Read a star by its colour.

Slide the peak toward the blue.

Drag the temperature and watch the black-body curve: its peak slides to shorter wavelengths as the star heats up, exactly as Wien's law demands, while the whole curve climbs because the power per unit area grows as T⁴. Add the radius to read off the luminosity L = 4πσr²T⁴.

Two laws, one radius.

The marks come from the two laws and the way they combine.

• Wien's displacement law: λₘₐₓT = 2.90 × 10⁻³ m K. The peak wavelength is inversely proportional to the absolute temperature, so hotter stars look bluer and cooler stars look redder.
• Stefan-Boltzmann law: L = 4πσr²T⁴, where σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴. The luminosity rises with the surface area (4πr²) and, very steeply, with the fourth power of temperature.
• Estimating the radius: rearrange to r = √(L / 4πσT⁴). Find T from the colour (Wien) and L from a standard candle, and the radius follows.
• Why it works: a star is close enough to a perfect black-body radiator that these laws give good estimates of temperature, size and even classification.