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Wien’s law calculator

A-level Thermal physics and gases

The peak wavelength of black-body radiation is inversely proportional to the temperature.

λmax T = b

This free calculator is for A-level physics. Choose the quantity you want to find, enter the other values with their units, and it shows the working in the layout used in exams, with the answer to the number of significant figures you choose. The values shown are an example. Change them to your own.

Quantity to find

5.00 × 10−7 m
m K

Working

  1. Write the equation
    λmax T = b
  2. Rearrange to make λmax the subject
    λmax = b / T
  3. Constants used
    b = 0.0029 m K
  4. Substitute the values
    λmax = 0.0029 ÷ 5800
  5. Calculate
    λmax = 5 × 10−7 m
  6. Give the answer to 3 significant figures
    λmax = 5.00 × 10−7 m

Worked example

Find λmax, the peak wavelength. Given: temperature T = 5800 K; Wien constant b = 0.0029 m K.

  1. Write the equation
    λmax T = b
  2. Rearrange to make λmax the subject
    λmax = b / T
  3. Constants used
    b = 0.0029 m K
  4. Substitute the values
    λmax = 0.0029 ÷ 5800
  5. Calculate
    λmax = 5 × 10−7 m
  6. Give the answer to 3 significant figures
    λmax = 5.00 × 10−7 m

Symbols and units

SymbolQuantitySI unit
λmaxPeak wavelengthm
bWien constant (constant)m K
TTemperatureK

Wien’s law: rearranged

  • To find peak wavelength: λmax = b / T
  • To find temperature: T = b / λmax

Exam tip

A hotter object has a shorter peak wavelength. Use kelvin.

Common questions

What is the formula for wien’s law?

The equation is λmax T = b, where λmax is the peak wavelength (m); T is the temperature (K); b is the Wien constant (m K).

What units should I use for wien’s law?

In SI units: peak wavelength in m, Wien constant in m K, temperature in K. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.

How do I rearrange λmax T = b?

Rearranging gives these forms: to find peak wavelength: λmax = b / T. to find temperature: T = b / λmax.

Practise wien’s law questions

Press the button for a question with random numbers. Work it out on paper first, then type your answer.

Related

More thermal physics and gases equations: Specific heat capacity, Specific latent heat, Ideal gas equation, Boyle’s law, Gas equation with molecules, Mean kinetic energy of a gas atom, Stefan–Boltzmann law. See the full list on the a-level physics equation calculator page.