Reynolds Number Calculator
The Reynolds number tells you whether fluid flow in a pipe is smooth and orderly (laminar), chaotic (turbulent), or somewhere in between (transitional). It's the first number you need before using the Moody Chart to find friction factor.
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What Is the Reynolds Number?
The Reynolds number (Re) is a dimensionless number that describes the nature of fluid flow. Think of it as a measure of how much inertia the fluid has compared to how "sticky" (viscous) it is. When inertia dominates, flow becomes turbulent - swirling and chaotic. When viscosity dominates, flow is laminar - smooth and layered.
It was first described by Osborne Reynolds in 1883, who showed that this single number could predict whether flow in a pipe would be orderly or chaotic. Engineers use it every day when designing water supply systems, HVAC ducts, oil pipelines, and chemical reactors.
The Formula Explained
Re = V × D / ν - Re - Reynolds number (dimensionless - no units)
- V - average flow velocity (m/s)
- D - pipe internal diameter (m)
- ν - kinematic viscosity of the fluid (m²/s)
You can also write it as Re = ρVD/μ, where ρ is density (kg/m³) and μ is dynamic viscosity (Pa·s). Both give the same result. If you have dynamic viscosity, use our Kinematic Viscosity Calculator to convert first.
Flow Regime Thresholds
Worked Example
Suppose water flows at 2 m/s through a 50 mm diameter pipe. The kinematic viscosity of water at 20°C is 1.004 × 10⁻⁶ m²/s.
Re = V × D / ν
Re = 2.0 × 0.05 / 0.000001004
Re = 0.1 / 0.000001004
Re ≈ 99,602 → Turbulent flow
At this Reynolds number, you'd use the Moody Chart Calculator with Re = 99,602 and the relative roughness ε/D for your pipe material to find the Darcy friction factor.
What's Kinematic Viscosity?
Kinematic viscosity (ν) is a measure of how thick or "syrupy" a fluid is relative to its density. Water has a kinematic viscosity of about 1 × 10⁻⁶ m²/s at 20°C - often written as 1 cSt (centistoke). Honey is thousands of times more viscous. Air is about 15 times less viscous than water.
If you know dynamic viscosity (μ) and density (ρ), convert with our Kinematic Viscosity Calculator: ν = μ/ρ.
Frequently Asked Questions
What Reynolds number is laminar vs turbulent in a pipe?
In a pipe, flow is laminar when Re < 2,300 and turbulent when Re > 4,000. Between 2,300 and 4,000 is the transitional zone, which is unpredictable and best avoided in engineering design.
Does pipe roughness affect the Reynolds number?
No. Reynolds number depends only on velocity, diameter, and viscosity - not on roughness. However, pipe roughness does affect the friction factor, especially in turbulent flow. Use the Moody Chart Calculator to account for both Re and ε/D.
How do I find velocity if I only know flow rate?
Use our Pipe Flow Velocity Calculator. It converts volumetric flow rate (m³/s) and pipe diameter (m) into average flow velocity (m/s) using V = Q / (π D²/4).
Why is the Reynolds number dimensionless?
When you multiply velocity (m/s) × diameter (m) and divide by kinematic viscosity (m²/s), all units cancel: (m/s × m) / (m²/s) = 1. This makes Reynolds number universal - valid for any fluid, pipe size, or unit system.
Related Tools
📊 Moody Chart Calculator
Use Re and ε/D to find the Darcy friction factor with an interactive Moody diagram.
🧪 Kinematic Viscosity Calculator
Convert dynamic viscosity and density to kinematic viscosity (ν = μ/ρ).
⚡ Pipe Flow Velocity Calculator
Find velocity from flow rate and diameter - needed to calculate Reynolds number.
📏 Relative Roughness Calculator
Calculate ε/D - the other input you need for the Moody Chart after Re.
➡️ Laminar Friction Factor Calculator
If Re < 2300, use f = 64/Re. Calculate it instantly here.
📉 Pressure Drop Calculator
Once you have Re and friction factor, calculate pipe pressure drop.
Learn More
Reynolds Number Explained
A deep dive into what Reynolds number means physically, with real-world examples.
How to Calculate Reynolds Number: Step-by-Step
A worked guide covering different units, fluid types, and common mistakes to avoid.
How to Read the Moody Chart
Learn how to use Reynolds number and roughness to read friction factor off the chart.