Reynolds Number Calculator
Find the Reynolds number and the flow regime for water or air at your temperature, or for any fluid whose density and viscosity you know. Choose a round pipe by bore or nominal size, or a rectangular duct, then enter the flow rate or the velocity. For what the number means and where it comes from, read the Reynolds number guide.
Water from 0 to 100 °C (32 to 212 °F) at atmospheric pressure, from the IAPWS formulations.
Roughness only changes the friction factor in turbulent flow. It has no effect on the Reynolds number.
Dye fed into the middle of the pipe, as in Reynolds' 1883 experiment, drawn for the Reynolds number below.
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Reynolds number resultFree download
Get the printable pipe flow chart
Schedule 40 pipe sizes, water flow in GPM and LPM at four design velocities, and recommended velocities by application. One PDF, made to pin above the bench.
How It Works
The Reynolds number compares the inertia of a moving fluid with its viscosity. It has no units, so the same value means the same kind of flow whatever the fluid or the size of the pipe. The calculator looks up the fluid's density and viscosity at your temperature, takes the inside diameter (or the hydraulic diameter of a duct), turns a flow rate into the mean velocity, then divides.
Reynolds Number Formula
Re = ρVD / μ = VD / ν
- • ρ = density (kg/m³)
- • V = mean velocity (m/s). From a flow rate Q, V = Q / A, with A the inside area: πD²/4 for a round pipe
- • D = inside diameter, or the hydraulic diameter Dh for any other shape (m)
- • μ = dynamic viscosity (Pa·s; 1 cP = 0.001 Pa·s)
- • ν = μ / ρ = kinematic viscosity (m²/s; 1 cSt = 1 mm²/s)
Any units work as long as they cancel. Use the inside diameter, not the nominal size: 2" Schedule 40 steel has a 2.067 in (52.5 mm) bore.
Hydraulic Diameter for Ducts
Dh = 4A / P rectangle a × b: Dh = 2ab / (a + b)
For a section that is not round, use four times the flow area divided by the wetted perimeter. For a round pipe running full it comes back to the diameter. A 12 × 8 in duct has Dh = 2 × 12 × 8 ÷ 20 = 9.6 in. Take the velocity from the real area of the duct, not the area of a 9.6 in circle.
Water and Air Properties
Water is taken at atmospheric pressure from 0 to 100 °C, with density from IAPWS-95 and viscosity from the IAPWS 2008 equation, the formulations the NIST Chemistry WebBook uses. Air is dry air at 1 atm from -50 to 300 °C, from the Lemmon reference equations. Between the tabulated points, every 5 °C for water and 25 °C for air, the calculator interpolates and stays within 0.2% of the full equations. For any other liquid or gas, choose Other fluid and enter its density and either viscosity.
Friction Factor
The result includes the Darcy friction factor used in the Darcy–Weisbach equation. Laminar flow in a round pipe has the exact result f = 64/Re. Laminar flow in a rectangular duct uses Shah and London's coefficient instead, from 56.9/Re for a square duct towards 96/Re for a very flat one. Turbulent flow uses the Colebrook equation with the wall roughness you choose, the same method as the pressure drop calculator. In the transition range no equation is reliable, so the calculator gives both the laminar and the turbulent value.
Flow Regimes
Osborne Reynolds published the experiment behind the number in 1883. He fed a thin streak of dye into water flowing from a tank through a glass tube. At low speed the streak stayed a straight line the length of the tube. Faster, it began to waver, then broke up and filled the tube with colour. He showed that the change depended on the combination VD/ν, not on the velocity, the diameter or the viscosity alone, which is why one number covers every fluid and pipe size.
Where the change happened depended on how disturbed the water was. With the tank left to settle, the streak held to a Reynolds number of about 13,000; with the inlet disturbed, it broke up near 2,000. Later work put the lowest value at which turbulence can sustain itself in a long pipe at about 2,040 (Avila and colleagues, 2011). The limits below are therefore conventions for ordinary pipework, not physical constants.
- Laminar, Re below 2,300. The fluid moves in smooth layers with a parabolic velocity profile, fastest on the centreline. The friction factor is 64/Re and the pressure drop rises in proportion to the velocity. Common with oils and other viscous liquids, small tubes and slow flows.
- Transitional, Re from 2,300 to 4,000. Turbulent puffs form, travel down the pipe and die away, so the flow switches between the two states. Friction and heat transfer are hard to predict here, and designs usually avoid it.
- Turbulent, Re above 4,000. Eddies mix the fluid across the whole section and the velocity profile is much flatter. The friction factor depends on both Re and the wall roughness, and the pressure drop rises with roughly the square of the velocity. Water and air in building services and process plant are almost always turbulent.
The dye streak at the top of the calculator shows the same three cases for the Reynolds number you enter.
Worked Example
Water in a Pipe
50 US GPM of water at 20 °C (68 °F) through 2" Schedule 40 steel pipe, which has a 2.067 in (52.5 mm) bore. These are the calculator's starting values.
- • Flow: 50 GPM = 0.003155 m³/s
- • Area: π × 0.0525² ÷ 4 = 0.002165 m²
- • Velocity: 0.003155 ÷ 0.002165 = 1.457 m/s (4.78 ft/s)
- • Water at 20 °C: ρ = 998.2 kg/m³, μ = 1.0016 mPa·s, so ν = 1.0034 mm²/s
- • Re = 1.457 × 0.0525 ÷ 0.0000010034 ≈ 76,242, turbulent
- • Friction factor (Colebrook, new steel at 0.045 mm): f = 0.0223
The flow would only turn laminar below 0.0440 m/s, about 1.5 GPM in this pipe. To choose a pipe size for a target velocity instead, use the pipe sizing calculator.
Air in a Duct
1,000 CFM of air at 20 °C through a 12 × 8 in rectangular duct:
- • Hydraulic diameter: 2 × 12 × 8 ÷ (12 + 8) = 9.6 in (243.8 mm)
- • Velocity: 1,000 ft³/min ÷ 0.667 ft² = 1,500 ft/min (7.62 m/s)
- • Air at 20 °C: ρ = 1.205 kg/m³, μ = 18.20 µPa·s, so ν = 15.11 mm²/s
- • Re = 7.62 × 0.2438 ÷ 0.00001511 ≈ 122,951, turbulent
Reference Tables
Re at 1 and 2 m/s by Schedule 40 Size
Water at 20 °C (ν = 1.0034 mm²/s) in ASME B36.10 Schedule 40 steel pipe, using the actual inside diameters, rounded to three significant figures. The last column is the velocity at which the flow stops being laminar (Re = 2,300).
| Size | ID (mm) | Re at 1 m/s | Re at 2 m/s | V at Re 2,300 (mm/s) |
|---|---|---|---|---|
| 1/2" | 15.8 | 15,700 | 31,500 | 146 |
| 3/4" | 20.9 | 20,900 | 41,700 | 110 |
| 1" | 26.6 | 26,600 | 53,100 | 86.6 |
| 1-1/4" | 35.1 | 34,900 | 69,900 | 65.8 |
| 1-1/2" | 40.9 | 40,800 | 81,500 | 56.4 |
| 2" | 52.5 | 52,300 | 105,000 | 44.0 |
| 2-1/2" | 62.7 | 62,500 | 125,000 | 36.8 |
| 3" | 77.9 | 77,700 | 155,000 | 29.6 |
| 4" | 102.3 | 102,000 | 204,000 | 22.6 |
| 6" | 154.1 | 154,000 | 307,000 | 15.0 |
| 8" | 202.7 | 202,000 | 404,000 | 11.4 |
| 10" | 254.5 | 254,000 | 507,000 | 9.07 |
| 12" | 303.2 | 302,000 | 604,000 | 7.61 |
Water Properties by Temperature
Liquid water at atmospheric pressure, the values the calculator uses. Re scales with 1/ν, so the same flow at 80 °C has a Reynolds number 2.75 times that at 20 °C.
| °C | °F | Density (kg/m³) | μ (mPa·s) | ν (mm²/s) |
|---|---|---|---|---|
| 0 | 32 | 999.8 | 1.792 | 1.792 |
| 10 | 50 | 999.7 | 1.306 | 1.306 |
| 20 | 68 | 998.2 | 1.002 | 1.003 |
| 30 | 86 | 995.6 | 0.7972 | 0.8007 |
| 40 | 104 | 992.2 | 0.6527 | 0.6578 |
| 50 | 122 | 988.0 | 0.5465 | 0.5531 |
| 60 | 140 | 983.2 | 0.4660 | 0.4740 |
| 70 | 158 | 977.8 | 0.4035 | 0.4127 |
| 80 | 176 | 971.8 | 0.3541 | 0.3644 |
| 90 | 194 | 965.3 | 0.3142 | 0.3255 |
| 100 | 212 | 958.3 | 0.2816 | 0.2938 |
Air Properties at 1 atm
Dry air at 101.325 kPa. Its kinematic viscosity is about 15 times that of water at 20 °C and rises steeply with temperature, so hot air runs at a lower Reynolds number than cold air at the same velocity.
| °C | °F | Density (kg/m³) | μ (µPa·s) | ν (mm²/s) |
|---|---|---|---|---|
| -20 | -4 | 1.396 | 16.20 | 11.61 |
| 0 | 32 | 1.293 | 17.22 | 13.32 |
| 20 | 68 | 1.205 | 18.20 | 15.11 |
| 40 | 104 | 1.127 | 19.16 | 17.00 |
| 60 | 140 | 1.060 | 20.10 | 18.97 |
| 80 | 176 | 0.9995 | 21.01 | 21.02 |
| 100 | 212 | 0.9459 | 21.90 | 23.15 |
| 150 | 302 | 0.8340 | 24.03 | 28.81 |
| 200 | 392 | 0.7458 | 26.05 | 34.92 |
| 300 | 572 | 0.6157 | 29.81 | 48.42 |
FAQ
Answers to common questions about Reynolds number calculations.
Frequently Asked Questions
How do you calculate the Reynolds number?
Multiply the mean velocity by the inside diameter and divide by the kinematic viscosity: Re = VD/ν, which is the same as ρVD/μ. Use units that cancel, such as metres, metres per second and square metres per second. Water at 20 °C has ν = 1.0034 mm²/s (0.0000010034 m²/s), so at 1 m/s in a 50 mm bore Re = 1 × 0.05 ÷ 0.0000010034 ≈ 49,800, well into turbulent flow.
What Reynolds number is laminar, transitional and turbulent?
For flow in a round pipe the usual limits are laminar below 2,300, transitional from 2,300 to 4,000 and turbulent above 4,000. They are engineering conventions, not physical constants. Reynolds kept water laminar to about 13,000 by letting it settle before it entered his tube, while a disturbed inlet turned it turbulent near 2,000. In ordinary pipework with bends, valves and pumps, treat anything above 4,000 as turbulent.
What temperature range does the calculator cover?
Water from 0 to 100 °C (32 to 212 °F) at atmospheric pressure, and dry air from -50 to 300 °C at 1 atm. Temperature matters because warm water is far less viscous, so at the same velocity and pipe size the Reynolds number rises with temperature. The kinematic viscosity of water falls from 1.792 mm²/s at 0 °C to 1.003 at 20 °C, 0.4740 at 60 °C and 0.2938 at 100 °C, so the same flow has a Reynolds number 2.12 times higher at 60 °C than at 20 °C. Density changes by only about 4% over the whole range.
How do I find the Reynolds number of a rectangular duct?
Use the hydraulic diameter, Dh = 4A/P, in place of the diameter. For a rectangle with sides a and b that is 2ab/(a + b), so a 12 × 8 in duct has Dh = 9.6 in (243.8 mm). Take the velocity from the real area, 96 in²: 1,000 CFM gives 7.62 m/s (1,500 ft/min). Air at 20 °C has ν = 15.11 mm²/s, about 15 times that of water, so Re = 7.62 × 0.2438 ÷ 0.00001511 ≈ 123,000, turbulent like nearly all ductwork.
At what velocity does water flow become turbulent?
Solve Re = VD/ν for the velocity at Re = 2,300 and 4,000: V = Re × ν ÷ D. For water at 20 °C in 1" Schedule 40 pipe (26.6 mm bore) laminar flow ends at 0.087 m/s (0.28 ft/s) and the flow is turbulent above 0.151 m/s (0.49 ft/s). Typical design velocities of 1 to 3 m/s are 11 to 35 times the laminar limit, which is why water in building and process pipework is almost always turbulent.
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