Dimensionless Number Calculators
Biot Number
Bi = h · L / k
Conductive vs convective resistance for transient heat-transfer analysis.
Calculate →Cauchy Number
Ca = ρ · v² / K
Compressibility ratio for high-speed flow with elastic effects.
Calculate →Cavitation Number
σ = (p − p_v) / (½ · ρ · v²)
Cavitation tendency for pumps, propellers, and hydraulic turbines.
Calculate →Eckert Number
Ec = v² / (cp · ΔT)
Kinetic energy vs enthalpy for high-velocity flow with viscous dissipation.
Calculate →Euler Number
Eu = Δp / (ρ · v²)
Pressure drop vs inertia for pipe flow and turbomachinery analysis.
Calculate →Fourier Number
Fo = α · t / L²
Dimensionless time for transient conduction heat transfer.
Calculate →Knudsen Number
Kn = λ / L
Continuum vs molecular flow regime for rarefied gas and microfluidic analysis.
Calculate →Lewis Number
Le = α / D
Thermal vs mass diffusivity for coupled heat-and-mass transfer.
Calculate →Mach Number
Ma = v / a
Flow speed vs local sound speed for compressible flow analysis.
Calculate →Nusselt Number
Nu = h · L / k
Convective vs conductive heat transfer for boundary-layer analysis.
Calculate →Peclet Number
Pe = v · L / α (= Re · Pr)
Advective vs diffusive transport for forced-convection analysis.
Calculate →Prandtl Design
Pr = ν / α
Momentum vs thermal diffusivity for boundary-layer prediction.
Calculate →Schmidt Number
Sc = ν / D
Momentum vs mass diffusivity for boundary-layer mass-transfer analysis.
Calculate →Sherwood Number
Sh = k_m · L / D
Convective vs diffusive mass transfer for boundary-layer analysis.
Calculate →Weber Number
We = ρ · v² · L / σ
Inertia vs surface tension for droplet, spray, and free-surface flow analysis.
Calculate →Calculators for the dimensionless numbers that drive fluid-mechanics and heat-transfer scaling: Reynolds, Froude, Prandtl, Nusselt, Mach, Weber, and similar.
When to use these calculators
Used in fluid mechanics, heat transfer, and aerodynamics — particularly for scaling experimental results from lab models to full-size systems.
Frequently Asked Questions
- How does the calculator show its work?
- Each calculator displays the substituted arithmetic step-by-step below the solution, so the user can verify the math by hand if needed. The 'Copy result' button captures the full formula → substitution → answer block.
- Are the formulas cross-verified?
- Every calculator's math has been cross-verified against textbook references and round-trip consistency tests (solve A from B, then solve B from A — the result must match the input). Spot-checks against Wolfram Alpha confirm the precision.
- How do I switch between solving for different variables?
- Most calculators in this category support multiple solve-for modes. Pick the unknown variable from the pill-toggle (or equation-card group) above the input fields, then enter the known values. The calculator auto-computes as you type.