Reynolds Number Calculator

The Reynolds number (Re) is a dimensionless quantity that predicts whether a flow is laminar or turbulent. It is the ratio of inertial forces to viscous forces: Re = rho x v x D / mu, where rho is fluid density, v is mean velocity, D is the characteristic length (pipe diameter), and mu is dynamic viscosity. Because every unit cancels, Re has no units. The same Re in two different setups means the flows are dynamically similar.

For flow inside a pipe, the engineering standard is: Re below 2300 is laminar, 2300 to 4000 is transitional, and above 4000 is turbulent. For flow over a flat plate, the critical value is Re_x = 5 x 10^5 based on distance from the leading edge. Worked example: water at 20 C flowing at 2 m/s through a 10 cm pipe gives Re = 199,122.37, which is far above 4000, so the flow is turbulent. This calculator shows both classifications automatically.

Both formulas give the same answer. Re = rho x v x D / mu uses dynamic viscosity mu, while Re = v x D / nu uses kinematic viscosity nu, where nu = mu / rho. For water at 20 C, nu = 1.004407 x 10^-6 m^2/s (about 1.0044 cSt), so with v = 2 m/s and D = 0.1 m, Re = 2 x 0.1 / 1.004407 x 10^-6 = 199,122.37, identical to the dynamic-viscosity formula. Use whichever viscosity value you have; the toggle above switches the form.

Use the inverse solver tab. Rearranging the formula: v = Re x mu / (rho x D) and D = Re x mu / (rho x v). Example: to hit exactly Re = 2300 (the laminar limit) in a 50 mm pipe with water at 20 C, you need v = 0.046203 m/s, about 4.6203 cm/s. Enter the target Re, the known variable, and the fluid, and the calculator returns the missing one in your chosen units.

Non-circular ducts (rectangular air ducts, square channels) do not have a single diameter, so you use the hydraulic diameter D_h = 4A / P, where A is the cross-sectional area and P is the wetted perimeter. For a rectangular duct a x b this simplifies to D_h = 2ab / (a + b); a square of side s has D_h = s, and a circle keeps D_h = d. Example: a 200 mm x 100 mm duct has D_h = 133.3333 mm. Compute it in the Hydraulic Diameter tab, then use it as D in the Reynolds calculation.

Liquid viscosity drops fast as temperature rises, and Re is inversely proportional to viscosity. Water at 20 C (mu = 1.0027 mPa.s) flowing at 2 m/s in a 10 cm pipe gives Re = 199,122.37, but the same flow at 60 C (mu = 0.4668 mPa.s) gives Re = 421,208.23, about 2.1153 times higher, because the water is less than half as viscous. Gas viscosity behaves the opposite way: air gets slightly MORE viscous when heated. Always use properties at your actual operating temperature; the fluid preset table above includes water at 0, 10, 20, 40 and 60 C and air at 0, 20 and 40 C.

Air at 20 C and 1 atm has density 1.204118 kg/m^3 and dynamic viscosity 18.13322 microPa.s (from the ideal gas law and the Sutherland formula). Air at 1 m/s past a 1 m object gives Re = 66,403.99, turbulent by pipe-flow standards. Because air is about 830 times less dense than water but only about 55 times less viscous, air flows reach high Re at modest speeds, which is why even a gentle breeze over a car is turbulent.

Re applies to Newtonian, incompressible fluids in steady flow. The 2300/4000 pipe thresholds are engineering rules of thumb: smooth pipes with careful inlet conditions can stay laminar past Re = 10,000, while rough pipes or disturbed inlets can trip turbulence below 2300. For compressible high-speed gas flow (Mach above ~0.3), density is no longer constant and Re alone does not describe the flow. It also does not give pressure drop by itself; for that you need the friction factor, which is what the darcy-weisbach calculator on this site computes from Re.

This is the dedicated Reynolds number calculator: two Re formulas with unit conversion, pipe and flat-plate regime classification, real fluid property presets at multiple temperatures, inverse solvers for v and D, and hydraulic diameter for non-circular ducts. Sibling tools use Re only as an intermediate step: darcy-weisbach computes head loss and the Colebrook friction factor from Re, pipe-velocity converts flow rate to velocity with a quick Re check, water-velocity-calculator sizes water pipes with Hazen-Williams, friction-factor solves the Moody chart, and drag-equation uses Re to judge drag-coefficient validity. If your question is simply what is my Reynolds number and what regime am I in, you are in the right place.