# What Reynolds number is my flow?

Reynolds number calculator for flow in a pipe: Re = ρvD ÷ η from the fluid, its speed and the pipe diameter, with laminar, transitional or turbulent flow and the kinematic viscosity.

- Page: https://www.acalculator.org/physics/reynolds-number-calculator
- JSON spec: https://www.acalculator.org/physics/reynolds-number-calculator.json
- Version: 308d5e040d43

## Default answer

Example with the default inputs (Fluid Water at 20 °C, Flow speed (v) 1.64041994750656 ft/s, Pipe diameter (D) 0.78740157480315 in): The Reynolds number is 9,962.08: Turbulent flow.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| f | Fluid | The fluid, which sets its density and viscosity (OpenStax Tables 14.1 and 14.4). |
| v | Flow speed (v) | The average speed of the fluid through the pipe. |
| D | Pipe diameter (D) | The inside diameter of the pipe (the characteristic length). |
| rho | Density (ρ) | The density of the fluid. |
| eta | Viscosity (η) | The dynamic viscosity of the fluid, in the unit chosen below. |
| eu | Viscosity unit | The unit of the viscosity you type. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| re | Reynolds number | Re = ρ × v × D ÷ η, a pure number. |
| regime | Flow | Laminar below 2,000, transitional from 2,000 to 3,000, turbulent above 3,000. |
| nu | Kinematic viscosity (m²/s) | η ÷ ρ, in square metres per second. |
| rho | Density used (kg/m³) | The density of the fluid in kilograms per cubic metre. |
| eta | Viscosity used (Pa·s) | The dynamic viscosity in pascal seconds. |
| laminarSpeed | Fastest laminar speed (m/s) | The speed at which Re reaches 2,000 in this pipe: 2,000 × η ÷ (ρ × D). |

## Method

Re = ρ × v × D ÷ η; kinematic viscosity ν = η ÷ ρ; laminar up to v = 2,000 × η ÷ (ρ × D).

## Assumptions

- Flow in a full round pipe, with D the inside diameter and v the average speed. OpenStax writes the same number as 2ρvr ÷ η with r the radius.
- Laminar below 2,000, transitional from 2,000 to 3,000, turbulent above 3,000 (OpenStax gives these as approximate limits).

## Worked examples

1. f = water20, v = 0.5, D = 0.02 gives re = 9,962.075848, regime = Turbulent, nu = 0.000001. Source: OpenStax, University Physics Volume 1, §14.7 Viscosity and Turbulence (N_R = 2ρvr ÷ η; laminar below about 2,000, turbulent above about 3,000; Table 14.4), https://openstax.org/books/university-physics-volume-1/pages/14-7-viscosity-and-turbulence (retrieved 2026-10-05); OpenStax, University Physics Volume 1, §14.1 Fluids, Density, and Pressure (Table 14.1), https://openstax.org/books/university-physics-volume-1/pages/14-1-fluids-density-and-pressure (retrieved 2026-10-05).
2. f = custom, rho = 1,000, eta = 1, eu = Pa-s, v = 0.1, D = 0.01 gives re = 1, regime = Laminar. Source: OpenStax, University Physics Volume 1, §14.7 Viscosity and Turbulence (N_R = 2ρvr ÷ η; laminar below about 2,000, turbulent above about 3,000; Table 14.4), https://openstax.org/books/university-physics-volume-1/pages/14-7-viscosity-and-turbulence (retrieved 2026-10-05).
3. f = custom, rho = 1,000, eta = 1, eu = mPa-s, v = 0.2, D = 0.01 gives re = 2,000, regime = Transitional (unstable), laminarSpeed = 0.2. Source: OpenStax, University Physics Volume 1, §14.7 Viscosity and Turbulence (N_R = 2ρvr ÷ η; laminar below about 2,000, turbulent above about 3,000; Table 14.4), https://openstax.org/books/university-physics-volume-1/pages/14-7-viscosity-and-turbulence (retrieved 2026-10-05).
4. f = air0, v = 10, D = 0.1 gives re = 75,438.596491, regime = Turbulent. Source: OpenStax, University Physics Volume 1, §14.7 Viscosity and Turbulence (N_R = 2ρvr ÷ η; laminar below about 2,000, turbulent above about 3,000; Table 14.4), https://openstax.org/books/university-physics-volume-1/pages/14-7-viscosity-and-turbulence (retrieved 2026-10-05); OpenStax, University Physics Volume 1, §14.1 Fluids, Density, and Pressure (Table 14.1), https://openstax.org/books/university-physics-volume-1/pages/14-1-fluids-density-and-pressure (retrieved 2026-10-05).

## FAQ

### How do you calculate the Reynolds number?

Multiply the density by the flow speed and the pipe diameter, then divide by the viscosity: Re = ρ × v × D ÷ η. Water at 20 °C (998.2 kg/m³, 0.001002 Pa·s) at 0.5 m/s in a 2 cm pipe gives 998.2 × 0.5 × 0.02 ÷ 0.001002 = 9,962.

### What Reynolds number is laminar flow?

In a pipe, flow is laminar below about 2,000 and turbulent above about 3,000. Between them it is unstable and can switch between the two.

### Does the Reynolds number have units?

No. The units of ρ × v × D ÷ η cancel, so Re is a pure number. Use one consistent set of units, such as kg/m³, m/s, m and Pa·s.

### What is the difference between dynamic and kinematic viscosity?

Dynamic viscosity η is in Pa·s. Kinematic viscosity is ν = η ÷ ρ, in m²/s. With ν the formula is Re = v × D ÷ ν.

### Why does the radius form give the same number?

OpenStax writes N_R = 2ρvr ÷ η with r the radius. Since 2r = D, that is the same as ρvD ÷ η.

### What is a centipoise?

A centipoise (cP) is 0.001 Pa·s, the same as 1 mPa·s. Water at 20 °C is about 1 cP.

## Sources

- OpenStax, University Physics Volume 1, §14.7 Viscosity and Turbulence: N_R = 2ρvr ÷ η, limits of about 2,000 and 3,000, Table 14.4 viscosities, retrieved 2026-10-05. https://openstax.org/books/university-physics-volume-1/pages/14-7-viscosity-and-turbulence
- OpenStax, University Physics Volume 1, §14.1 Fluids, Density, and Pressure: Table 14.1 densities of water and air, retrieved 2026-10-05. https://openstax.org/books/university-physics-volume-1/pages/14-1-fluids-density-and-pressure
- NIST Special Publication 811 (2008), Appendix B.8: 1 ft = 0.3048 m, 1 in = 0.0254 m, 1 lb = 0.45359237 kg, 1 mph = 0.44704 m/s, retrieved 2026-10-05. https://www.nist.gov/pml/special-publication-811