Prandtl Number Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/6/2026
The Prandtl number is calculated with Pr = cp × μ ÷ k, where cp is the fluid's specific heat, μ its dynamic viscosity, and k its thermal conductivity. For air at room temperature, it is about 0.70 — a widely documented value in heat transfer.
Explanation
The Prandtl number compares two different diffusion mechanisms within the same fluid: the diffusion of momentum (governed by viscosity) and the diffusion of heat (governed by thermal conductivity). Unlike our pipe diameter and flow rate calculator or our aerodynamic drag force calculator, which both depend on a velocity and a characteristic length specific to a given flow, the Prandtl number is an intrinsic property of the fluid itself at a given temperature: it doesn't depend on any geometry or flow velocity. A low Prandtl number (well below 1, as for liquid metals) means heat diffuses much faster than momentum in that fluid; a high Prandtl number (well above 1, as for viscous oils) means the opposite. Gases like air have a Prandtl number close to 0.7, while water is around 7 at room temperature, and some motor oils can exceed 1000: this wide range of values explains why the Prandtl number is central in thermal engineering for predicting the relative thickness of the velocity and temperature boundary layers in a flow, a key factor in the design of heat exchangers.
Example: air at room temperature
Inputs
Specific heat: 1005 J/(kg·K). Dynamic viscosity: 1.81×10⁻⁵ Pa·s. Thermal conductivity: 0.026 W/(m·K).
Calculation
Pr = (1005 × 0.0000181) ÷ 0.026 = 0.0181905 ÷ 0.026 ≈ 0.6996.
Result
Air at room temperature has a Prandtl number of about 0.70, a widely documented value in heat transfer.
Frequently asked questions
Why doesn't the Prandtl number depend on any flow velocity?
Because it only compares two physical properties of the fluid itself (its viscosity and thermal conductivity, weighted by its specific heat) — unlike flow-specific numbers, which describe a particular flow and therefore necessarily include a velocity and a characteristic length. The Prandtl number stays the same regardless of the speed at which this fluid flows, as long as its temperature doesn't change.
Why do liquid metals have a very low Prandtl number?
Because liquid metals, thanks to their free electrons, conduct heat exceptionally efficiently (very high thermal conductivity k) while having relatively modest viscosity. This imbalance gives a Prandtl number often below 0.01, meaning heat diffuses there much faster than momentum — a property exploited in certain nuclear reactors cooled with liquid sodium.
What is the Prandtl number actually used for in engineering?
It allows comparing the relative thickness of two boundary layers that develop along a heated wall: the velocity boundary layer (where viscosity slows the flow) and the thermal boundary layer (where heat propagates). This comparison is essential for sizing heat exchangers, radiators, or cooling systems, where the efficiency of heat transfer depends directly on this ratio.