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Reynolds Number Calculator

Enter the Fluid Density, Viscosity, and Linear Dimension in the calculator to find the Reynolds Number of a liquid.

Fluid Substance:

Dynamic viscosity

kg/m³ ▾

Fluid density

kg-m-s ▾

Reynolds Number

m-s ▾

Kinematic Viscosity

mm ▾

Related

The Reynolds Number Calculator determines the dimensionless ratio between the inertia and viscosity of a fluid, helping to predict whether flow is laminar or turbulent.

What is Reynolds Number?

Reynolds Number (Re) is a dimensionless quantity that compares the inertial forces to viscous forces in a fluid. It characterizes the nature of fluid flow: laminar, transitional, or turbulent. Re remains consistent for a given flow, independent of changes in velocity or characteristic length.

Reynolds Number Formula

The Reynolds number can be calculated using either dynamic or kinematic viscosity:

Using dynamic viscosity (μ): Re = (ρ × u × L) / μ
Using kinematic viscosity (ν): Re = (u × L) / ν, where ν = μ / ρ

Where:

Re = Reynolds Number
ρ = fluid density (kg/m³)
u = fluid velocity relative to the object (m/s)
L = characteristic linear dimension of the object or domain (m)
μ = dynamic viscosity (Pa·s or kg/(m·s))
ν = kinematic viscosity (m²/s)

How to Calculate Reynolds Number Online

Using an online Reynolds Number Calculator, you can either input custom fluid properties or select common fluids (like air, water, or ethanol) to automatically use standard density and viscosity values at a given temperature.

Example Values

Water at 10°C: Re = 764,297 (for u = 1 m/s, L = 1 m)
Water at 50°C: Re = 1,805,886 (same u and L)

Viscosity and Reynolds Number

Dynamic Viscosity (μ)

Represents internal fluid friction. Units: Pa·s, N/(m²·s), or kg/(m·s).

Kinematic Viscosity (ν)

Calculated as ν = μ/ρ, representing dynamic viscosity per unit density. Units: m²/s. Fluid density can be obtained via a density calculator.

Reynolds Number Example

Problem: Find Re for water flowing through a pipe with diameter L = 2.5 cm, velocity u = 1.7 m/s, temperature = 10°C.

L = 0.025 m
u = 1.7 m/s
ρ = 999.7 kg/m³
μ = 0.001308 kg/(m·s)
ν = μ/ρ ≈ 1.308 × 10^-6 m²/s

Calculation:

Re = (u × L) / ν = (1.7 × 0.025) / 1.308 × 10^-6 ≈ 32,483

Result: Re ≈ 32,483, indicating turbulent flow.

How the Calculator Works

Steps to calculate Reynolds Number:

Input fluid velocity (u) and characteristic length (L).
Enter fluid properties: density (ρ) and dynamic viscosity (μ) or select a common fluid for automatic values.
Click "Calculate".

Output:

Kinematic viscosity (ν)
Reynolds Number (Re)

References

From Wikipedia: Reynolds Number. From Vedantu.com: Reynolds Number Formula and Examples.

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