Bragg's Law Calculator
Diffractometers report each peak position as 2θ, the angle on the scan axis. Bragg's law works with θ, so this page halves the 2θ value you enter before computing the lattice spacing d. If you already have θ, switch the angle toggle and the number is used as θ directly.
Bragg's law links the order n, the X-ray wavelength λ, the plane spacing d and the angle θ: nλ = 2d sin θ. Solving for d gives d = nλ / (2 sin θ), shown here in Å and in nm.
d-spacing from a peak position
nλ = 2d sin θ: —
How to use the calculator
- Leave the order n at 1 unless you are working with a higher-order reflection; it accepts integers from 1 to 20.
- Choose the wavelength: Cu Kα1 (1.5406 Å), Mo Kα (0.7107 Å), or Custom and type λ in Å.
- Keep the angle toggle on 2θ for a value read from the diffractometer, or switch to θ if you already halved it.
- Type the peak position in degrees. The d-spacing in Å and nm appears as you type, together with θ, sin θ and the Bragg equation filled in.
Silicon powder check
| hkl | Published 2θ (°) | d from this page (Å) |
|---|---|---|
| 111 | 28.441 | 3.1357 |
| 220 | 47.301 | 1.9202 |
| 311 | 56.120 | 1.6375 |
Source: Black, Mendenhall, Henins, Filliben, Cline, Certification of SRM 640f Line Position and Line Shape Standard for Powder Diffraction, Powder Diffraction 35(3), 2020. Silicon lattice parameter a = 0.5431144 nm at 22.5 °C; Cu Kα wavelength 0.15405929 nm; the 2θ values are information values, not certified. d computed here with 1.5405929 Å as Custom.
Worked case: silicon 111
With Custom λ = 1.5405929 Å and n = 1, the peak at 2θ = 28.441° gives θ = 28.441 / 2 = 14.2205° and sin θ = 0.24565.
d = 1 × 1.5405929 / (2 × 0.24565) = 3.1357 Å = 0.31357 nm.
Cubic cross-check: d = a / √(h² + k² + l²) with a = 5.431144 Å gives 5.431144 / √3 = 3.1357 Å for 111 and 5.431144 / √8 = 1.9202 Å for 220, within 0.0001 Å of the table.
Frequently asked questions
Why does the calculator ask for 2θ?
Diffractometers report peak positions as 2θ. Bragg's law uses θ, so in 2θ mode the page halves the value before computing d. If you already have θ, switch the toggle to θ.
Which wavelength should I choose?
Choose Cu Kα1 (1.5406 Å) or Mo Kα (0.7107 Å) to match your X-ray source, or pick Custom and type the wavelength in Å, from 0.01 to 10 Å.
What does the order n do?
n is the diffraction order in nλ = 2d sin θ. For the same peak, d grows in proportion to n, so order 2 gives twice the d of order 1. Enter an integer from 1 to 20.
What happens if 2θ is outside 0 to 180 degrees?
The page shows an error and no number. 2θ must be above 0 and below 180 degrees, and θ must be above 0 and below 90 degrees.
Disclaimer: This calculator gives a preliminary estimate only. Verify results against the governing standard or with a qualified professional before relying on them.