Reynolds Number Calculator
Reynolds Number
What Is a Reynolds Number Calculator?
A Reynolds number calculator compares inertial and viscous effects in fluid flow. This calculator supports two geometries: internal pipe flow and external flow over a flat plate. The characteristic length is the pipe diameter for pipe flow and the plate length for flat-plate flow.
The calculator finds Reynolds number by converting velocity, characteristic length, density, and dynamic viscosity to SI units and evaluating Re = ρVL/μ. It then classifies the result using the selected pipe or flat-plate thresholds and, when applicable, calculates a smooth-pipe friction factor or smooth-plate skin friction coefficient.
You can use built-in property values for water, seawater, air, SAE 30 engine oil, glycerin, ethanol, or mercury at 20°C. A Custom option lets you enter density and dynamic viscosity manually. The result depends entirely on the values and geometry selected.
How the Reynolds Number Calculation Works
The main calculation uses fluid density, velocity, characteristic length, and dynamic viscosity:
In this formula, Re is the Reynolds number, ρ is fluid density, V is fluid velocity, L is the characteristic length, and μ is dynamic viscosity. Reynolds number is dimensionless.
For pipe flow, L is the pipe diameter. For flat-plate flow, L is the plate length. The calculator converts all supported input units to meters, meters per second, kilograms per cubic meter, and pascal-seconds before applying the equation.
Pipe Friction Factor
For pipe flow classified as laminar or creeping, the calculator uses:
For pipe flow classified as turbulent, it uses the Blasius-type relationship:
No pipe friction factor is calculated for the transitional regime.
Flat-Plate Skin Friction Coefficient
For flat-plate flow classified as laminar or creeping, the average skin friction coefficient is:
For flat-plate flow classified as turbulent, the calculator uses:
No skin friction coefficient is calculated while the Reynolds number is in the flat-plate transitional band.
Worked Example
Suppose you select Pipe / Internal Flow and the Water (20°C) preset. Use a fluid velocity of 1.5 m/s and a pipe diameter of 0.05 m. The preset supplies a density of 998.2 kg/m³ and a dynamic viscosity of 0.0010016 Pa·s.
The main Reynolds number display rounds this result to 74,745. The calculator also shows scientific notation as approximately 7.47 × 10⁴. Under the pipe-flow rules, this is classified as turbulent.
The displayed Darcy friction factor is therefore 0.0191.
How to Use the Reynolds Number Calculator
- Select a fluid preset, or choose Custom if you want to enter density and dynamic viscosity manually.
- Select Pipe / Internal Flow or Flat Plate / External Flow. The length field changes between Pipe Diameter and Plate Length.
- Enter the fluid velocity and choose its unit.
- Enter the pipe diameter or plate length and choose its unit.
- Check the density and dynamic viscosity values and their units. A fluid preset fills these fields automatically.
- Select Calculate to display the Reynolds number, flow regime, and the geometry-specific friction result.
The velocity field supports m/s, ft/s, cm/s, km/h, mph, and knots. Length can be entered in meters, millimeters, centimeters, feet, or inches. Density supports kg/m³, g/cm³, and lb/ft³. Dynamic viscosity supports Pa·s, mPa·s or cP, Poise, lb/(ft·s), and lbf·s/ft².
Selecting a built-in fluid also switches density to kg/m³ and viscosity to Pa·s. Choosing Custom does not automatically erase or replace the current property values, so enter the values you want to use manually.
Understanding the Flow Regime and Calculator Results
The calculator uses different Reynolds number thresholds for pipe flow and flat-plate flow. It also treats Reynolds numbers below 1 as creeping flow.
| Flow Regime | Pipe / Internal Flow | Flat Plate / External Flow |
|---|---|---|
| No Flow | Re = 0 | Re = 0 |
| Laminar (Creeping) | 0 < Re < 1 | 0 < Re < 1 |
| Laminar | 1 ≤ Re ≤ 2,300 | 1 ≤ Re ≤ 500,000 |
| Transitional | 2,300 < Re < 4,000 | 500,000 < Re < 3,000,000 |
| Turbulent | Re ≥ 4,000 | Re ≥ 3,000,000 |
If velocity is zero, Reynolds number is zero and the flow regime is shown as No Flow. No friction factor or skin friction coefficient is calculated in that case. The geometry-specific coefficient row remains visible and displays the same “Not defined in the transitional band” text used when the result is transitional.
For pipe geometry, the calculator displays the Darcy friction factor row. For flat-plate geometry, it displays the average skin friction coefficient row instead. The coefficient is formatted to four decimal places when it is at least 0.001 and in scientific notation when it is smaller.
The main Reynolds number display changes formatting with its size. Values of 1,000 or more are displayed without decimal places until scientific notation is triggered. Values from 1 to below 1,000 can show up to three decimal places, while smaller values can show up to five. Values at least 10,000,000 or below 0.0001 use scientific notation. A separate line always reports Reynolds number in scientific notation with a two-decimal mantissa.
Built-In Fluid Properties
| Fluid Preset | Density (kg/m³) | Dynamic Viscosity (Pa·s) |
|---|---|---|
| Water (20°C) | 998.2 | 0.0010016 |
| Seawater (20°C) | 1025 | 0.00108 |
| Air (20°C) | 1.204 | 0.00001825 |
| Engine Oil SAE 30 (20°C) | 890 | 0.72 |
| Glycerin (20°C) | 1260 | 1.412 |
| Ethanol (20°C) | 789 | 0.0012 |
| Mercury (20°C) | 13546 | 0.001526 |
The calculator requires velocity, length, density, and dynamic viscosity to contain valid numbers. Velocity may be zero but cannot be negative. Characteristic length, density, and dynamic viscosity must all be greater than zero.
The calculator assumes Newtonian fluids under steady, uniform conditions. Its own note describes the smooth-pipe Blasius correlation as applicable for 4,000 < Re < 100,000. The calculation code applies that formula whenever pipe flow is classified as turbulent, including values at or above 100,000, so results outside the stated correlation range should be interpreted with care.
Results in transitional ranges and near regime boundaries are approximations. The calculator's guidance recommends checking critical designs against computational fluid dynamics or experimental data.
Frequently Asked Questions
What does the Reynolds number tell you?
The Reynolds number is a dimensionless value based on density, velocity, characteristic length, and dynamic viscosity. This calculator uses the value to label the selected flow geometry as no flow, creeping laminar, laminar, transitional, or turbulent according to its built-in thresholds.
What length should I enter?
Enter pipe diameter when Pipe / Internal Flow is selected. Enter plate length when Flat Plate / External Flow is selected. The calculator automatically changes the field label when you switch between the two geometries.
Can I calculate Reynolds number using feet, inches, or mph?
Yes. The calculator accepts several non-SI units, including ft/s, mph, feet, inches, lb/ft³, and lb/(ft·s). It converts the entered values internally to the SI units used in the Reynolds number equation before calculating the result.
What happens when I select a fluid preset?
A preset fills the density and dynamic viscosity fields with the calculator's stored values and changes those property units to kg/m³ and Pa·s. The available presets are water, seawater, air, SAE 30 engine oil, glycerin, ethanol, and mercury, all labeled at 20°C.
When does the calculator show a pipe friction factor?
The pipe friction-factor row is shown whenever pipe geometry is selected. A numerical factor is calculated for creeping or laminar flow with 64/Re and for turbulent flow with 0.3164/Re0.25. A numerical friction factor is not calculated in the transitional regime.
When does it calculate a flat-plate skin friction coefficient?
The skin friction coefficient is shown for flat-plate geometry. The calculator uses 1.328/√Re for creeping and laminar results and 0.074/Re0.2 for turbulent results. It does not calculate a coefficient while the result is classified as transitional.
What does the Reset button do?
Reset clears the velocity and length fields, selects Water (20°C), restores the water density and viscosity values, returns their units to kg/m³ and Pa·s, selects m/s and meters, switches the geometry back to Pipe / Internal Flow, and hides the results.