How to use the fret position calculator
- Enter the scale length, the distance from the nut to the bridge saddle measured along the string, and choose inches or millimeters.
- Enter the number of frets, from 1 to 36.
- Read the table. Each row gives the distance of the fret from the nut, the distance from the previous fret and the distance still left to the bridge.
- Mark the frets by measuring each one from the nut so that errors do not build up from one fret to the next.
Formula
distance from the nut to fret n = scale x (1 - 2^(-n/12))
each fret shortens the string by a factor of 2^(1/12), about 1.05946
fret 12 is at exactly half the scale length
The formula is for equal temperament, in which each fret raises the pitch by one semitone and twelve frets make an octave.
A 25.5 inch scale and a 650 mm scale
For a scale length of 25.5 inches, fret 1 is 25.5 x (1 - 2^(-1/12)) = 1.4312 inches from the nut. Fret 12 is at 12.75 inches, exactly half the scale length. Fret 22 is at 18.3443 inches and fret 24 at 19.125 inches. The spacing from fret 11 to fret 12 is 0.7582 inches, and from fret 21 to fret 22 it is 0.4255 inches.
For a classical guitar with a 650 mm scale, fret 1 is 36.48 mm from the nut and fret 12 is 325 mm. A 24.75 inch scale has its twelfth fret at 12.375 inches. The spacing gets narrower along the neck because each fret removes about 5.6 percent of the remaining string.
Measure from the nut, not from the last fret
If you measure each fret from the one before it, a small error of a fraction of a millimeter gets added to every later fret. Measuring all of them from the same starting point, the nut, keeps each error independent. A fretting template or a slotting jig from the same table makes this easy. The spacing column is there to check your marks, not to mark from.
Compensation and test cuts
A stiff string sounds a little sharp when pressed, so the bridge saddle is set slightly farther from the nut than the scale length. The amount depends on the strings and the action height. These figures are the theoretical positions only. Cut test slots, check the intonation by ear or with a tuner, and adjust. For note pitches, see the Note Frequency Converter, and for pitch relations between two frets use the Musical Interval Calculator.
More electronics and audio tools
For related music and electronics work, try the ADC Resolution Calculator, RC Filter Time Constant Calculator and AWG Wire Gauge Converter.
Assumptions and limits
- The scale is equal tempered with twelve semitones to the octave.
- The string is ideal, with no stiffness, so no compensation is applied.
- The scale length is measured along the string from the nut to the saddle.
- The number of frets is a whole number from 1 to 36.
- The scale length and fret count in the form are examples to replace with your own.
Frequently asked questions
Why is fret 12 at half the scale length?
Halving the vibrating length of a string doubles its pitch, which is an octave. Twelve semitones make an octave, so the twelfth fret sits at the midpoint of the scale.
Why do the frets get closer together?
Each fret removes the same fraction, about 5.6 percent, of the string that remains. The remaining string gets shorter, so the same fraction is a smaller distance.
Does the scale length include the width of the nut and the saddle?
The scale is measured from the point where the string leaves the nut to the point where it leaves the saddle, so it follows the string, not the body of the instrument.
Can I use this for a ukulele or a bass?
Yes. Any fretted instrument tuned in equal temperament follows the same rule. Enter its scale length and the number of frets it has.