What Reynolds number is my flow?
Pick the fluid or type its density and viscosity, then type the flow speed and the inside diameter of the pipe. The Reynolds number calculator gives Re, says whether the flow is laminar or turbulent, and gives the fastest laminar speed.
- Reynolds number
- 9,962.08
The Reynolds number is 9,962.08: Turbulent flow.
- Flow
- Turbulent
- Kinematic viscosity (m²/s)
- 0.00000100381
- Density used (kg/m³)
- 998.2
- Viscosity used (Pa·s)
- 0.001002
- Fastest laminar speed (m/s)
- 0.100381
Reynolds number: 9,962.08. The Reynolds number is 9,962.08: Turbulent flow.
How to calculate
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.
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.
Method: Re = ρ × v × D ÷ η; kinematic viscosity ν = η ÷ ρ; laminar up to v = 2,000 × η ÷ (ρ × D).
- 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
Each example is checked against the calculator on every build.
- Fluid Water at 20 °C, Flow speed (v) 1.64 ft/s, Pipe diameter (D) 0.7874 in gives Reynolds number 9,962.075848, Flow Turbulent, Kinematic viscosity (m²/s) 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)
- Fluid Other: type the density and viscosity, Density (ρ) 62.43 lb/ft³, Viscosity (η) 1, Viscosity unit Pa·s, Flow speed (v) 0.3281 ft/s, Pipe diameter (D) 0.3937 in gives Reynolds number 1, Flow 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)
- Fluid Other: type the density and viscosity, Density (ρ) 62.43 lb/ft³, Viscosity (η) 1, Viscosity unit mPa·s (centipoise, cP), Flow speed (v) 0.6562 ft/s, Pipe diameter (D) 0.3937 in gives Reynolds number 2,000, Flow Transitional (unstable), Fastest laminar speed (m/s) 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)
- Fluid Air at 0 °C, 1 atm, Flow speed (v) 32.81 ft/s, Pipe diameter (D) 3.937 in gives Reynolds number 75,438.596491, Flow 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)
How it works
- Reynolds number Re = ρ × v × D ÷ η, with ρ the density, v the average flow speed, D the inside pipe diameter and η the dynamic viscosity.
- Kinematic viscosity ν = η ÷ ρ.
- Fastest laminar speed = 2,000 × η ÷ (ρ × D), the speed at which Re reaches 2,000.
- Flow: Laminar when Re is below 2,000; Transitional (unstable) from 2,000 to 3,000, both included; Turbulent above 3,000.
Fluids (OpenStax Tables 14.1 and 14.4): water at 20 °C, 998.2 kg/m³ and 0.001002 Pa·s; water at 0 °C, 999.8 kg/m³ and 0.001792 Pa·s; water at 100 °C, 958.4 kg/m³ and 0.000282 Pa·s; air at 0 °C and 1 atm, 1.29 kg/m³ and 0.0000171 Pa·s. Or type your own density (kg/m³, g/cm³ or lb/ft³) and viscosity (Pa·s, mPa·s, poise, or lb/(ft·s)).
Unit sizes (exact): 1 mPa·s = 1 cP = 0.001 Pa·s; 1 P = 0.1 Pa·s; 1 lb/(ft·s) = 0.45359237 ÷ 0.3048 Pa·s; 1 km/h = 5/18 m/s; 1 mph = 0.44704 m/s; 1 ft/s = 0.3048 m/s.
Rules
- Speed from 10⁻⁶ to 10,000 m/s; diameter from 10⁻⁶ m (1 µm) to 1,000 m; a typed density from 0.001 to 30,000 kg/m³; a typed viscosity from 10⁻⁹ to 10⁹ in its unit.
- A Reynolds number too small or too large to show as a number has no answer.
Output format
Re, ν, the density, the viscosity and the fastest laminar speed show to 6 significant figures. Typed values are read back as exact decimals and the arithmetic is exact, so Re is compared with 2,000 and 3,000 exactly and rounded once.
Worked examples by hand
Water in a small pipe. Water at 20 °C at 0.5 m/s in a 2 cm pipe: Re = 998.2 × 0.5 × 0.02 ÷ 0.001002 = 9,962.08, turbulent. ν = 0.001002 ÷ 998.2 = 1.00381 × 10⁻⁶ m²/s.
A thick fluid. 1,000 kg/m³ and 1 Pa·s at 0.1 m/s in a 1 cm pipe: Re = 1,000 × 0.1 × 0.01 ÷ 1 = 1, laminar.
On the limit. 1,000 kg/m³ and 1 mPa·s at 0.2 m/s in a 1 cm pipe: Re = 1,000 × 0.2 × 0.01 ÷ 0.001 = 2,000, transitional; the fastest laminar speed is 2,000 × 0.001 ÷ (1,000 × 0.01) = 0.2 m/s.
Air in a duct. Air at 0 °C at 10 m/s in a 10 cm duct: Re = 1.29 × 10 × 0.1 ÷ 0.0000171 = 75,438.6, turbulent.
Other questions people ask
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.