Miller Indices Calculator

This Miller Indices Calculator make your calculations so easy and quick by just providing the required inputs. To find the exact result in less time, you need to enter the miller index like h,k,l of the material you choose and hit the calculate button.

Miller Indices Calculator from Intercepts: Are you wondering how miller indices calculations are done with in seconds? Here is the perfect solution with us ie., free miller indices calculator online. This tool will make you learn and understand how do you calculate miller indices manually with some miller indices example problems. Also, you gonna see miller indices definition formula examples, etc from the below modules.

What is Miller Index? Miller Indices Definition

A representative vector drawing for the orientation of an atomic plane in a crystal lattice is called miller indices. Also, it is determined as the reciprocals of the fractional intercepts that plane come across the crystallographic axes.

The notation used for indicating the miller indices is 'hkl' and basically it indicate the plane which is closest to the origin without passing through it. Based on the reprsentation the notation of miller indices (hkl) gets changed such as:








Family of planes




Family of directions

Go through the below modules and know how miller indices for plane calculated with examples.

How to Calculate Miller Indices Manually?

We can determine the miller indices with the help of intersection of the plane with a set of crystallographic axes.

The manual process of calculating miller indices planes is explained in the below steps. Take a look at the following steps and make your calculations at a faster pace:

  • In the initial step, you need to determine the intercepts of the plane by the axes x, y, z.
  • Next, define the intercepts in fractional co-ordinates
  • Now, take the reciprocals of the intercepts to get the miller indices.
  • As the next process, reduce to lowest intergers in the same ration.
  • Finally, enclose the result in parentheses.

Note: Whenever you get the negatives just represent them with a bar before the number. The family of planes is indicated using the curly brackets.

Solved Miller Indices Examples


Calculate the miller indices for the given x, y, z intercepts: 2, 3, 1?


Given intercepts are 2, 3, 1
Now, take the reciprocals which are 1/2, 1/3, 1/1
As the next step, just do fractions by multiplying with 6 and we get: 3, 2, 6
Finally, check the miller indices need to reduce to smallest terms are not. Here, it is already reduced.
Hence, the miller indices (hkl) are 3, 2, 6.

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FAQs on How to Draw Miller Indices using Miller Index Calculator

1. What the features of miller indices

A few crucial features of miller indices are listed here:

  • Miller indices not only determine particular plane but also a set of parallel planes.
  • A plane parallel to one of the coordinate axes has a intercept of ∞.
  • The distance d between adjacent planes of a set of parallel planes of the indices (h k I) is written as d = a/ sqrt of h^2+k^2+l^2, where a is the cube edge.

2. How do you calculate Miller indices?

In order to calculate the miller indices of planes you need to follow the three basic steps which are explained in our page. So, check out the process and use the miller indices calculator for quick results.

3. What are the 7 types of crystals?

The seven crystal systems which are categorized based on relationships between lattice parameters are as cubic (or isometric), tetragonal, orthorhombic, rhombohedral (or trigonal), hexagonal, monoclinic, and triclinic.