What is the grating equation?

d · sin(θ) = m · λ, where d is the grating spacing (distance between adjacent slits), m is the integer diffraction order, λ is the wavelength, and θ is the diffraction angle measured from the normal.

How do I convert lines per mm to grating spacing?

Divide 1 mm by the number of lines: d = 1,000,000 nm / (lines per mm). For example, 600 lines/mm gives d ≈ 1666.7 nm.

Why does the calculator say "no solution" for some inputs?

If m·λ > d, then sin(θ) would exceed 1, which is physically impossible. The diffracted beam does not exist for that combination of order and wavelength.

What is the zeroth order (m = 0)?

The zeroth-order beam passes straight through (θ = 0°) regardless of wavelength. It is the undiffracted beam and carries no spectral information.

Does this assume normal incidence?

Yes. The standard grating equation d · sin(θ) = m · λ assumes the incoming light hits the grating at 90° (normal incidence, angle of incidence = 0°).

Diffraction Grating Calculator

Name: Diffraction Grating Calculator
Availability: InStock
Author: Nham Vu

Enter grating spacing (or lines/mm), diffraction order, and wavelength to find diffraction angles — or solve for any missing variable.

Inputs

Solve for

Grating Spacing

d in nm

lines / mm

Diffraction Order (m) Integer; 0 = straight-through

Wavelength λ (nm) Visible range: 380–700 nm

Results

Fill in the inputs and click Calculate

Summary

Enter grating spacing (or lines/mm), diffraction order, and wavelength to find diffraction angles — or solve for any missing variable.

How it works

Enter the grating spacing d in nanometers, or the lines-per-mm value (the tool converts automatically).
Select the diffraction order m (0, ±1, ±2, …).
Enter the incident wavelength λ in nanometers.
Click Calculate to get the diffraction angle θ for that order.
Switch to "Solve for λ" mode to find the wavelength when you know the angle.
The visible-spectrum bar shows where the wavelength falls in the 380–700 nm range.

Use cases

Predict the angle at which a laser beam will appear for a given diffraction order.
Identify an unknown wavelength by measuring the diffraction angle experimentally.
Design spectroscopy setups by comparing first-order and second-order separations.
Verify grating specifications when the lines/mm rating is known.
Teach and visualize the grating equation in optics coursework.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu