Hydraulic Cylinder Flow & Speed Calculator

Calculate hydraulic cylinder extension and retraction speed from the oil flow rate, or calculate the flow rate required to reach a target speed. This free calculator supports Metric and Imperial units and accounts for the different effective areas used during push and pull motion.

The cylinder speed depends on the flow reaching the cylinder port and the effective area for the selected direction.

1. Online Hydraulic Cylinder Flow & Speed Calculator

Select the unit system and calculation mode, enter the cylinder dimensions and flow rate or target speed, then calculate.

Unit system Metric (L/min, mm) Imperial (GPM, in)

Calculation mode Calculate speed from flow Calculate flow from target speed

Cylinder motion Push / Extend Pull / Retract

Cylinder bore diameter D (mm)

D is the internal bore diameter, not the barrel outside diameter.

Piston rod diameter d (mm)

For pull/retract, the rod diameter is used to calculate the annular area.

Flow rate (L/min)

Use the flow actually available at the cylinder port.

Target cylinder speed (mm/s)

Calculated cylinder speed

169.94 mm/s

Effective area used

1,963.50 mm²

Bore area

1,963.50 mm²

Annular area

1,347.74 mm²

Calculation: v = Q / A, using the full piston area for push/extend.

Important: This is a theoretical calculation. Actual cylinder speed can differ because of pump output, valve and line losses, leakage, load conditions, and other system effects.

2. How the Calculator Works

The calculator uses the effective hydraulic area for the selected direction of cylinder motion. To keep the formulas consistent with the technical illustration, this article uses A₁ and A₂ for the two effective piston areas, and vₑ and vᵣ for the corresponding cylinder speeds.

When the cylinder extends (pushes out), oil acts on the full piston area. When the cylinder retracts (pulls in), the piston rod occupies part of the piston area, so the effective hydraulic area is smaller.

1. INPUTEnter bore diameter, rod diameter, and flow rate or target speed.

2. SELECTChoose Metric or Imperial units and push or pull motion.

3. CALCULATECalculate cylinder speed or the required flow rate.

4. CHECKCompare the theoretical result with actual system conditions.

3. Hydraulic Cylinder Flow and Speed Formulas

3.1. Piston area for push / extend

During extension, pressurized oil acts on the full piston face. The effective area is A₁:

A₁ = πD² / 4

Where D is the internal bore diameter of the cylinder.

3.2. Annular area for pull / retract

During retraction, the piston rod occupies part of the piston face. The effective area is the full piston area minus the rod cross-sectional area, defined as A₂:

A₂ = π(D² − d²) / 4

Where d is the piston rod diameter.

3.3. Relationship between A₁, A₂ and A

A₁ and A₂ describe the effective hydraulic areas for two different directions. In the general calculator formula, A means the effective area selected for the current calculation:

Push / Extend: A = A₁

Pull / Retract: A = A₂

Therefore, A is a general symbol used by the calculator, while A₁ and A₂ identify the specific area for extension and retraction, respectively.

3.4. Relationship between vₑ, vᵣ and v

The general speed formula is:

v = Q / A

Here, v represents the calculated speed for the selected direction. The specific symbols are:

Push / Extend: v = vₑ = Q / A₁

Pull / Retract: v = vᵣ = Q / A₂

In other words, vₑ is the extension speed, vᵣ is the retraction speed, and v is the general symbol used for whichever speed is being calculated. The calculator selects A₁ or A₂ according to the chosen cylinder motion.

For Metric inputs in L/min and area in mm²:

v (mm/s) = Q (L/min) × 1,000,000 / [60 × A (mm²)]

For Imperial inputs in US gallons per minute (GPM) and area in in²:

v (in/min) = Q (GPM) × 231 / A (in²)

3.5. Calculate required flow from target speed

The same relationship can be rearranged to calculate the flow rate required to achieve a target speed:

Q (L/min) = v (mm/s) × A (mm²) × 60 / 1,000,000

Q (GPM) = v (in/min) × A (in²) / 231

For extension, use A₁ and the target extension speed vₑ. For retraction, use A₂ and the target retraction speed vᵣ. The calculator applies the appropriate effective area according to the selected motion.

Use a consistent unit system. The calculator handles unit conversions for the selected Metric or Imperial mode.

4. Worked Examples

4.1. Metric example — calculate speed

Given: flow rate = 20 L/min, bore diameter D = 50 mm, rod diameter d = 28 mm.

• Full piston area = π × 50² / 4 = 1,963.50 mm².
• Rod area = π × 28² / 4 = 615.75 mm².
• Annular area = 1,963.50 − 615.75 = 1,347.74 mm².
• Push speed = 20 × 1,000,000 / (60 × 1,963.50) ≈ 169.77 mm/s.
• Pull speed = 20 × 1,000,000 / (60 × 1,347.74) ≈ 247.33 mm/s.

At the same flow rate, the theoretical retract speed is higher because the annular area is smaller than the full piston area.

4.2. Metric example — calculate required flow

For a 50 mm bore cylinder extending at a target speed of 100 mm/s:

Q = 100 × 1,963.50 × 60 / 1,000,000 ≈ 11.78 L/min.

4.3. Imperial example — calculate speed

Given: flow rate = 5 GPM, bore diameter D = 4 in, rod diameter d = 2 in.

• Full piston area = π × 4² / 4 = 12.566 in².
• Annular area = π × (4² − 2²) / 4 = 9.425 in².
• Push speed = 5 × 231 / 12.566 ≈ 91.91 in/min.
• Pull speed = 5 × 231 / 9.425 ≈ 122.55 in/min.

5. Metric and Imperial Reference

Quantity	Metric	Imperial
Flow rate	L/min	US GPM
Bore and rod diameter	mm	in
Area	mm²	in²
Calculated speed	mm/s and m/min	in/min and ft/min

• 1 US gallon = 231 in³.
• 1 in = 25.4 mm.
• 1 m/min = 1,000 mm/min = 16.667 mm/s.

6. Engineering Notes and Limitations

• Use the flow rate actually reaching the cylinder port, not simply the pump's rated flow.
• These equations calculate theoretical speed and flow; they do not automatically account for leakage, flow-control settings, pressure losses or changing pump output.
• Push/extend and pull/retract speeds differ because the effective areas differ.
• Stroke length is not required to calculate ideal speed. It is needed if you want to estimate travel time, which is outside this calculator's V1 scope.
• This tool does not select a cylinder bore, recommend a standard cylinder size, calculate force, or verify whether a cylinder is suitable for a particular load.

7. Frequently Asked Questions

7.1. How do I calculate hydraulic cylinder speed?

Calculate the effective piston area for the selected direction, then divide the flow rate by that area. The calculator performs the required unit conversion.

7.2. Why is retract speed usually higher than extension speed?

For the same flow rate, the rod-side annular area is smaller than the full piston area. Dividing the same flow by a smaller area gives a higher theoretical speed.

7.3. Does the calculator need cylinder stroke length?

No. Stroke length is not needed to calculate speed from flow and area. It would be needed to estimate the time required to complete a stroke.

7.4. Why might actual speed differ from the result?

Actual flow can vary with pump speed, control-valve settings, leakage, load and system pressure losses. Treat the result as a theoretical estimate and verify it under real operating conditions.

8. Related Hydraulic Calculators

• Hydraulic Cylinder Force Calculator – Push & Pull Force (Tool #001)
• Hydraulic Cylinder Bore Size Calculator (Tool #002)

Scope note: Scope: This calculator focuses on hydraulic cylinder flow rate and speed. For hydraulic cylinder force calculations, see [Hydraulic Cylinder Force Calculator – Push & Pull Force (Tool #001)]..