Quick answer
The Reynolds number is Re = ρ v D ÷ μ, the ratio of inertial to viscous forces. Water (998.2 kg/m³, 0.001002 Pa·s) at 1.5 m/s in a 0.05 m pipe has Re = 74,716, a turbulent flow.
Enter fluid density, velocity, pipe diameter and dynamic viscosity. The calculator returns the Reynolds number and the flow regime.
Related tools: Flow Rate Calculator: Volumetric flow rate from area and velocity, or volume and time. Specific Gravity Calculator: Specific gravity from density, relative to water at 1,000 kg/m³. Water Viscosity Calculator: Dynamic viscosity of liquid water at a temperature.
How to use the Reynolds Number Calculator
- Enter fluid density (kg/m³) (above 0).
- Enter flow velocity (m/s) (above 0).
- Enter pipe diameter (m) (above 0).
- Enter dynamic viscosity (Pa·s) (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Fluid density | A number, in kg/m³ | > 0 |
| Flow velocity | A number, in m/s | > 0 |
| Pipe diameter | A number, in m | > 0 |
| Dynamic viscosity | A number, in Pa·s | > 0 |
Formula and method
Formula
Re = ρ v D ÷ μ
IEEE-754 double precision; shown to the decimals indicated.
For pipe flow: laminar below about 2,300, turbulent above about 4,000.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Fluid density = 998.2; Flow velocity = 1.5; Pipe diameter = 0.05; Dynamic viscosity = 0.001002.
| Result | Value |
|---|---|
| Reynolds number | 74,716 |
| Flow regime | Turbulent (Re > 4,000) |
Example 2
Inputs: Fluid density = 1.225; Flow velocity = 20; Pipe diameter = 0.3; Dynamic viscosity = 1.81e-05.
| Result | Value |
|---|---|
| Reynolds number | 406,077 |
| Flow regime | Turbulent (Re > 4,000) |
Example 3
Inputs: Fluid density = 900; Flow velocity = 0.2; Pipe diameter = 0.02; Dynamic viscosity = 0.2.
| Result | Value |
|---|---|
| Reynolds number | 18 |
| Flow regime | Laminar (Re < 2,300) |
The first line is the headline result (reynolds number). Below it the reynolds Number Calculator lists flow regime, which describe the same case from other angles. IEEE-754 double precision; shown to the decimals indicated.
Regimes
In pipes, Re below about 2,300 is laminar, above about 4,000 turbulent, and between is transitional. Regime limits are approximate and depend on pipe roughness and disturbances.
Consequences
Laminar flow is smooth with low mixing; turbulent flow has eddies and higher friction. The Reynolds number is needed for the friction factor in pressure-drop calculations. Use consistent SI units.
How the result changes with fluid density
Holding every other input at the first worked example, this table changes only fluid density. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Fluid density | Reynolds number | Flow regime |
|---|---|---|
| 499.1 | 37,358 | Turbulent (Re > 4,000) |
| 998.2 | 74,716 | Turbulent (Re > 4,000) |
| 1996 | 149,401 | Turbulent (Re > 4,000) |
| 3993 | 298,877 | Turbulent (Re > 4,000) |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Fluid density: entering "0" shows "Fluid density must be greater than 0." beside that field and no result.
- Dynamic viscosity: entering "0" shows "Dynamic viscosity must be greater than 0." beside that field and no result.
Choosing between the Reynolds Number Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Flow Rate Calculator](/science/flow-rate-calculator/) | use | Flow rate |
| [Specific Gravity Calculator](/science/specific-gravity/) | density | Specific gravity |
| [Water Viscosity Calculator](/science/water-viscosity/) | temperature | Dynamic viscosity |
| [Water Velocity Calculator](/science/water-velocity-calculator/) | flow and inside diameter | Velocity |
| [Pressure Calculator](/science/pressure-calculator/) | force and area | Pressure |
Background: fluid flow
Volumetric flow rate is Q = A × v (cross-sectional area times average velocity). Bernoulli's equation, P + ½ρv² + ρgh = constant, holds along a streamline for steady, incompressible, frictionless flow, so real pipes need friction corrections. The Reynolds number Re = ρvL/μ compares inertia with viscosity.
Laminar flow in a pipe is usually quoted below Re of about 2,100 to 2,300 and fully turbulent above about 4,000, with an uncertain transition between; treat the thresholds as approximate.
Assumptions and limitations
- Regime limits are approximate
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for fluid density and dynamic viscosity to confirm this.
Frequently asked questions
What is dynamic viscosity of water?
About 0.001 Pa·s at 20 °C.
Does Re apply to air?
Yes, with air's density and viscosity.
What does Re mean physically?
How much inertia dominates over viscosity.
What does the Reynolds Number Calculator calculate?
Reynolds number and flow regime in a pipe. It returns Reynolds number and Flow regime.
What formula does the Reynolds Number Calculator use?
Re = ρ v D ÷ μ. For pipe flow: laminar below about 2,300, turbulent above about 4,000.
What do I need to enter in the reynolds Number Calculator?
You enter Fluid density (kg/m³), Flow velocity (m/s), Pipe diameter (m) and Dynamic viscosity (Pa·s).
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. Regime limits are approximate.
What is an example of a reynolds Number result?
With fluid density 998.2, flow velocity 1.5, pipe diameter 0.05 and dynamic viscosity 0.001002, the reynolds number is 74,716.
Where does the method come from?
The method follows: Standard fluid mechanics (e.g. White, Fluid Mechanics).
Related calculators
- Flow Rate Calculator — Volumetric flow rate from area and velocity, or volume and time.
- Specific Gravity Calculator — Specific gravity from density, relative to water at 1,000 kg/m³.
- Water Viscosity Calculator — Dynamic viscosity of liquid water at a temperature.
- Water Velocity Calculator — Water velocity in a pipe from flow and inside diameter.
- Pressure Calculator — Pressure from force and area, with unit conversions.
- Buoyant Force Calculator — Upward buoyant force on a submerged object (Archimedes' principle).
Sources
- Standard fluid mechanics (e.g. White, Fluid Mechanics)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.