Diffraction Grating Calculator

The grating equation relates line spacing, wavelength, and order to the diffraction angle. A bright fringe forms where the path difference equals a whole number of wavelengths.

If the order and wavelength would require a sine greater than one, that fringe cannot physically form, so no angle exists.

Finer gratings with more lines per millimeter spread the colors over wider angles for the same wavelength.

No. It accepts any wavelength and any diffraction order, so X-ray or large-order inputs are allowed. The tool applies no visible-range limit and only flags a case as physically impossible when the required sine would exceed one. The visible band of roughly 380 to 700 nm is simply the most common use.

The angular dispersion is dθ ÷ dλ = m ÷ (d cosθ), so the spread grows with higher orders m and with denser gratings (smaller d), and it increases as the angle θ itself grows toward 90 degrees.

Common laboratory gratings run from about 300 to 1,200 lines/mm, with 600 lines/mm a frequent all-purpose choice for visible spectroscopy. A standard CD acts as a reflection grating at roughly 625 lines/mm (1.6 micrometre track pitch), and a DVD at about 1,350 lines/mm. Denser gratings spread the spectrum over wider angles and give finer resolution, but push higher orders past 90 degrees where they no longer appear.