Bragg Law Calculator: X-ray Diffraction Angle, Plane Spacing and Wavelength

Bragg's law for X-ray diffraction.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose what to find.

Enter the order, and two of the spacing, the wavelength and the angle.

The calculator gives the result and the 2 theta angle.

Formulas used

  • n\lambda = 2d\sin\theta
  • \theta = \arcsin\left(\frac{n\lambda}{2d}\right)
  • d = \frac{n\lambda}{2\sin\theta}

Worked example

With the default numbers in the calculator above:

  1. Angle between the beam and the planes: 22.644 degrees
  2. Angle between the incoming and diffracted beams: 45.287 degrees

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want to find? The plane spacing d; Angle between the beam and the planes theta 22.6437 deg.

  1. Spacing between the planes: 0.2 nm

Common questions

What does Bragg's law say?

Waves reflected from neighbouring crystal planes add up only when the extra path length is a whole number of wavelengths. That gives sharp peaks at particular angles.

Is the angle measured from the plane or from the normal?

From the plane itself. The angle between the incoming and diffracted beams is twice the Bragg angle (2 theta).

Why is there sometimes no answer?

If n times the wavelength is bigger than 2 d, the sine would need to be above 1, so no reflection is possible.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any physics or materials science text (X-ray diffraction, Bragg's law).

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