Hydraulic and pneumatic calculations

Hydraulic and pneumatic calculation centre

15 tools · SI and US customary units · Live results

WHAT WOULD YOU LIKE TO CALCULATE?

01PIPE DIAMETER CALCULATIONFlow line sizing 02BUCKLING CALCULATIONEuler critical load 03FLOW RATE CALCULATIONVolumetric flow calculation 04FORCE CALCULATIONPush and pull force 05TORQUE CALCULATIONTorque 06MOTOR POWER CALCULATIONRequired drive power 07AIR CONSUMPTION CALCULATIONPneumatic cylinder calculation 08CYLINDER SPEEDSpeed and cycle time 09CYLINDER FLOWRequired flow from speed 10Piston diameterBore from force 11MOTOR SPEEDMotor speed from flow 12Pump displacementPump sizing from flow 13PUMP INPUT TORQUERequired shaft torque 14LINE PRESSURE DROPDarcy–Weisbach calculation 15HEAT LOSSPower loss from efficiency

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01 / HYDRAULICS

PIPE DIAMETER CALCULATION

Find the minimum internal diameter required for your flow rate and target velocity.

Operating values

Check the units

Line flow rateTarget flow velocity

Calculation method

d = √(4Q / (60000 × π × v)) × 1000

Flow rate and target velocity

In formulas, η = efficiency / 100.

Calculated using example values

Calculated result—mm

Enter values and calculate.

The result updates when values change.

02 / HYDRAULICS

BUCKLING CALCULATION

Assess the ideal elastic buckling load of a solid circular rod.

Operating values

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Solid rod diameterUnsupported rod lengthModulus of elasticityN/mm²Effective length factor K—Safety factor—

Calculation method

Fcr [N] = π² × E [N/mm²] × I [mm⁴] / (K × L [mm])²

Length, cross-section and support effects

In formulas, η = efficiency / 100.

Assumes a solid circular slender rod with ideal elastic behaviour. K: fixed-free 2; pinned-pinned 1; fixed-pinned ≈0.7; fixed-fixed 0.5. Euler's method may not apply to short, thick rods.

Calculated using example values

Critical load—kN

Enter values and calculate.

The result updates when values change.

03 / HYDRAULICS

FLOW RATE CALCULATION

Calculate pump flow from displacement, speed and volumetric efficiency.

Operating values

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Pump displacementPump speedrpmVolumetric efficiency%

Calculation method

Q = V × n × η / 1000

Displacement × speed × efficiency

In formulas, η = efficiency / 100.

Calculated using example values

Calculated result— L/min

Enter values and calculate.

The result updates when values change.

04 / HYDRAULICS

FORCE CALCULATION

Find the force applied by your system from pressure and cylinder dimensions.

Operating values

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Operating pressurePiston diameterRod diameterBack pressureMechanical efficiency%

Calculation method

F [N] = (p [bar] × A [mm²] − pr × Akarşı) × η / 10

Effective area × pressure

In formulas, η = efficiency / 100.

Pressures are gauge values. Back pressure acts on the opposite area; mechanical efficiency applies to net force.

Calculated using example values

Push force—kN

Enter values and calculate.

The result updates when values change.

05 / HYDRAULICS

TORQUE CALCULATION

Find torque from differential pressure, motor displacement and mechanical efficiency.

Operating values

Check the units

Differential pressureMotor displacementMechanical efficiency%

Calculation method

T = Δp × V × η / (20π)

Differential pressure × displacement

In formulas, η = efficiency / 100.

Calculated using example values

Calculated result—Nm

Enter values and calculate.

The result updates when values change.

06 / HYDRAULICS

MOTOR POWER CALCULATION

Estimate the motor power required for the specified pressure and flow.

Operating values

Check the units

Operating pressureSystem flow rateOverall efficiency%

Calculation method

P = p × Q / (600 × η)

Pressure × flow rate / efficiency

In formulas, η = efficiency / 100.

Calculated using example values

Calculated result—kW

Enter values and calculate.

The result updates when values change.

07 / PNEUMATICS

AIR CONSUMPTION CALCULATION

Calculate the free-air requirement per minute for a double-acting cylinder.

Operating values

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Piston diameterRod diameterStroke lengthOperating cyclescycles/minGauge pressure

Calculation method

Q [ L/min] = (2Ap − Am) [mm²] × s [mm] × n × (pg + p₀) / (10⁶ × p₀)

Cycle and pressure effects

In formulas, η = efficiency / 100.

p₀ = 1.01325 bar; constant temperature assumed. Dead volume and leakage excluded.

Calculated using example values

Calculated result— L/min

Enter values and calculate.

The result updates when values change.

08 / HYDRAULICS

CYLINDER SPEED

Calculate extension and retraction speed, time and stroke volume from flow.

Operating values

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Piston diameterRod diameterStroke lengthSystem flow rate

Calculation method

v [mm/s] = Q [ L/min] × 10⁶ / (60 × A [mm²]); t = s / v

Dwell time, acceleration and leakage excluded.

In formulas, η = efficiency / 100.

Calculated using example values

Calculated result—mm/s

Enter values and calculate.

The result updates when values change.

09 / HYDRAULICS

CYLINDER FLOW

Find the flow required in both directions at the desired cylinder speed.

Operating values

Check the units

Piston diameterRod diameterCylinder speed

Calculation method

Q [ L/min] = A [mm²] × v [mm/s] × 60 / 10⁶

Assumes constant speed and incompressible fluid.

In formulas, η = efficiency / 100.

Calculated using example values

Calculated result— L/min

Enter values and calculate.

The result updates when values change.

10 / HYDRAULICS

Piston diameter

Find the required piston diameter from extension force, pressure and efficiency.

Operating values

Check the units

Required extension forceOperating pressureMechanical efficiency%

Calculation method

D [mm] = √(40000 × F [kN] / (π × p [bar] × η))

Extension direction; zero back pressure assumed.

In formulas, η = efficiency / 100.

Calculated using example values

Calculated result—mm

Enter values and calculate.

The result updates when values change.

11 / HYDRAULICS

MOTOR SPEED

Find motor speed from flow, displacement and volumetric efficiency.

Operating values

Check the units

System flow rateMotor displacementVolumetric efficiency%

Calculation method

n = 1000 × Q × ηv / V

For a motor, volumetric efficiency reduces the flow available for rotation.

In formulas, η = efficiency / 100.

Calculated using example values

Calculated result—rpm

Enter values and calculate.

The result updates when values change.

12 / HYDRAULICS

Pump displacement

Calculate pump displacement for the required flow and speed.

Operating values

Check the units

System flow ratePump speedrpmVolumetric efficiency%

Calculation method

V = 1000 × Q / (n × ηv)

Check catalogue ratings and speed limits separately.

In formulas, η = efficiency / 100.

Calculated using example values

Calculated result—cm³/rev

Enter values and calculate.

The result updates when values change.

13 / HYDRAULICS

PUMP INPUT TORQUE

Find pump shaft torque from differential pressure and displacement.

Operating values

Check the units

Differential pressurePump displacementMechanical efficiency%

Calculation method

T = Δp × V / (20π × ηm)

Pump input torque divides by efficiency; motor output torque multiplies by efficiency.

In formulas, η = efficiency / 100.

Calculated using example values

Calculated result—Nm

Enter values and calculate.

The result updates when values change.

14 / HYDRAULICS

LINE PRESSURE DROP

Calculate friction loss from fluid properties and pipe geometry.

Operating values

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Line flow ratePipe inside diameterPipe lengthKinematic viscositycStFluid densitykg/m³Absolute roughnessMinor loss coefficient ΣK—

Calculation method

Δp [bar] = (fL/d + ΣK) × ρv² / (2 × 10⁵); Re = vd/ν (SI)

Single-phase, fully developed flow. Evaluate elevation, valve and filter losses separately.

In formulas, η = efficiency / 100.

Laminar flow: f = 64/Re. Turbulent flow: Colebrook–White. A transition notice appears for Re = 2300–4000. Enter viscosity at operating temperature.

Calculated using example values

Calculated result—bar

Enter values and calculate.

The result updates when values change.

15 / HYDRAULICS

HEAT LOSS

Calculate continuous power dissipated as heat from overall efficiency.

Operating values

Check the units

Operating pressureSystem flow rateOverall efficiency%

Calculation method

Pkayıp = pQ/600 × (1/η − 1)

Assumes continuous duty; cooler sizing requires ambient conditions and duty cycle.

In formulas, η = efficiency / 100.

Calculated using example values

Calculated result—kW

Enter values and calculate.

The result updates when values change.

From calculation to the right application. Results are for preliminary sizing. Losses, operating conditions, safety factors and product limits must be assessed separately during technical selection.

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