Fret Calculation on the Classical Guitar

How to calculate the fret positions for the given scale:

The nominal scale length (without any compensation) is divided by 17.817 (the 1/12th root of 2) and this gives the distance to the first fret from the nut. This distance to the first fret is then subtracted from the nominal scale length to yield the new shorter scale length. This new shorter scale length is then divided by 17.817 to give us the distance to the next fret. This process is repeated for the number of frets required.

Example: Call the scale Length = L  and the Distance to fret(n)= D(n),  and then let us say the scale length is 650mm, a common scale length on guitars.

Fret Calculation on the classical guitar
Calculate distance to first fret Divide 650 by 17.817 (rule of 17). The result is 36.48mm. This is the distance from the nut to the first fret. L/17.817=D(1)
650/17.817=36.48
Re-calculate scale length Subtract 36.48 from 650. This gives us 613.52. our new scale length (L) L=L-D(1)
650-36.48=613.52
Calculate distance to next fret Divide 613.52 by 17.817. The result is 34.43. This is the distance from the first fret to the second fret. 613.52/17.817=34.43
Re-calculate scale length Subtract 34.43 from 613.52. This is our new scale length (L). 613.52-4.43=579.08
Calculate distance to next fret Continue these calculations for the number of frets required. 579.08/17.817= 2.50

For those who are interested I have included a simple spreadsheet that will calculate the fret positions for any scale length. Download FretCalculator.xls . The output of the program is similar to the table below.

Example of the output of the Fret calculator
650mm Scale Distance from previous fret New Scale length Distance from nut
Fret 1 36.48201156 613.5179884 36.48201156
Fret 2 34.43441592 579.0835725 70.91642748
Fret 3 32.50174398 546.5818285 103.4181715
Fret 4 30.67754552 515.904283 134.095717
Fret 5 28.95573234 486.9485507 163.0514493