Look for some papers written by John H. Scolfield of Oberlin College, he also has some excel template for doing calculations you are looking for

We have only the Bragg's law at hand, which gives us the connection between the interplaner spacing of the reflection set of crystalline planes and the sinus of the halve of the Bragg's angle (2 Theta)  that the diffracted beam makes with the transmitted beam from the sample: Namely  n Lamda = 2 dhkl sin Theta.         dhkl   has well defined mathematical connections  for a given class of  crystal structure, which relate dhkl  to   the lattice parameters through the h,k,l Miller indices. Therefore the first thing to do index the spectral lines in terms of   h k l indices according to the observed  2theta values of the line spectrum. This is a very tedious job for crystal systems other than  SC, BCC, FCC, HCP and Tetragonal.

For cubic system one can write:

sin2 theta /(h2 + k2 + l2) = Lamda2 /4 a2  ,  since  the denominator of the left side is always integer, and  the right side is a constant for any one pattern, the problem of indexing the pattern of a cubic substance  is one of finding a set of integers  s=(h2 + k2 + l2 ) ,which will yield  a constant quotient when divided one by  one into the observed  sin2 theta  values. Once the proper integers  s are found, the indices hkl of each line can be written down by inspection, or using some standard tables.  the mean Inverse constant quotent is   4 a2 / lamda2, . EQD. Slide Rule would be very helpful or already prepared strips1may be useful  for indexing.

1) Elements of X-ray Diffraction by R. D. Cullity

2) X-Rat Diffraction Procedures for Polycrystalline and Amorphous Materials, by H. P. Klug and L. E. Alexander,  2nd Ed. 1974.

Look for some papers written by John H. Scolfield of Oberlin College, he also has some excel template for doing calculations you are looking for