Reynolds Number Calculator
The Reynolds number Re is the ratio of inertial forces to viscous forces in a fluid flow, defined as Re = ρVD/μ (or equivalently VD/ν or 4ṁ/πDμ for mass flow). Re determines...
Formula
Source: White, F.M. (2016) Fluid Mechanics (8th ed.); Moody, L.F. (1944) Trans. ASME | Last reviewed: July 3, 2026
Examples
2 velocity
= 200000 reynolds
- diameter = 100
- rho = 1000
- mu = 0.001
Water at 2 m/s in 100 mm pipe → Re = 200,000 (turbulent)
0.05 velocity
= 500 reynolds
- diameter = 10
- rho = 1000
- mu = 0.001
Water at 0.05 m/s in 10 mm tube → Re = 500 (laminar)
5 velocity
= 16931 reynolds
- diameter = 50
- rho = 1.225
- mu = 0.0000181
Air at 5 m/s in 50 mm duct → Re = 16,931 (transitional)
Quick Reference Table
| T (°C) | ρ (kg/m³) | μ (Pa·s) | ν (m²/s) |
|---|---|---|---|
| 0 | 999.8 | 0.00179 | 0.00000179 |
| 10 | 999.7 | 0.00131 | 0.00000131 |
| 20 | 998.2 | 0.001 | 0.000001 |
| 40 | 992.1 | 0.000653 | 6.58e-7 |
| 60 | 983.2 | 0.000467 | 4.75e-7 |
| 80 | 971.8 | 0.000355 | 3.65e-7 |
| 100 | 958.4 | 0.000282 | 2.94e-7 |
| T (°C) | ρ (kg/m³) | μ (Pa·s) | ν (m²/s) |
|---|---|---|---|
| 0 | 1.293 | 0.0000171 | 0.0000132 |
| 20 | 1.205 | 0.0000181 | 0.000015 |
| 40 | 1.127 | 0.000019 | 0.0000169 |
| 60 | 1.06 | 0.00002 | 0.0000189 |
| 80 | 1 | 0.0000209 | 0.0000209 |
| 100 | 0.946 | 0.0000218 | 0.000023 |
Where is this used?
It appears in: pipe flow friction factor correlations (Moody chart, Colebrook-White), heat transfer correlations (Nusselt number, Reynolds analogy), pump affinity laws, flow meter selection (turbine, vortex, Coriolis all have Reynolds-dependent accuracy), entrance length calculations, and open channel flow.
For pipe flow: Re < 2,300 → laminar (Hagen-Poiseuille, f=64/Re).
Re > 4,000 → turbulent (use Colebrook-White or Swamee-Jain).
Re between 2,300 and 4,000 → transitional (engineering practice: use turbulent correlations for design safety).
Real-World Usage Scenarios
Cooling Water Pipe Sizing Verification
A chemical plant has a 6-inch Schedule 40 steel pipe (D = 154.1 mm) carrying cooling water at 400 GPM (V = 1.85 m/s). At 25°C: ρ = 997 kg/m³, μ = 0.00089 Pa·s. Re = 997 × 1.85 × 0.1541 / 0.00089 = 319,500. The flow is fully turbulent (Re >> 4,000). The engineer notes this is in the fully turbulent regime, so the friction factor is independent of Re (depends only on relative roughness ε/D ≈ 0.00015/0.1541 = 0.001). Per the Moody chart or Swamee-Jain: f ≈ 0.020. Pressure drop per 100 m: hf = 0.020 × (100/0.1541) × (1.85² / (2 × 9.81)) = 2.25 m.
Hydraulic Oil in Hydraulic System
A hydraulic power unit uses ISO VG 46 oil (ρ = 870 kg/m³, μ at 40°C = 0.038 Pa·s). The return line is 1/2-inch Schedule 80 steel pipe (D = 12.5 mm) at 8 L/min (V = 1.09 m/s). Re = 870 × 1.09 × 0.0125 / 0.038 = 312 — fully laminar. The engineer uses Hagen-Poiseuille for pressure drop: hf = 32μLV/(ρgD²) = 32 × 0.038 × 100 × 1.09 / (870 × 9.81 × 0.0125²) = 98.9 m per 100 m — a 980 kPa pressure drop. The high viscosity of the oil causes significant friction loss; the system designer should consider a larger return line.
Common Mistakes to Avoid
Mixing SI and US customary units
Mixing units (e.g., V in m/s, D in inches) gives wrong Re. The most common error: using ρ in lb/ft³ with V in m/s — the units don't cancel, giving Re off by a factor of 106. Always convert all inputs to a consistent unit system before calculating.
Using kinematic viscosity incorrectly
Re = V×D/ν uses kinematic viscosity (ν = μ/ρ, in m²/s or ft²/s). Re = ρ×V×D/μ uses dynamic viscosity (μ, in Pa·s or lb/(ft·s)). These are different quantities. Using ν in cP (which is dynamic) instead of cSt (which is kinematic) is a common error that gives Re off by 1000x.
Ignoring temperature effect on viscosity
Water viscosity varies 3x from 0°C (1.79 cP) to 100°C (0.28 cP). Hot water at 90°C has Re 6x higher than cold water at 5°C at the same flow rate. Always use viscosity at the operating temperature, not ambient.
Industry Standards Referenced
Frequently Asked Questions
What is the Reynolds number formula?
Three equivalent forms: 1) Re = ρVD/μ (density, velocity, diameter, dynamic viscosity). 2) Re = VD/ν (velocity, diameter, kinematic viscosity). 3) Re = 4ṁ/(πDμ) (mass flow, diameter, dynamic viscosity). All are dimensionless. The first is most common.
What are the boundaries between laminar, transitional, and turbulent flow?
Per White's Fluid Mechanics: Re < 2,300 → laminar. 2,300 < Re < 4,000 → transitional. Re > 4,000 → turbulent. Some sources use 2,000/2,500 (more conservative) or 2,300/4,000 (most common). The transition zone is unstable; engineering design uses turbulent correlations (Moody chart) for safety even when Re is in the 2,300-4,000 range.
What Reynolds number is typical for industrial pipe flow?
Most industrial pipe flows are turbulent (Re > 10,000). Water in a 4-inch pipe at 100 GPM has Re ≈ 47,000. Air in a 12-inch duct at 5,000 CFM has Re ≈ 200,000. Laminar flow in industry is rare but occurs in: lubrication systems, viscous fluid handling, microfluidic devices, and some hydraulic systems.
Reviewed for accuracy
Cross-referenced against White's Fluid Mechanics and Engineering Toolbox Reynolds calculator · Last reviewed: July 3, 2026
All calculations are for reference only. Always verify with manufacturer data and a qualified engineer for critical applications. Learn about our editorial process.