the return line, valve and any counterbalance.
- Units and format
- Enter a number in bar gauge: bar gauge. The form accepts 0 bar gauge to 10000 bar gauge. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 bar gauge as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Higher return pressure lowers the net force in both directions.
- Get it right
- Do not assume zero: return lines and valves create back pressure that reduces net force.
What this means: Inlet flow
- What it is
- The oil flow actually delivered into the driving chamber of the cylinder.
- Units and format
- Enter a number in L/min: litres per minute. The form accepts 0.000001 L/min to 1000000 L/min. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 L/min as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Extension and retraction speeds are directly proportional to flow.
- Get it right
- Use flow reaching the cylinder after relief and leakage, not the pump’s rated flow.
What this means: Stroke
- What it is
- The distance the piston travels between the two positions you are analysing.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Extension and retraction times are directly proportional to stroke.
- Get it right
- Use the working stroke used, which can be less than the full catalogue stroke.
Method and formulas
- Piston area A = π × bore² / 4; annular area B = π × (bore² − rod²) / 4.
- Extension force (N) = 0.1 × (supply bar × A − return bar × B). Retraction uses 0.1 × (supply × B − return × A).
- Speed (mm/s) = inlet flow × 10⁶ / (60 × active area). Time (s) = stroke / speed.
- For 50/25 mm, 100/5 bar and 10 L/min, extension force is about 18.899 kN and extension time is 1.1781 s over 100 mm.
Limitations
- Theoretical port forces only; seal friction, leakage, acceleration and pressure losses are excluded.
- No rod buckling, mounting, load holding or pressure-rating check. Regenerative circuits need a different model.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- cylinder force
- hydraulic ram
- stroke time
Who it is for
- Hydraulic engineers
- Maintenance teams
What you get
- Ideal extension force
- Ideal retraction force
- Extension speed
- Retraction speed
- Extension time
- Retraction time
Interpreting the result
- Use measured port pressures and verify return-flow capacity and load control.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 365–368; CD pp. 3416–3420. Topic reference; no source tables or recommended settings are reproduced.
- Parker: Basic Hydraulic Formulas — https://www.parker.com/content/dam/Parker-com/Literature/Accumulator---Cooler-Division---Americas/Catalogs---Bulletins/GAD-HY10-1630-5-2012/ACD_CoolerCatalog_HY10_1700.pdf
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