Prandtl Number Calculator

How to use this Prandtl number calculator

What this calculator does. It estimates the Prandtl number, a dimensionless transport-property ratio used in heat-transfer and fluid-flow work. Pr compares momentum diffusivity with thermal diffusivity: Pr = ν/α. In property mode the same identity is evaluated as Pr = μCₚ/k, with dynamic viscosity converted from mPa·s to Pa·s. The result helps characterize the relative rates at which velocity disturbances and temperature disturbances diffuse through a fluid. It does not, by itself, calculate a heat-transfer coefficient, Nusselt number, boundary-layer thickness, or a complete convection solution. For context, the NIST discussion of gas transport-property measurements explicitly connects viscosity, heat capacity, thermal conductivity, and Prandtl number.

When to use it. Use this calculator when checking fluid-property data for a convection correlation, comparing two operating temperatures after you obtain temperature-specific properties, converting a property set into ν and α, or validating a CFD or hand-calculation input. It is also useful for teaching because both equivalent definitions of Pr are available.

How to calculate. The calculator opens with a complete water demonstration, so finite results and an example Excel workbook are available immediately.

1. Choose Fluid properties or Diffusivities under Calculation method. The first route uses μ, Cₚ and k; the second uses ν and α directly.
2. In property mode, keep a Fluid preset or choose Custom and replace the property values. In diffusivity mode, enter both diffusivities in mm²/s. Results update live after every valid change.
3. Read Prandtl number (Pr) first, then use Momentum diffusivity (ν) and Thermal diffusivity (α) to see the two transport rates behind the ratio. The Calculation details table repeats those canonical values with their roles.
4. Select Download Excel to export the current validated inputs and outputs to an XLSX workbook. Reset clears the demonstration and all data fields; after Reset, Excel export stays disabled until you enter a complete valid state again.

Input guide. Calculation method is required and accepts one of two choices; changing it changes which input set is authoritative. Fluid preset is a property-mode convenience: Water fills ρ = 997 kg/m³, μ = 1.002 mPa·s, Cₚ = 4184 J/(kg·K), and k = 0.607 W/(m·K); editing a property switches the preset to Custom. Density (ρ) is a required positive decimal in kg/m³. It cancels from Pr = μCₚ/k but is needed to derive ν and α, so an incorrect density can leave Pr unchanged while corrupting both diffusivities. Dynamic viscosity (μ) is required, positive, and entered in mPa·s; entering a Pa·s value without converting is a common factor-of-1000 error. Specific heat (Cₚ) is required, positive, and entered in J/(kg·K); use constant-pressure specific heat for this standard definition. Thermal conductivity (k) is required, positive, and entered in W/(m·K); zero is invalid because it appears in the denominator. In diffusivity mode, Momentum diffusivity (ν) and Thermal diffusivity (α) are both required positive decimals in mm²/s; values such as 1.005 and 0.1455 are realistic for the startup water example. All numeric fields use a decimal point, do not accept scientific notation or comma decimal separators, and reject zero or negative values.

Output guide. Prandtl number (Pr) is an exact identity from the entered property values, displayed as a dimensionless decimal. Values below 1 mean thermal diffusivity exceeds momentum diffusivity; values above 1 mean momentum diffusivity is larger; a value near 1 means the two diffusivities are similar in scale. Momentum diffusivity (ν) is shown in m²/s and equals μ/ρ when property mode is used. Thermal diffusivity (α) is shown in m²/s and equals k/(ρCₚ). In direct diffusivity mode those same outputs are unit-converted versions of your inputs. The summary pills, cards, table, and workbook all read from the same model, so they are alternative presentations rather than separate calculations.

Worked example. For the startup water data, μ = 1.002 mPa·s = 0.001002 Pa·s, Cₚ = 4184 J/(kg·K), and k = 0.607 W/(m·K). Therefore Pr = (0.001002 × 4184) / 0.607 = 6.907. With ρ = 997 kg/m³, ν = 0.001002/997 = 1.005 × 10⁻⁶ m²/s, while α = 0.607/(997 × 4184) = 1.455 × 10⁻⁷ m²/s. Their ratio gives the same 6.907. This cross-check is useful because Pr should be identical whether calculated from μCₚ/k or ν/α.

Learn more. For additional property context, the NIST thermophysical-property database description lists viscosity, thermal conductivity, heat capacity, kinematic viscosity, and Prandtl number among its supported properties. For an engineering application example, NASA's CFD variable definitions include the freestream Prandtl number as a model parameter.