Reynolds Number Calculator: Re = rho v D / mu

The Reynolds number tells you whether pipe flow is smooth or turbulent.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose which quantity you want to find.

Enter the other values in the units shown.

The calculator gives the answer with the formula, the substituted numbers, and the answer in other units.

Formulas used

  • Re = \frac{\rho vD}{\mu}
  • v = \frac{Re\,\mu}{\rho D}
  • D = \frac{Re\,\mu}{\rho v}

Worked example

With the default numbers in the calculator above:

  1. The formula, arranged to find the reynolds number: reynolds number = (density x velocity x diameter) / (dynamic viscosity)
  2. Put the values in (every value in its SI unit): reynolds number = (998 x 1.5 x 0.05) / (0.001)
  3. The answer: reynolds number: 74850

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want to find? Diameter; Reynolds number (leave it as it is if this is what you are finding) 74850; Dynamic viscosity (leave it as it is if this is what you are finding) 0.001 Pa s.

  1. The formula, arranged to find the diameter: diameter = (reynolds number x dynamic viscosity) / (density x velocity)
  2. Put the values in (every value in its SI unit): diameter = (74850 x 0.001) / (998 x 1.5)
  3. The answer: diameter: 0.05 m
  4. The same answer in other units: 50 mm; 1.9685 inches

Common questions

What is the Reynolds number?

The ratio of inertial forces to viscous forces, density times velocity times diameter divided by the viscosity.

When is pipe flow turbulent?

When the Reynolds number is above about 4000. Below about 2300 it is laminar.

Why does it matter?

The pressure loss and the heat transfer are very different in laminar and turbulent flow.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any fluid mechanics text (Reynolds number).

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