# Bragg's Law Calculator

This Bragg's law calculator is the perfect tool to understand how an incident X-ray on a crystal relates to the wavelength of the reflected radiation and the distance between atoms in the crystal.

This tool is also called d-spacing calculator because you can easily find the interplanar spacing with it.

Keep reading to learn more about Bragg's diffraction law and Bragg's equation.

## What does Bragg's difraction law tell us?

Bragg's law describes the condition for when the reflected radiation from X-rays incident on a crystal produces maximum constructive interference.

Two parallel X-rays interacting with different layers of the crystals separated by $d$ travel different lengths.

If this *path length difference* is equal to an **integer multiple of the X-rays' wavelength**, then both reflected waves interfere **constructively**. Otherwise, they interfere **destructively**.

The result is that we can observe *peaks in the intensity of the scattered radiation* at some angles. **Bragg's equation** expresses the relationship between these angles, wavelength, and distance between planes.

🙋 If you're already familiar with these concepts, **feel free to start working with our Bragg's law calculator!** Input *any three parameters*, and our tool will automatically complete the missing one.

## Bragg's equation

The extra distance that the beam in the lower layer travels is related to the distance between layers of molecules and angle of incidence by:

where:

- $d$ is the interplanar spacing or distance between layers of molecules.
- $\theta$ is the angle of incidence.
*Note: we will use both of these parameters in Bragg's equation*.

As we said, **maximum constructive interference will appear when this distance equals an integer multiple of the wavelength**.

We summarize this condition in Bragg's equation:

where:

- $n$ is called the
**diffraction order**; and - $\lambda$ is the wavelength of the X-ray.

## How to use this Bragg's law calculator

Our Bragg's law calculator is straightforward:

- Input the
**wavelength**$\lambda$. - Input the
**interplanar distance**. - The diffraction order tells us how many times $\lambda$ fits within the space between molecules. Its
**maximum value**is:`(2 * d) / λ`

. Therefore, we should input*every integer equal to or less than this maximum*within this field (one at a time). - For each diffraction order, the calculator will output a different angle at which the scattered radiation's intensity will be maximum.

Alternatively, if we know the diffraction order, we can use this tool as a **d-spacing calculator** by filling every field and letting it complete the interplanar distance automatically!