Reynolds Number Calculator
Reynolds number Re = ρ v D ÷ μ (or v D ÷ ν) for flow in a pipe, from the speed or the flow rate, and whether the flow is laminar, transitional or turbulent, for water, air or any fluid in SI or imperial units.
Result…
How it's calculated
Re = ρ v D ÷ μ = v D ÷ ν ν = μ ÷ ρ From a flow rate: v = Q ÷ (π D² ÷ 4) Pipe flow: laminar Re ≤ 2300, transitional 2300 to 4000, turbulent Re > 4000
The Reynolds number compares the inertia of a moving fluid with its viscosity. Low values mean smooth, layered (laminar) flow; high values mean chaotic, mixing (turbulent) flow. For a round pipe the length is the inside diameter and the speed is the average speed, the flow rate divided by the pipe area. The regime limits follow the common pipe-flow guide given by SimScale: laminar up to 2300, transition from 2300 to 4000, turbulent above 4000. The water preset uses 998.21 kg/m³ and 0.0010016 Pa·s, and the air preset 1.204 kg/m³ and 18.13 μPa·s, both at 20 °C from Engineering ToolBox tables. Unit factors are exact: 1 ft = 0.3048 m, 1 in = 0.0254 m, 1 lb = 0.45359237 kg, 1 US gal = 3.785411784 L.
Your numbers, step by step
About the Reynolds Number calculator
This Reynolds number calculator works out Re = ρ v D ÷ μ, or v D ÷ ν, for flow in a round pipe and says whether the flow is laminar, transitional or turbulent. Pick water or air at 20 °C, or enter your own fluid's density and dynamic viscosity, or its kinematic viscosity alone. Give the flow as an average speed in m/s, km/h, mph or ft/s, or as a flow rate in L/s, L/min, m³/h, US or UK gallons per minute or ft³/s, and the pipe's inside diameter in mm, cm, m, inches or feet. Viscosity works in Pa·s, mPa·s (cP), lbf·s/ft² or lb/(ft·s), so SI and imperial data both work. It also shows the speeds at which this pipe would reach Re = 2300 and 4000. It suits pipe sizing, lab work and fluid mechanics homework, with every step shown.
How to use it
- Choose the “Fluid”, or pick another fluid and say whether its “Viscosity known as” dynamic or kinematic, then enter the values and units.
- Under “Flow given as”, choose average speed or flow rate and enter the “Average flow speed” or “Flow rate”.
- Enter the “Pipe inside diameter” and its unit.
- Read the Reynolds number, the flow regime and the speeds where the flow would reach the laminar and turbulent limits.
Worked example
Water at 20 °C (998.21 kg/m³, 0.0010016 Pa·s) flows at 0.3 L/s through a pipe with a 20 mm inside diameter. The pipe area is π × 0.02² ÷ 4 = 0.000314 m², so the average speed is 0.955 m/s. The kinematic viscosity is 0.0010016 ÷ 998.21 = 1.0034 × 10⁻⁶ m²/s, giving Re = 0.955 × 0.02 ÷ 1.0034 × 10⁻⁶ = 19,034: turbulent. The flow would stay laminar only below about 0.115 m/s.
Updated
Questions people ask
How do I calculate the Reynolds number for a pipe?
Multiply the fluid density by the average speed and the inside diameter, then divide by the dynamic viscosity: Re = ρ v D ÷ μ. With kinematic viscosity ν, it is simply v D ÷ ν. Use consistent SI units (kg/m³, m/s, m, Pa·s) and Re has no units.
At what Reynolds number does pipe flow become turbulent?
The common guide for fully developed flow in a round pipe is laminar up to about 2300, transitional between 2300 and 4000 and turbulent above 4000, as summarised by SimScale. Rough walls, bends and vibration can trigger turbulence earlier.
What is the difference between dynamic and kinematic viscosity?
Dynamic viscosity μ (Pa·s or cP) measures a fluid's resistance to shearing; kinematic viscosity ν (m²/s or cSt) is μ divided by density. A common mistake is to put a value in centipoise into a formula that expects Pa·s: 1 cP is 0.001 Pa·s.
What viscosity does the calculator use for water and air?
Water at 20 °C uses 998.21 kg/m³ and 0.0010016 Pa·s, and air at 20 °C and 1 atm uses 1.204 kg/m³ and 18.13 μPa·s, from Engineering ToolBox tables. Viscosity changes a lot with temperature, so enter your own values for hot or cold fluids.
What does this Reynolds number calculator not cover?
It uses the pipe-flow limits only; open channels, ducts of other shapes, flat plates and flow around objects use other lengths and other limits. It does not give pressure drop or friction losses, so have a qualified engineer check real pipe designs. To get the speed from a flow rate on its own, use the flow rate calculator.