What is the diffraction grating equation?

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

How do I convert lines per mm to grating spacing d?

Grating spacing d = 1 / (lines per mm), giving d in mm. For example, a 600 lines/mm grating has d = 1/600 mm ≈ 1666.7 nm. The calculator accepts lines/mm and converts automatically.

Can the diffraction order m be negative?

Yes. Negative orders exist on the opposite side of the grating normal from positive orders. m = 0 is the straight-through (zero-order) beam, m = ±1 are the first-order beams, and so on. This calculator accepts any integer m.

What happens when sin(θ) would exceed 1?

If the calculated sin(θ) > 1, the requested combination of m, λ, and d is physically impossible — that order does not exist for those parameters. The tool flags this with an error rather than returning a nonsense angle.

Is this the same as the Bragg equation used in X-ray diffraction?

They are related but not identical. Bragg's law (2d·sin(θ) = nλ) describes reflection from crystal planes at a glancing angle, while the optical grating equation describes transmission/reflection from ruled gratings at the angle from the normal. The physics differs, but both arise from constructive interference.

What units should I use?

Any consistent unit pair works (both λ and d in nm, or both in µm). Visible-light wavelengths are typically 380–700 nm, UV down to ~10 nm, and grating spacings range from ~300 nm (3000 lines/mm, deep-UV) to ~3.3 µm (300 lines/mm, IR). The calculator lets you choose nm or µm for λ and d.

Diffraction Grating Equation Calculator

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

Pick which variable to solve for, enter the other three, and instantly get the result from m·λ = d·sin(θ).

Grating Equation Solver

m · λ = d · sin(θ)

Solve for

Wavelength (λ)

Grating spacing (d)

Diffraction order (m)

Diffraction angle (θ)

deg

Select what to solve for, fill in the three known values, then click Calculate.

Summary

Pick which variable to solve for, enter the other three, and instantly get the result from m·λ = d·sin(θ).

How it works

Select which quantity you want to solve for: wavelength (λ), grating spacing (d), diffraction order (m), or angle (θ).
Enter values for the three known quantities in the input fields that appear.
Click Calculate — the tool rearranges the grating equation and computes the unknown.
Results include the derived value with its unit, plus a summary equation showing all four variables.
Use the unit toggles to switch between nm/mm/lines-per-mm as needed for your setup.

Use cases

Identify an unknown spectral line wavelength by measuring the diffraction angle experimentally.
Determine the grating spacing needed to resolve two wavelengths at a target angle.
Find which diffraction order a detected peak corresponds to in a spectrometer.
Calculate the angular position of a known wavelength before aligning an optical bench.
Cross-check grating manufacturer specs against measured diffraction angles.
Design monochromator exit slit positions for a given wavelength range.
Verify student lab measurements of sodium doublet lines with the D1/D2 wavelengths.

Frequently Asked Questions

Last updated: 2026-07-01 · Reviewed by Nham Vu