X-rays bounce off the atomic layers inside a crystal the way light bounces off a CD's grooves — and the angles where the reflections line up reveal the spacing between atoms. That is Bragg's law, the founding equation of crystallography: nλ = 2d sin θ. In plain words, the path difference between X-rays reflecting off neighboring atomic planes (2d sin θ) must equal a whole number of wavelengths (nλ) for a bright spot to appear.

From those bright spots, scientists reverse-engineer the crystal: table salt's cubic lattice, diamond's tetrahedral network, and the double helix of DNA — famously photographed as "Photo 51" — were all decoded this way. Pharmaceutical companies use the same technique to verify that every batch of a drug crystallized in the correct form, since the wrong crystal shape can make a pill dissolve too fast or too slow.

This calculator handles the path-difference multiplication at Bragg's law's core. Type twice the interplanar spacing (2d) in the Variable A box and the sine of the reflection angle in the Variable B box — for example, sin 15° ≈ 0.2588. The Result box gives the path difference 2d sin θ. Divide it by your X-ray wavelength λ to find n, the reflection order — whole numbers confirm a genuine crystal reflection.

With the pre-filled defaults — Variable A 10, Variable B 5 — the Crystallography Calculator returns Result 50.0000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.