What Reynolds number is laminar flow?

In a full circular pipe, flow is laminar below about 2,300 and turbulent above 4,000 by the usual engineering limits; in between it can switch back and forth. Those limits are a convention: Wikipedia’s article gives turbulent flow from about 2,900 for fully developed pipe flow. The calculator labels by 2,300 and 4,000.

What is the Reynolds number of air?

It depends on speed and size. With air at 20 °C (1.204 kg/m³, 0.00001813 Pa·s), 10 m/s over 0.1 m gives 66,409.3, while 0.5 m/s in a 10 mm tube gives 332.046.

Does water temperature change the Reynolds number?

Yes, mainly through viscosity, which falls as water warms. In a 50 mm pipe at 0.1 m/s, Re is 3,827.34 at 10 °C (transitional), 4,983.08 at 20 °C and 10,549.4 at 60 °C (both turbulent).

Do the 2,300 and 4,000 limits apply to a plate, a hull or a river?

No. The critical Reynolds number is different for every geometry; a boundary layer on a flat plate turns turbulent near 500,000, measured from the leading edge. Use the number for those cases, but not the pipe-flow label.

What units does it use?

SI only: density in kg/m³, velocity in m/s, length in m and dynamic viscosity in Pa·s, or kinematic viscosity in m²/s. Viscosity in centipoise divides by 1,000 (1 cP = 0.001 Pa·s), and centistokes by 1,000,000 to give m²/s. For a non-circular duct, enter the hydraulic diameter as the length. Every value must be above 0.

Can I use kinematic viscosity instead?

Yes. Set Viscosity given as to kinematic and Re = v × L ÷ ν, with no density field. Switching converts the typed value with ν = μ ÷ ρ. With ν = 0.000001 m²/s (about water at 20 °C), 1 m/s in a 50 mm pipe gives 50,000. The presets fill both forms: air at 20 °C is 0.000015158 m²/s.

Reynolds Number

Reynolds number Re = ρvL/μ, or vL/ν from kinematic viscosity, in SI units with water and air presets, labeled laminar, transitional or turbulent for pipe flow. How it works

Fluid preset

Fills density and viscosity. Typing in either field switches back to Custom.

Viscosity given as

Fluid density

Flow velocity

Pipe diameter or characteristic length

Dynamic viscosity

Reynolds number (Re)

100,000

Regime Turbulent flow

Re = density × velocity × length ÷ dynamic viscosity, or velocity × length ÷ kinematic viscosity (kinematic viscosity is dynamic viscosity ÷ density, so the two forms agree). Shown to 6 significant digits.

Water rows come from a handbook table (CRC Handbook / IAPWS-based, interpolated); air is at 20 °C and 1 atm. Real fluids vary with temperature and composition, so check your own figures for critical work.

The regime label uses the limits for flow in a full circular pipe with the diameter as the length: laminar below 2,300, transitional from 2,300 to 4,000, turbulent above 4,000. The critical Reynolds number is different for every geometry, so for flow over a flat plate, around a sphere or a hull, or in an open channel the number is the same formula but the label does not apply (a flat-plate boundary layer, for example, turns turbulent near 500,000). For a non-circular duct use the hydraulic diameter as the length.

About the Reynolds Number

Water at 20 °C moving at 0.1 m/s through a 50 mm pipe has a Reynolds number of 4,983.08, just above the turbulent limit of 4,000. Re = ρvL ÷ μ: density times velocity times pipe diameter, divided by dynamic viscosity. This Reynolds number calculator labels the result laminar below 2,300, transitional from 2,300 to 4,000 and turbulent above 4,000, the usual limits for flow in a pipe.

Reynolds numbers for water and air

Fluid	Density (kg/m³)	Viscosity (Pa·s)	Velocity (m/s)	Length (m)	Re	Pipe-flow label
Water, 20 °C	998.21	0.0010016	0.02	0.05	996.615	Laminar
Water, 20 °C	998.21	0.0010016	0.046	0.05	2,292.22	Laminar
Water, 20 °C	998.21	0.0010016	0.05	0.05	2,491.54	Transitional
Water, 20 °C	998.21	0.0010016	0.08	0.05	3,986.46	Transitional
Water, 20 °C	998.21	0.0010016	0.1	0.05	4,983.08	Turbulent
Water, 20 °C	998.21	0.0010016	1	0.05	49,830.8	Turbulent
Water, 20 °C	998.21	0.0010016	1	0.1	99,661.5	Turbulent
Water, 10 °C	999.70	0.0013060	0.1	0.05	3,827.34	Transitional
Water, 60 °C	983.20	0.0004660	0.1	0.05	10,549.4	Turbulent
Air, 20 °C, 1 atm	1.204	0.00001813	0.5	0.01	332.046	Laminar
Air, 20 °C, 1 atm	1.204	0.00001813	2	0.05	6,640.93	Turbulent
Air, 20 °C, 1 atm	1.204	0.00001813	10	0.1	66,409.3	Turbulent
Air, 20 °C, 1 atm	1.204	0.00001813	30	1	1,992,280	Turbulent

Fluid properties from The Engineering ToolBox tables: water density 999.70, 998.21 and 983.20 kg/m³ and viscosity 0.0013060, 0.0010016 and 0.0004660 Pa·s at 10, 20 and 60 °C; air at 20 °C and 1 atm 1.204 kg/m³ and 18.13 µPa·s. The tool’s own fluid presets use slightly different handbook figures (water at 20 °C 0.001002 Pa·s, air 0.00001825 Pa·s), so with a preset the 0.1 m/s water row gives 4,981.09. The label assumes flow inside a full circular pipe with L as its diameter.

Frequently asked questions

What Reynolds number is laminar flow?: In a full circular pipe, flow is laminar below about 2,300 and turbulent above 4,000 by the usual engineering limits; in between it can switch back and forth. Those limits are a convention: Wikipedia’s article gives turbulent flow from about 2,900 for fully developed pipe flow. The calculator labels by 2,300 and 4,000.
What is the Reynolds number of air?: It depends on speed and size. With air at 20 °C (1.204 kg/m³, 0.00001813 Pa·s), 10 m/s over 0.1 m gives 66,409.3, while 0.5 m/s in a 10 mm tube gives 332.046.
Does water temperature change the Reynolds number?: Yes, mainly through viscosity, which falls as water warms. In a 50 mm pipe at 0.1 m/s, Re is 3,827.34 at 10 °C (transitional), 4,983.08 at 20 °C and 10,549.4 at 60 °C (both turbulent).
Do the 2,300 and 4,000 limits apply to a plate, a hull or a river?: No. The critical Reynolds number is different for every geometry; a boundary layer on a flat plate turns turbulent near 500,000, measured from the leading edge. Use the number for those cases, but not the pipe-flow label.
What units does it use?: SI only: density in kg/m³, velocity in m/s, length in m and dynamic viscosity in Pa·s, or kinematic viscosity in m²/s. Viscosity in centipoise divides by 1,000 (1 cP = 0.001 Pa·s), and centistokes by 1,000,000 to give m²/s. For a non-circular duct, enter the hydraulic diameter as the length. Every value must be above 0.
Can I use kinematic viscosity instead?: Yes. Set Viscosity given as to kinematic and Re = v × L ÷ ν, with no density field. Switching converts the typed value with ν = μ ÷ ρ. With ν = 0.000001 m²/s (about water at 20 °C), 1 m/s in a 50 mm pipe gives 50,000. The presets fill both forms: air at 20 °C is 0.000015158 m²/s.

Who checks the Reynolds number

Process and HVAC engineers check whether water or oil in a pipe is laminar or turbulent, because that decides which friction and heat-transfer formulas apply; fluid mechanics students check homework. Water at 20 °C moving at 1 m/s in a 50 mm pipe gives Re = 49,830.8, well into turbulent flow, while the same pipe at 0.02 m/s gives 996.615, laminar.

Reynolds number formula

Re = ρ × v × L ÷ μ, where ρ is the fluid density (kg/m³), v the mean velocity (m/s), L the characteristic length (m: the inside diameter for a pipe, the hydraulic diameter for a non-circular duct) and μ the dynamic viscosity (Pa·s). With kinematic viscosity ν (m²/s) chosen instead, Re = v × L ÷ ν and no density is needed, because ν = μ ÷ ρ. Re has no unit. With the starting values, 1000 × 1 × 0.1 ÷ 0.001 = 100,000. The label uses the usual limits for a full circular pipe: laminar below 2,300, transitional from 2,300 to 4,000, turbulent above 4,000. Those limits are a pipe-flow convention; the critical value is different for every geometry (a boundary layer on a flat plate turns turbulent near 500,000), so for a plate, a hull or an open channel use the number but not the label. Every input must be above 0, and the result shows 6 significant digits; the label follows the number shown, so a value that rounds to 2,300 is labeled transitional. Viscosity in centipoise divides by 1,000 to give Pa·s. Presets fill in water at 10 to 80 °C and air at 20 °C: air at 1 m/s over 0.1 m gives 6,597.26.

Fun Fact: George Stokes introduced the ratio in 1851. Osborne Reynolds made it widely used in 1883 with a stream of dyed water in a glass pipe, which stayed a thin line at low speed and broke up across the pipe at higher speed, and Arnold Sommerfeld named the number after him in 1908.

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Reynolds Number

Use the Reynolds Number

About the Reynolds Number

Reynolds numbers for water and air

Frequently asked questions

Who checks the Reynolds number

Reynolds number formula

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