Reynolds Number Calculator
Reynolds number for pipes, ducts and annuli from velocity or flow, with water properties from 0 to 100 °C, oil and air presets, and the flow regime.
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About this toolWhat is the Reynolds Number Calculator?
The Reynolds number tells you whether a flow is smooth and layered or chaotic and mixing, and almost every pipe friction or heat transfer correlation needs it first. This calculator works out Re = ρvD/μ for a round pipe, a rectangular duct, an annulus or any characteristic length, and labels the result laminar, transitional or turbulent. With the defaults, water at 20 °C moving at 1 m/s through a 50 mm bore gives Re = 49,830, firmly turbulent.
Fluid properties are the part people usually get wrong, so the water preset looks up density and viscosity from a 0 to 100 °C table and interpolates between points. Hot water is much thinner than cold: the same pipe and velocity at 60 °C gives Re = 105,500, more than double. Presets for seawater, air, ISO VG 32 and VG 68 oils, diesel and glycerol fill in typical values you can overwrite.
You can enter a velocity or a flow rate. For non-circular sections the tool computes the hydraulic diameter, Dh = 4A/P, so a 400 × 200 mm duct uses 266.7 mm. It also reports the kinematic viscosity, the velocities that would put you at Re = 2300 and 4000, and an entrance-length estimate.
- Re = ρvD/μ for round pipes, rectangular ducts, annuli and custom lengths
- Water density, viscosity and vapour pressure from 0 to 100 °C with interpolation
- Presets for seawater, air, ISO VG 32 and VG 68 oil, diesel and glycerol, all editable
- Regime badge plus a log-scale marker, threshold velocities and entrance length
- Velocity or flow input with SI and US units, copy and share
How to use the Reynolds Number Calculator
- Pick the fluid. For water, type the temperature between 0 and 100 °C. For anything else, choose a preset or enter density and dynamic viscosity directly.
- Choose the flow section: round pipe, rectangular duct, annulus, or a custom characteristic length for plates, spheres or other shapes.
- Enter the dimensions in mm, cm, m, inches or feet.
- Enter either the mean velocity or the volumetric flow rate.
- Read Re, the regime badge and the marker on the log scale, plus kinematic viscosity, hydraulic diameter, the laminar and turbulent threshold velocities and the entrance length.
Worked examples
Cold versus hot water
Input
50 mm bore, 1 m/s, water at 10 °C and at 60 °C
Output
Re = 38,270 at 10 °C; Re = 105,500 at 60 °C
Viscosity falls from 1.306 to 0.466 mPa·s. Both are turbulent, but the friction factor and heat transfer coefficient differ noticeably.
Hydraulic oil in a pressure line
Input
ISO VG 32 at 40 °C, 25 mm bore, 2 m/s
Output
Re = 1,563, laminar
Oil hydraulics often run laminar. Friction follows 64/Re, and the loss changes strongly as the oil warms up and thins.
Air in a rectangular duct
Input
400 × 200 mm duct, air at 20 °C, 5 m/s
Output
Dh = 266.7 mm, Re = 88,690
HVAC ducts are almost always turbulent. Using the width or the height instead of Dh would misstate Re by 25 to 50%.
Background and insight
Osborne Reynolds published his dye experiments in 1883, showing that the switch from straight streaks to mixing depended on one group of variables, inertia over viscous force, now written Re = ρvD/μ = vD/ν. Because it is dimensionless, a water test and an oil test with the same Re behave alike, which is the basis of model testing.
For flow in round pipes, engineers conventionally treat Re below about 2300 as laminar and above about 4000 as fully turbulent, with a transition band in between. Those limits are conventions, not physical constants. Carefully disturbance-free laboratory pipes have stayed laminar far beyond 2300, while rough, vibrating or pulsing systems can go turbulent sooner. Other geometries use other numbers: flow over a flat plate stays laminar to roughly Re = 5 × 10⁵ based on distance from the leading edge.
The water table uses CRC Handbook density and IAPWS viscosity values: 1.792 mPa·s at 0 °C, 1.002 at 20 °C, 0.547 at 50 °C and 0.282 at 100 °C. Oil presets use the ISO 3448 grade midpoint, so VG 32 means 32 cSt at 40 °C. Oil viscosity changes several-fold over a normal operating range, so enter the value at your temperature.
Common use cases
Choosing a friction factor
Find out whether to use 64/Re or the Colebrook equation before working out pipe pressure drop.
Heat exchanger design
Pick the right Nusselt correlation by checking the tube-side and shell-side Reynolds numbers.
Lubrication and hydraulics
See whether an oil line runs laminar at cold start and at operating temperature.
Lab and teaching
Reproduce a Reynolds dye experiment on paper and show how temperature and size shift the regime.
Tips and limitations
- Use dynamic viscosity in Pa·s with density in kg/m³, or kinematic viscosity on its own. Mixing centipoise and centistokes without density is the classic error.
- Use the hydraulic diameter for friction in non-round ducts, but remember laminar friction in rectangles also depends on aspect ratio, so 64/Re is only exact for circles.
- An annulus uses Dh = outer bore minus inner pipe outside diameter.
- Do not design right in the 2300 to 4000 band. Pressure drop and heat transfer can jump unpredictably there.
- Gas viscosity rises with temperature while liquid viscosity falls, so hot air gives a lower Re than cold air at the same velocity.
Frequently asked questions
How do you calculate the Reynolds number for pipe flow?
Re = ρvD/μ, where ρ is density, v the mean velocity, D the inside diameter and μ the dynamic viscosity. Water at 20 °C (998.2 kg/m³, 0.001002 Pa·s) at 1 m/s in a 50 mm bore gives 998.2 × 1 × 0.05 / 0.001002 = 49,830.
What Reynolds number is laminar and what is turbulent?
For round pipes the usual convention is laminar below about 2300, transitional from 2300 to 4000 and turbulent above 4000. Some texts use 2000 or 2100 as the lower limit. The exact switch depends on disturbances and is not a sharp line.
What is hydraulic diameter?
Four times the flow area divided by the wetted perimeter, Dh = 4A/P. It equals D for a full round pipe, 2ab/(a + b) for a rectangle, and the gap times two (outer minus inner diameter) for an annulus. It lets round-pipe correlations be applied to other shapes.
What is the difference between dynamic and kinematic viscosity?
Dynamic viscosity μ (Pa·s or centipoise) measures resistance to shear. Kinematic viscosity ν = μ/ρ (m²/s or centistokes) divides out density. Water at 20 °C is about 1.0 cP and 1.0 cSt; oil grades are quoted in cSt.
Why does temperature change the Reynolds number so much?
Because liquid viscosity is very temperature sensitive. Water viscosity drops by more than half between 10 °C and 60 °C, and lubricating oils can change ten-fold between a cold start and running temperature, so Re rises as a liquid warms.
Does the Reynolds number have units?
No. Every unit cancels, which is why the same value means the same flow behaviour in any unit system. If your Re comes out in strange units, one input is in the wrong unit.
Is there an in-depth guide to the Reynolds Number Calculator?
Yes. “Reynolds Number Explained: Laminar, Transitional and Turbulent Flow” covers the background, how it works, common pitfalls and worked examples. Read the full guide.
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