Wien's Law Calculator

What the Wien's law calculator does

Every warm object glows, and the colour of that glow depends on its temperature. This calculator applies Wien's law, which connects a body's temperature to the peak of the light it radiates. Give it any one of the temperature, the peak wavelength, or the peak frequency, and it finds the other two.

Below is what Wien's law is, the equation behind it, why hot things shift colour as they heat, and a worked example.

How to use it

1. Choose what you are entering: the black body temperature, the peak wavelength, or the peak frequency.
2. Enter that one value, with its unit.
3. Press Calculate to get the other two, or Reset to clear it.

What Wien's law is

Any object warmer than absolute zero gives off thermal radiation, a spread of electromagnetic waves across many wavelengths. That spread is not even: it peaks at one particular wavelength where the object radiates most strongly. Wien's law, also called Wien's displacement law, tells you where that peak falls, and its answer is simple: the hotter the object, the shorter the wavelength of the peak.

This is the rule behind the glow of hot things. A body radiates across a whole band of wavelengths, but the location of the brightest part of that band slides toward shorter wavelengths as the temperature climbs. An idealised perfect radiator is called a black body, and Wien's law describes its peak exactly, while real objects follow it closely. The law connects something you can see, the colour of a glow, to something you often want to know, the temperature, which is why it is a cornerstone of thermal physics and astronomy.

The equation it uses

Wien's law relates the peak wavelength to the absolute temperature through a fixed constant:

λ_peak = b ÷ T

Here λ_peak is the wavelength of strongest emission, T is the absolute temperature, and b is Wien's displacement constant, about 2.898 × 10⁻³ metre-kelvin. The relationship is an inverse one: because the temperature sits in the denominator, doubling the temperature halves the peak wavelength. The calculator uses this to convert between temperature and peak wavelength in either direction, and works internally in absolute temperature so the physics stays correct whatever scale you enter.

Why hot things change colour

Wien's law explains the familiar sequence a heated object runs through. A piece of metal warming in a fire first glows a dull red, then brightens to orange, then yellow, and if it could be pushed hot enough, to white and even bluish. Each step is the peak wavelength sliding shorter as the temperature rises, moving from the red end of the visible spectrum toward the blue.

The same logic reads the temperatures of the stars. Cool stars glow red, because their peak sits at long wavelengths; hotter stars shine white or blue, with their peak pushed to short wavelengths. Our own Sun, at around 5,800 kelvin, peaks in the middle of the visible range, which is no accident, since our eyes evolved under its light. Cooler objects, like a human body or a warm room, peak in the infrared, well beyond what the eye can see, which is why we do not glow visibly but can be seen by an infrared camera. Wien's law ties all of this together, turning colour into a thermometer.

The frequency form

The same idea can be cast in terms of frequency instead of wavelength, and the calculator offers both. In the frequency version, the peak frequency rises in direct proportion to the temperature, the hotter the body, the higher the frequency of its peak, using its own constant of about 5.879 × 10⁹ hertz per kelvin.

It is worth knowing a subtlety here. The wavelength at which the radiation peaks and the frequency at which it peaks are not simply related by the speed of light, as you might expect, because the spectrum has a slightly different shape depending on whether you plot it against wavelength or against frequency. The two peaks genuinely sit at different points, which is why the calculator uses a separate constant for each form rather than converting one into the other. Both are correct ways to describe where a body radiates most strongly.

Units and precision

The calculator works in SI units underneath, with temperature in kelvin, wavelength in metres, and frequency in hertz, while the menus let you enter and read values in many other units, from angstroms and nanometres to kilohertz and terahertz. Temperature, being absolute here, converts cleanly between Celsius, Fahrenheit, and kelvin, and the calculator checks that it stays above absolute zero. The relationship is exact for an ideal black body. Results carry several significant figures.

A worked example

Take the Sun, whose surface temperature is about 5,778 kelvin.

Its peak wavelength is λ_peak = b ÷ T = (2.898 × 10⁻³) ÷ 5,778 ≈ 5.0 × 10⁻⁷ metres, which is about 500 nanometres, in the green-blue part of the visible spectrum. By contrast, a human body at about 310 kelvin peaks near 9.4 micrometres, deep in the infrared, far beyond visible light, which is exactly why body heat shows up on a thermal camera but not to the naked eye.

Questions people ask

What is Wien's law formula?

The peak wavelength equals Wien's constant divided by the absolute temperature, λ_peak = b/T, with b about 2.898 × 10⁻³ metre-kelvin.

Why do hotter objects glow bluer?

Because Wien's law is inverse: a higher temperature gives a shorter peak wavelength. As an object heats, its peak emission shifts from red toward blue, so the glow changes colour from red to white to bluish.

How does Wien's law apply to stars?

A star's colour reveals its temperature. Red stars are cooler, with peaks at long wavelengths; blue-white stars are hotter, with peaks at short wavelengths. The Sun, peaking in visible light, sits in between.

Why are the wavelength peak and frequency peak different?

The radiation spectrum has a slightly different shape plotted against wavelength versus frequency, so the two peaks fall at different points and are not related by the speed of light. The calculator uses a separate constant for each.

References

A quick note on where the physics comes from. Wien's displacement law and its role in blackbody radiation are standard physics, set out in OpenStax's University Physics and in Georgia State University's HyperPhysics. The value of Wien's displacement constant follows the US National Institute of Standards and Technology. The HyperPhysics link is worth a quick click to confirm it lands where you expect.

1. OpenStax, University Physics Volume 3, Section 6.1, Blackbody Radiation. https://openstax.org/books/university-physics-volume-3/pages/6-1-blackbody-radiation
2. HyperPhysics, Wien's Displacement Law. http://hyperphysics.phy-astr.gsu.edu/hbase/wien.html
3. National Institute of Standards and Technology (NIST), Fundamental Physical Constants, Wien wavelength displacement law constant. https://physics.nist.gov/cgi-bin/cuu/Value?bwien