Biot Number Calculator

About this calculator

The Biot number (Bi) is a dimensionless ratio used in transient heat transfer: Bi = h·Lc/k, where h is the convective heat transfer coefficient at the surface, Lc is a characteristic length (typically volume/surface area), and k is the thermal conductivity of the solid. It compares how quickly heat moves through the material's interior to how quickly it's carried away at the surface.

When Bi < 0.1, temperature within the object stays nearly uniform as it heats or cools, which justifies the much simpler “lumped capacitance” model that ignores internal temperature gradients entirely. This calculator checks that condition for you, which is why it's a standard first step for mechanical and chemical engineers analyzing quenching, heat treatment, and cooling problems before deciding whether a full conduction analysis is even necessary.