Reynolds Number Calculator
Calculate the Reynolds number to determine laminar or turbulent fluid flow.
Fluid Presets
ρ=998 kg/m³, μ=0.001002 Pa·s
Re = ρvL/μ. All calculations run live in your browser using standard fluid mechanics formulas. Critical velocity calculated at Re = 2300.
What Is the Reynolds Number Calculator?
The Reynolds number (Re) is a dimensionless parameter that characterizes whether fluid flow is laminar (smooth, ordered), transitional, or turbulent (chaotic). It equals the ratio of inertial forces to viscous forces: Re = ρvL/μ. This calculator includes 6 fluid presets and shows the critical velocity at which flow transitions from laminar to turbulent.
- ›ρ = fluid density (kg/m³), v = velocity (m/s)
- ›L = characteristic length, pipe diameter, plate length, or body size (m)
- ›μ = dynamic viscosity (Pa·s), ν = μ/ρ = kinematic viscosity (m²/s)
- ›Critical velocity = 2300 × μ / (ρ × L), the speed at which laminar flow breaks down
Formula
Reynolds Number Formula
Reynolds Number
Re = ρvL / μ
With kinematic ν
Re = vL / ν (where ν = μ/ρ)
Kinematic viscosity
ν = μ / ρ (m²/s)
Laminar (pipe)
Re < 2,300
Transitional
2,300 ≤ Re ≤ 4,000
Turbulent (pipe)
Re > 4,000
How to Use
- 1Select a fluid preset (Water, Air, Oil…) to auto-fill ρ and μ, or choose Custom
- 2Enter the flow velocity v in m/s
- 3Enter the characteristic length L (pipe inner diameter for pipe flow)
- 4Click "Calculate Re", the Reynolds number, flow regime, and friction factor appear
- 5The scale bar shows where your Re falls in the laminar–turbulent spectrum
- 6The critical velocity shows the threshold for laminar flow at your L and fluid
Example Calculation
Water in a 25mm pipe at 1 m/s:
μ = 0.001002 Pa·s
v = 1 m/s, L = 0.025 m (25mm diameter)
Re = (998 × 1 × 0.025) / 0.001002 = 24,900
Flow regime: Turbulent (Re > 4,000)
Friction factor: Moody/Colebrook equation
Critical velocity (Re=2300) = (2300 × 0.001002)/(998 × 0.025) = 0.0922 m/s
Air vs. Water comparison
Air (ν=1.5×10⁻⁵ m²/s) has kinematic viscosity 15× higher than water (ν=10⁻⁶ m²/s). So the same geometry needs 15× higher velocity to reach the same Reynolds number in air as in water.
Understanding Reynolds Number
Common Fluid Properties at 20°C
| Fluid | ρ (kg/m³) | μ (Pa·s) | ν (m²/s) |
|---|---|---|---|
| Water (20°C) | 998 | 1.00×10⁻³ | 1.00×10⁻⁶ |
| Air (20°C) | 1.204 | 1.81×10⁻⁵ | 1.51×10⁻⁵ |
| Engine oil (SAE 10) | 884 | 3.19×10⁻¹ | 3.61×10⁻⁴ |
| Olive oil | 900 | 8.10×10⁻² | 9.00×10⁻⁵ |
| Glycerol (100%) | 1260 | 1.49 | 1.18×10⁻³ |
| Honey | 1400 | 10 | 7.14×10⁻³ |
Frequently Asked Questions
What does the Reynolds number physically represent?
The Reynolds number is a ratio: how much does the fluid's momentum resist change (inertia) vs. how much internal friction resists flow (viscosity)?
- ›Low Re (viscous dominates): smooth parallel streamlines, laminar flow
- ›High Re (inertia dominates): eddies and mixing, turbulent flow
- ›Re is dimensionless, the same Re gives the same flow pattern at any scale
- ›This is why wind tunnel tests on scale models predict full-size aircraft behavior
What is the characteristic length?
L sets the relevant length scale for the flow geometry. Different L choices change Re and the critical thresholds.
- ›Pipe/duct: hydraulic diameter D_h = 4A/P (A=area, P=wetted perimeter)
- ›Circular pipe: D_h = pipe inner diameter
- ›Flat plate: distance from leading edge, Re changes along the plate
- ›Sphere/cylinder: diameter of the body
What is kinematic viscosity?
Kinematic viscosity is convenient because it absorbs density, allowing Re = vL/ν without needing ρ and μ separately.
- ›Water at 20°C: ν = 1.004×10⁻⁶ m²/s
- ›Air at 20°C: ν = 1.51×10⁻⁵ m²/s (15× water)
- ›Honey: ν ≈ 10⁻² m²/s (10,000× water), flows very slowly
- ›Kinematic viscosity decreases with temperature for liquids, increases for gases
Why are the transition thresholds 2300 and 4000?
The 2300/4000 values apply specifically to pipe flow. Other geometries have different critical Reynolds numbers based on their specific flow patterns.
- ›Pipe flow laminar-turbulent: Re_crit ≈ 2300–4000
- ›Flat plate boundary layer: Re_crit ≈ 5×10⁵
- ›Flow past a sphere: drag coefficient changes rapidly around Re ≈ 3×10⁵
- ›Very smooth pipes can maintain laminar flow up to Re ≈ 100,000 in controlled conditions
How does the friction factor relate to Reynolds number?
The Darcy-Weisbach equation: ΔP = f × (L/D) × (ρv²/2). The friction factor f depends on Re and pipe roughness.
- ›Laminar: f = 64/Re, exact, independent of roughness
- ›Turbulent smooth pipe: Blasius formula f = 0.316/Re^0.25 (valid Re 4000–100,000)
- ›Turbulent rough pipe: Moody chart or Colebrook equation
- ›Churchill (1977) provides a single equation covering all regimes
What is dynamic similarity?
If Re is the same, flow patterns are geometrically similar regardless of scale, velocity, or fluid. This is the basis of wind tunnel and water tunnel testing.
- ›Wind tunnel: smaller model at higher velocity gives same Re as full-size aircraft
- ›Ship hull: water tunnel test at model scale predicts drag at full scale
- ›Microfluidics: very small L keeps Re low (laminar) even at high velocity
- ›Cardiovascular modeling: blood flow Re ≈ 4000 in aorta, near turbulent
How does viscosity change with temperature?
Viscosity is strongly temperature-dependent, which matters in heat exchangers, industrial processes, and engine cooling systems.
- ›Water: μ ≈ 1.79 mPa·s at 0°C, 1.00 mPa·s at 20°C, 0.28 mPa·s at 100°C
- ›Air: μ ≈ 1.72×10⁻⁵ Pa·s at 0°C, 2.18×10⁻⁵ Pa·s at 100°C
- ›Engine oil: μ drops dramatically with temperature (that's how viscosity grades work)
- ›Use temperature-correct μ values for accurate Re calculations