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Diffraction Grating Calculator

Work out diffraction grating instantly with clear inputs, formula shown and shareable results.

About Diffraction Grating Calculator

A grating sends light of wavelength lambda to angles where d sin(theta) = m.lambda. A 600 line/mm grating has d = 1.667 microns, so 550 nm light appears at 19.25 degrees in first order. Higher orders sit at larger angles until sin(theta) would exceed one, which caps the observable orders at three here.

Formulas

Grating equation

d sin(theta) = m lambda

Grating spacing

d = 1 / lines per metre

Worked example

With the default values below, Diffraction Grating Calculator returns Diffraction Angle of 19.269. Change any input above and every figure here is recalculated in your browser.

Inputs used

Grating line densityminimum 0 lines/mm
600 lines/mm
Wavelengthminimum 0 nm
550 nm
Diffraction order mminimum 1
1

Results

Diffraction Angle
19.269 deg
Grating Spacing d
1.6667 × 10⁻⁶ m
Highest Observable Order
3
Angular Dispersion
6.3561 × 10⁵ rad/m

Step by step

  1. 1Values used
  2. 2Grating equation
  3. 3Grating spacing
  4. 4Diffraction Angle= 19.269 deg
  5. 5Grating Spacing d= 0.0000 m
  6. 6Highest Observable Order= 3
  7. 7Angular Dispersion= 635,606.0000 rad/m

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why do gratings beat prisms for spectroscopy?

Because dispersion is far larger and is calculable from geometry alone, and higher orders can be used to multiply resolution.

What limits the number of orders?

The requirement that sin(theta) stays under one, so m cannot exceed d/lambda. Coarse gratings show many orders, fine ones only a few.

Related Calculators

Diffraction Grating Calculator – Calculate Diffraction Angle