Reynolds Number Calculator — Flow Regime, Velocity and Viscosity Validator
Calculate Reynolds number using flow velocity or volumetric flow rate, pipe diameter, density, and dynamic viscosity.
Enter the known values and review the calculated result
Input parameters
Use consistent values and select the intended engineering units.
Flow mode
Flow definition
Fluid properties
Geometry
Results
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Method, application and limitations
Review the calculation method, intended application and engineering assumptions before using the result in a design decision.
Formula and calculation method
Reynolds number formula:
Re = (v · D) / ν
ν = μ / ρ
Velocity from volumetric flow rate:
A = π · D² / 4
v = Q / A
Direct velocity mode:
v = user-defined flow velocity
where:
- Re — Reynolds number (dimensionless)
- v — Flow velocity (m/s)
- D — Pipe diameter (m)
- ν — Kinematic viscosity (m²/s)
- μ — Dynamic viscosity (Pa·s)
- ρ — Density (kg/m³)
- Q — Volumetric flow rate (m³/s)
- A — Pipe cross-sectional area (m²)
When to use this calculator
When to use this calculator:
- Check whether pipe flow is laminar, transitional, or turbulent from fluid density, viscosity, diameter, and velocity.
- Calculate Reynolds number when the flow input is given as volumetric flow rate instead of direct velocity.
- Validate whether selected pipe diameter and flow conditions produce very low or very high Reynolds number results.
- Compare the effect of pipe diameter, flow velocity, density, and dynamic viscosity on the resulting flow regime.
- Calculate supporting flow values such as kinematic viscosity, mass flow rate, shear rate, and characteristic time.
How to interpret the result
Reynolds number is defined as the ratio between flow velocity times pipe diameter and kinematic viscosity.
Reynolds number depends on flow velocity, pipe diameter, density, and dynamic viscosity. Increasing flow velocity, pipe diameter, or density increases Reynolds number. Increasing dynamic viscosity decreases Reynolds number.
- Safe — Reynolds number is below 2300, which is classified as laminar flow.
- Warning — Reynolds number is from 2300 to below 4000, which is classified as transitional flow.
- Info — Reynolds number is 4000 or higher, which is classified as turbulent flow.
- Warning — Reynolds number above 1000000 is flagged as very high.
- Warning — Reynolds number below 1 is flagged as very low.
- Warning — flow velocity above 50 m/s is flagged.
- Warning — pipe diameter below 0.0001 m combined with Reynolds number below 100 is flagged.
- Invalid — the result is invalid when required fluid, geometry, or flow inputs are missing, non-finite, zero, negative, or outside the validation limits defined in the calculator.
The result is used to classify the flow regime and to verify whether the selected flow input, fluid properties, and pipe diameter produce a valid Reynolds number.
Calculation example
Example:
A user wants to check the flow regime in a pipe using direct flow velocity.
- v — Flow velocity = 2 m/s
- D — Pipe diameter = 0.05 m
- ρ — Density = 1000 kg/m³
- μ — Dynamic viscosity = 0.001 Pa·s
ν = 0.001 / 1000 = 1.0 × 10⁻⁶ m²/s
Re = (2 · 0.05) / 1.0 × 10⁻⁶ = 100000
Result: Re = 100000, so the flow regime is Turbulent.
Assumptions and limitations
- The flow is represented by one characteristic flow velocity and one pipe diameter.
- Kinematic viscosity is calculated only from dynamic viscosity divided by density.
- When volumetric flow rate mode is used, the pipe cross-sectional area is calculated as a circular area from pipe diameter.
- The flow regime classification uses Reynolds number limits: below 2300, from 2300 to below 4000, and 4000 or higher.
- The calculator assumes positive density, positive dynamic viscosity, positive pipe diameter, and positive velocity or volumetric flow rate.