# Bragg’s Law Calculator

URL: https://speedycalculator.com/calculators/physics/braggs-law/
Last updated: 2026-10-30

> The Bragg's law calculator relates X-ray wavelength, the spacing of crystal planes, the diffraction order and the angle of incidence – solving for any one of them.

## Inputs

- Find
- Order n
- Wavelength λ (nm, Å, pm, m)
- Interplanar distance d (nm, Å, pm, m)
- Incidence angle θ (°, rad, arcmin, arcsec, mrad)

## Results

- Wavelength λ
- Interplanar distance d
- Angle θ

## Formula

```
n·λ = 2·d·sin θ
```

## Explanation

When X-rays reflect from layers of atoms in a crystal, they interfere constructively only at angles that satisfy Bragg's law. William and Lawrence Bragg used it in 1913 to determine crystal structures – later including DNA and proteins.

### How to use the Bragg's Law Calculator

- **Find**
- **Order n**
- **Wavelength λ**
- **Interplanar distance d**
- **Incidence angle θ**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Choose what to find and enter the other values. θ is the glancing angle between the beam and the crystal planes (not the normal).

### Inputs explained

FieldWhat to enterFindChoose one: Wavelength λ, Interplanar distance d, Angle θOrder nA numberWavelength λUnits: nm, Å, pm, mInterplanar distance dUnits: nm, Å, pm, mIncidence angle θUnits: °, rad, arcmin, arcsec, mrad

### What each result means

- **Wavelength λ** = 2×[Interplanar distance d]×sin(rad([Incidence angle θ]))÷[Order n]
- **Interplanar distance d** = [Order n]×[Wavelength λ]÷(2×sin(rad([Incidence angle θ])))
- **Angle θ** = deg(asin([Order n]×[Wavelength λ]÷(2×[Interplanar distance d])))

### Example values

How the main result changes when **Order n** changes and everything else stays at the example values above:

Order nWavelength λ (nm)10.15371.250.1231.50.102520.0769

## Worked example

Inputs — Find: Wavelength λ; Order n: 1; Interplanar distance d: 0.2 nm; Incidence angle θ: 22.6 °.

Results — **Wavelength λ = 0.153718 nm**.

## Key terms

- **Interplanar spacing**: Distance between parallel planes of atoms.

## FAQ

**What is Bragg's law used for?**
X-ray crystallography – finding atomic spacings and crystal structures.

**Why must the waves be X-rays?**
Their wavelengths (≈0.1 nm) match the spacing of atomic planes.

**What is the diffraction order?**
The number of whole wavelengths of path difference.

**What if nλ > 2d?**
No diffraction peak is possible for that order.


## Sources

- [OpenStax – University Physics Volume 3](https://openstax.org/details/books/university-physics-volume-3)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)
- [OpenStax – Chemistry 2e](https://openstax.org/details/books/chemistry-2e)