Engineering

Reynolds Number Calculator

Calculate Reynolds number from density, mean velocity, hydraulic diameter, and dynamic viscosity. Also show kinematic viscosity, relative roughness, ratios to both reference values, and position across the entered transition span.

Fluid density (kg/m³)Mean velocity (m/s)Hydraulic diameter (mm)Dynamic viscosity (mPa·s)Entered laminar reference ReEntered turbulent reference ReEntered roughness (mm)

Hydraulic diameter (m)-

Dynamic viscosity (Pa·s)-

Reynolds number-

Re divided by laminar reference-

Re divided by turbulent reference-

Kinematic viscosity (m²/s)-

Relative roughness-

Decision view

Logarithmic Reynolds regime threshold map

Logarithmic Reynolds regime threshold mapCalculated Reynolds number and both entered references remain readable even when they span several orders of magnitude.

Exact scenario comparisonMean velocity (m/s) changes while all other entered assumptions remain constant.

Mean velocity (m/s)	Hydraulic diameter (m)	Dynamic viscosity (Pa·s)	Reynolds number	Re divided by laminar reference	Re divided by turbulent reference	Kinematic viscosity (m²/s)	Relative roughness

How to use Reynolds Number Calculator

Enter density and mean flow velocity.
Enter hydraulic diameter in millimetres.
Enter dynamic viscosity in mPa-s.
Choose comparison references and inspect the logarithmic regime scale.

Calculator guide

Understanding Reynolds Number Calculator

Reynolds number compares inertial and viscous effects in a flow. This calculator performs every unit conversion explicitly and positions the result against user-entered laminar and turbulent references without claiming those thresholds are universal.

Conversions matter mm and mPa-s must become SI units.

Re is unitless Dimensions cancel exactly.

References are entered They are comparisons, not universal rules.

Log scale helps Large regime spans remain readable.

Calculation method

How the calculation works

Form Reynolds number from density, mean velocity, hydraulic diameter, and dynamic viscosity, with entered regime references shown as comparisons rather than automatic labels. Convert hydraulic diameter from millimetres to metres and viscosity from mPa-s to Pa-s, then multiply density, velocity, and diameter and divide by dynamic viscosity.

Detailed calculation process

Make the dimensionless inertia-to-viscosity ratio explicit

The defaults use water-like properties: 998 kg/m3, 1.8 m/s, 75 mm hydraulic diameter, and 1.002 mPa-s viscosity.

General formula: D = D_mm/1000; mu = mu_mPas/1000; Re = rho v D/mu = vD/nu; nu = mu/rho; epsilon_r = epsilon/D The numerator combines density, velocity, and characteristic length; dynamic viscosity resists deformation. Their units cancel, leaving Reynolds number dimensionless.

What each symbol means

rho Fluid density, measured in kg/m3.

v Mean flow velocity, measured in m/s.

D Hydraulic diameter, measured in m.

mu Dynamic viscosity, measured in Pa-s.

nu Kinematic viscosity, measured in m2/s.

Re / epsilon_r Dimensionless Reynolds number and relative roughness.

Worked substitution with the default inputs

1. Convert hydraulic diameter: D = 75 mm/1000 = 0.075 m The length must use metres to match SI viscosity units.

2. Convert dynamic viscosity: mu = 1.002 mPa-s /1000 = 0.001002 Pa-s One millipascal-second is one thousandth of a pascal-second.

3. Calculate Reynolds number: Re = 998 x 1.8 x 0.075 /0.001002 = 134,461.08 All physical units cancel, so Re has no unit.

4. Compare entered references: Re/2300 = 58.4613; Re/4000 = 33.6153; span position = 7,774.18% The value lies far beyond both entered references; the percentage is intentionally not clamped.

5. Calculate viscosity and roughness ratios: nu = 0.001002/998 = 1.00401e-6 m2/s; epsilon_r = 0.15/75 = 0.002 Relative roughness uses matching millimetre units and is also dimensionless.

The default Reynolds number is about 134,461, well beyond the entered 2,300 and 4,000 references; kinematic viscosity is 1.004e-6 m2/s and relative roughness is 0.002.

Regime threshold

Place Reynolds number on a logarithmic reference map

The scale preserves widely separated values without compressing the thresholds into one corner.

Lower zone Below entered laminar reference.

Transition zone Between the two references.

Upper zone Above entered turbulent reference.

Calculated marker Exact Re from current inputs.

Worked situations

Practical examples

75 mm converts to 0.075 m.
1.002 mPa-s converts to 0.001002 Pa-s.
The resulting Re is approximately 134,461.

Better inputs

Useful tips

Use properties at the actual fluid temperature.
Choose hydraulic diameter appropriate to the geometry.
Treat thresholds as context-specific references.

Before relying on the result

Limitations and common mistakes

Transition depends on geometry, disturbances, entry length, roughness, and boundary conditions.
Non-Newtonian, compressible, multiphase, and unsteady flows require additional treatment.
Reynolds number alone does not calculate friction factor or pressure loss.

Reference

Key terms

Reynolds number: Dimensionless ratio of inertial to viscous effects.
Hydraulic diameter: Characteristic length used for noncircular ducts and pipes.
Kinematic viscosity: Dynamic viscosity divided by density.

Important note

Calculated from the entered values using the displayed engineering relationship. Confirm design values, load cases, safety factors, standards, and field conditions with a qualified professional.

Frequently asked questions

Why is Reynolds number dimensionless?

The units in rho-v-D divided by mu cancel.

Are 2,300 and 4,000 universal?

No. They are familiar pipe-flow references, but geometry and conditions matter.

Why use a logarithmic chart?

It keeps references and very large or small calculated values visible together.

Does roughness change Re?

Not directly in this formula, though roughness affects flow behavior and friction.