Thermal Diffusivity Calculator: alpha = k / (rho cp)

How quickly a temperature change spreads through a material.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose which quantity you want to find.

Enter the other values in the units shown.

The calculator gives the answer with the formula, the substituted numbers, and the answer in other units.

Formulas used

  • \alpha = \frac{k}{\rho c_p}
  • k = \alpha\rho c_p

Worked example

With the default numbers in the calculator above:

  1. The formula, arranged to find the thermal diffusivity: thermal diffusivity = (thermal conductivity) / (density x specific heat)
  2. Put the values in (every value in its SI unit): thermal diffusivity = (50) / (7800 x 490)
  3. The answer: thermal diffusivity: 1.30822e-5 m2/s
  4. The same answer in other units: 13.0822 mm2/s

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

What is thermal diffusivity?

The thermal conductivity divided by the volumetric heat capacity. It tells you how quickly a temperature change moves through a solid.

What is the difference between conductivity and diffusivity?

Conductivity is how much heat flows for a temperature gradient. Diffusivity also includes how much heat the material stores, which slows down the change.

Which has the highest diffusivity?

Metals like copper and silver, and diamond. Insulators have very low values.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any heat transfer text (transient conduction).

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