Diffraction Calculator — Grating & Single Slit Angles
Find the angle at which light diffracts through a grating or single slit — enter wavelength, spacing, and order to get the diffraction angle instantly.
Diffraction type
nm
μm
sin θ = 0.32934
- 1
Wavelength in μm
550 nm ÷ 1000 = 0.55 - 2
sin θ = m × λ / d
1 × 0.55 ÷ 1.67 = 0.32934Grating equation: constructive interference at this ratio. - 3
Angle θ = arcsin(sin θ)
arcsin(0.32934) = 19.229
How does this calculator work?
The diffraction grating equation d·sin θ = mλ gives the angle θ for order m when light of wavelength λ hits a grating of spacing d. For a single slit, a·sin θ = mλ gives the m-th minimum. Enter wavelength (nm), spacing (μm), and order to get the diffraction angle in degrees.
Formula
How this is calculated
A diffraction grating separates light by wavelength because constructive interference occurs only where the path difference between adjacent slits equals a whole number of wavelengths. The grating equation d·sin θ = mλ relates the grating spacing d (μm), the order of diffraction m (1, 2, 3 …), the wavelength λ (nm), and the angle θ at which that order appears. For a fixed d, longer wavelengths diffract more, producing colour separation in white light.
For a single slit, destructive interference (minima) occurs where the slit width a satisfies a·sin θ = mλ. The first minimum (m = 1) defines the half-angle of the central bright maximum; doubling it gives the full width of the central lobe. Wider slits produce narrower diffraction patterns; narrower slits spread light more broadly — the classic trade-off between resolution and diffraction.
The calculator assumes monochromatic, coherent, far-field (Fraunhofer) diffraction, a planar wavefront, and that the grating is used in transmission. For angles approaching 90°, the small-angle approximation sin θ ≈ θ breaks down, and the full arcsin formula used here gives the correct result. Orders where mλ > d cannot physically exist (sin θ > 1) and are flagged as invalid.
Frequently asked questions
The highest order is the largest integer m satisfying mλ ≤ d. For example, a 600-lines/mm grating (d ≈ 1.67 μm) illuminated at λ = 550 nm supports at most m = floor(1670/550) = 3 orders.
Diffraction spreads waves around obstacles. A narrower slit means fewer path differences cancel out, so the central bright region fans out more. The half-angle of the central maximum is arcsin(λ/a), which grows as a shrinks.
Angular dispersion dθ/dλ ≈ m/(d·cos θ) measures how quickly the angle changes with wavelength. High dispersion means wavelengths close together are resolved at wide angles — important for spectrometers to distinguish spectral lines.
Also known as
TG we-Calculate Editorial Team. (2026). Diffraction Calculator — Grating & Single Slit Angles [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/diffraction-calculator
TG we-Calculate Editorial Team. "Diffraction Calculator — Grating & Single Slit Angles." TG we-Calculate. 2026. https://we-calculate.com/calculator/diffraction-calculator.
TG we-Calculate Editorial Team, "Diffraction Calculator — Grating & Single Slit Angles," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/diffraction-calculator
@misc{wecalculate_diffraction_calculator, title = {Diffraction Calculator — Grating & Single Slit Angles}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/diffraction-calculator}}, year = {2026}, note = {TG we-Calculate} }
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