I know that good people like Stewmac have them online, but my formula allows you to have, at your fingertips, the ability to find fret positions for any scale length for any instrument, be it a uke or a giant Mexican guitar, instantly. All you will need is a simple, cheap calculator. A friend of mine gave me this formula a few years ago but it wasn’t exactly accurate. So I tinkered with it for a couple of hours until it was as perfect as possible.

Just to prove that it works perfectly lets use 600mm as the scale length (nut to bridge). The scale length can be as long or short as you care to make it. By using 600mm it will be easy to see that at the 12^{th} fret the distance should be half of the scale length (300mm), and at the 24^{th} fret a quarter (150mm) thus proving the formula.

Lets enter 0.943878 x 600

Now press = once

We get 566.3268

This is the distance from the bridge to the 1^{st} fret.

Press = once again and we get 534.5434

This is the distance from the bridge to the 2^{nd} fret.

Press = once again for the 3^{rd} fret and so on.

When you get to the 12^{th} fret it should read 300.01402 (octave).

Keep going to the second octave (24^{th} fret) and we get 150.01399 thus proving that the formula is accurate for our purposes. Only use 2 digits after the decimal point, ignore the rest that follow as they are too small to be relevant.

Now here’s an interesting thing I discovered quite by chance. I wanted to turn metal slugs on the lathe to the sizes of the spaces between the frets so that I could line them all up in a slot cut in a piece of flat board, and clamped to my pull-saw. Then cut each fret taking away one slug at a time until I had a perfectly cut fingerboard. The way to find these sizes leapt off the page at me – EUREKA!

Put in our formula again as before 0.943878 x 600.

Now press = 10 times and we get 336.75

Move the decimal point one place to the left and we get 33.67

This is the distance from the nut to the 1^{st} fret.

Press = once and we get 317.85

Move decimal point again (once to the left) and we get 31.78 which is the distance between 1^{st} and 2^{nd} frets.

Keep pressing = until all distances between frets are found.

You can use wooden dowel for the distance pieces. All you will need is a drop-saw, lots of dowel and lots of patience. It helps to use a digital vernier.

I hope this is of use to you. Have fun! John Stax

P.S. Write down the formula in a few places that you can locate when needed. JS.

## Replies

Great man, very nice of you to share, always handy to have as it is only one number to have to do the job.

Cheers Ron.

Borders has them, but you need to hurry, they are going out of business.

john stax said:

endof the scale length, which, of couse, makes no difference whatsoever. Somehow, though, calculating your own fret positions seems more satisfying for us DIYers. Thanks, John! I will put this formula in my Big Book of Knowledge!