Calculating fret distances

The fret constant 17.817

When pressing a string against a fret the string's vibrating length is shortened to a precisely determined value. With each fret the frequency of the string's vibration increases by a semitone. Since an octave is divided into 12 semitones the pitch of a string pressed down on the 12th fret is twice as high as that of the open string.

To calculate the length by which a string has to be shortened to increase its pitch by a semitone the string length has to be divided by the twelfth root of two. With the fret constant thus determined it becomes possible to calculate by how much each string has to be shortened. Measuring the distances between the frets from a point on the fingerboard is obviously more practical than measuring them from the body-end of the string.

By dividing the total scale length by 17.817 you will get the length by which a string has to be shortened to increase its pitch by a semitone, i.e. the distance between the nut and the first fret. This constant is used like other constants such as the circle constant pi (=3.1415) and others. It guarantees a well-tempe- red fret distribution, and the three digits behind the comma (of this constant) are totally sufficient as we shall also see later when marking the fret positions.

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Calculating fret distances

If you divide any scale length by the constant 17.817, you will get the distance from the front edge of the nut to the first fret. Here is one example: a scale length of 25.5" (650mm) divided by 17.817 gives 1.4312173" (36.482011mm), which can be rounded down to 1.431" (36.48mm). Three digits behind the comma are sufficient when using Imperial measurements (two when using metric units), as it is virtually impossible to place a fret much

more accurately than to 1/1000 of an inch. The first fret is therefore

placed at a distance of 1.431" (36.48mm) from the nut. To calculate the position of the second fret, the remaining scale length (25.5" minus 1.431" = 24.069") is again divided by 17.817. This gives the distance from the first fret at which the second fret has to be placed - in the above example this would be 1.351" (34.43mm). All fret distances should ideally be measured from the front side of the nut or a potential zero-fret, as otherwise several minor errors in the actual fretting could eventually add up to quite considerable differences. It is consequently advisable to determine all fret positions by measuring from the nut: the first fret is placed at a distance of 1.431" from the nut, the second at 1.431" + 1.351" (=2.782") from the nut, and so on. For calculating the position of the third fret, the remaining scale length - i.e. the distance from the second fret to the bridge - is again divided by 17.817, and so on for all other frets. For the 12th fret the calculations have to give exactly half of the total scale length (at least if you ignore anything beyond the 3rd (or 2nd) digit behind the comma as there are always unavoidable rounding errors if you use a calculator or a spreadsheet program).

Using a spreadsheet program

Doing all these calculations with a calculator can be a bit tedious, but it can easily be automated with a spreadsheet program such as

Microsoft EXCEL:

Enter the scale length in field B1 assign the value “0” to B2, and enter the formula “=(B$1-B2) / 17.817 + B2” for calculating the distance between the nut and the first fret into field B3. To calculate all other fret distances simply copy the formula of field B2 into the other fields below it. Finally number all frets in column A and then print out the sheet, checking that no errors have occurred and that, for instance, the distance calculated for the 12th fret is exactly half of the total scale length (ignore unavoidable rounding errors past the second or third digit behind the comma).

On-line fret calculator

If you have access to the World Wide Web you are invited to use my on-line fret calculator at: www.BuildYourGuitar.com/resources