Wien's Displacement Law Calculator: Peak Wavelength = b / T

The colour a hot object glows, from its temperature.

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

  • \lambda_{max} = \frac{b}{T}
  • T = \frac{b}{\lambda_{max}}

Worked example

With the default numbers in the calculator above:

  1. The formula, arranged to find the peak wavelength: peak wavelength = (2.898e-3) / (absolute temperature)
  2. Put the values in (every value in its SI unit): peak wavelength = (2.898e-3) / (5778)
  3. The answer: peak wavelength: 5.01518e-7 m
  4. The same answer in other units: 501.518 nm; 0.501518 micrometres

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

A second worked example

A different case, with these numbers: What do you want to find? Absolute temperature; Peak wavelength (leave it as it is if this is what you are finding) 5.0148E-7 m.

  1. The formula, arranged to find the absolute temperature: absolute temperature = (2.898e-3) / (peak wavelength)
  2. Put the values in (every value in its SI unit): absolute temperature = (2.898e-3) / (5.0148e-7)
  3. The answer: absolute temperature: 5778.44 K

Common questions

What is Wien's law?

The wavelength at which a hot object radiates the most is inversely proportional to its absolute temperature.

What is Wien's constant?

2.898 millimetre kelvin, or 2.898e-3 metre kelvin.

How do I find the temperature of a star?

Divide Wien's constant by the wavelength of the strongest radiation.

Related calculators

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

Further reading: Any physics text (blackbody radiation). Constant from the 2019 SI values.

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