Fret Spacing Calculator — equal-tempered fret positions

Fret positions on a guitar, bass, mandolin or any other fretted instrument in standard Western tuning are not spaced evenly. They follow a geometric series, and the ratio that governs it is the twelfth root of two. This fret spacing calculator applies that ratio to whatever scale length you enter and returns the distance from the nut to every fret, the gap between consecutive frets, and the remaining distance to the saddle.

Arb Digital publishes this alongside the other music and measurement tools our team builds, because the fret question sits at a useful intersection: it is pure physics, the maths is short, and getting it slightly wrong produces an instrument that is audibly out of tune with itself in a way that is very hard to diagnose afterwards.

What This Fret Spacing Calculator Does

Enter a scale length and a fret count and it returns the full position table measured from the nut, in whichever unit you chose. Alongside each position it gives the distance from the previous fret, which is what you feel when you play, and the remaining distance to the saddle, which is the speaking length of the string when that fret is stopped.

It also runs the historical rule of 18 in parallel, using a divisor you can change, and reports how far that older method drifts from equal temperament by the twelfth fret. That comparison is the quickest way to see why the refined constant matters.

The tool computes geometry. It does not set up an instrument, and it does not account for compensation at the bridge, which is a separate matter covered below.

How to Use It

1. Enter the scale length. This is the theoretical nut-to-saddle distance. If you do not know it, measure nut to twelfth fret and double it — that measurement is exact by definition.
2. Pick a unit. Inches, millimetres or centimetres. The ratio is dimensionless, so the unit only affects the numbers you read.
3. Set the fret count to match the neck you are building or measuring.
4. Leave the divisor at 17.817 unless you want to see what the older rule of 18 does. Change it to 18 and watch the twelfth-fret error appear.
5. Read the full table below the results and always measure each fret from the nut, never cumulatively from the last one.

The Formula: The Twelfth Root of Two

Twelve-tone equal temperament divides the octave into twelve semitones of equal frequency ratio. Since an octave is a doubling of frequency, each semitone must multiply frequency by 2^1/12, approximately 1.059463. The University of New South Wales physics group's reference page on Note names, MIDI numbers and frequencies states this directly: an octave comprises twelve equal semitones, each with a ratio of 2^1/12. HyperPhysics at Georgia State University sets out the same system and its consequences on its Equal Temperament page, noting that the scheme's advantage is that music transposes cleanly into every key.

For a string, frequency is inversely proportional to speaking length. So raising a note by n semitones means dividing the speaking length by 2^n/12. The distance from the nut to fret n is therefore the scale length minus what remains:

d(n) = S − S ÷ 2^n/12, where S is the scale length.

Two checks fall straight out. At n = 12, 2^12/12 = 2, so d(12) = S − S/2 = S/2. The twelfth fret is always exactly halfway, on every instrument, at every scale length. At n = 24 the twenty-fourth fret sits three quarters of the way along, because the remaining quarter is an octave above the twelfth.

Worked through at a 25.5 inch scale: fret 1 is 25.5 − 25.5 ÷ 1.059463 = 25.5 − 24.069 = 1.431 inches from the nut. Fret 12 is 12.750 inches. Fret 22 is 25.5 − 25.5 ÷ 3.5636 = 25.5 − 7.156 = 18.344 inches, and the gap between fret 21 and fret 22 is only 0.425 inches — under a third of the first-fret gap. That compression is why the top of a neck feels cramped, and it is geometric, not a design choice.

The Rule of 18, and Why It Was Nearly Right

Long before anyone was taking twelfth roots on a workbench, luthiers used a subtraction rule: to place the next fret, divide the remaining string length by 18 and step that far along. Repeat. It is a beautiful piece of practical mathematics, because it needs nothing but division and it produces a geometric series automatically.

It is also slightly wrong. Dividing by 18 means each step leaves 17/18 of the remaining length, so after twelve frets the remaining length is (17/18)¹² = 0.5036 of the scale — not 0.5. The twelfth fret lands about 0.093 inches short on a 25.5 inch scale, which puts the octave noticeably sharp, and the error compounds above it.

The fix is to use the constant that makes the rule exact rather than the round number. For the remaining fraction to be exactly one half after twelve steps, the divisor must satisfy (1 − 1/x)¹² = 0.5, which gives x = 17.817. Use 17.817 instead of 18 and the subtraction method agrees with the twelfth root of two to well under a thousandth of an inch across a whole neck. That is why the constant appears in workshop literature and why this calculator defaults to it. Change the divisor field to 18 and the tool will show you the error directly.

Which Temperament This Uses, and What Else Exists

This calculator implements twelve-tone equal temperament, which is what standard fretted instruments use and what the twelfth root of two describes. It is not the only system. Just intonation uses small whole-number frequency ratios and produces intervals that beat less but only in one key. Historical temperaments such as meantone and well temperaments distribute the compromise differently. Instruments built for those systems have unevenly spaced or curved frets, and the arithmetic here does not apply to them.

Equal temperament is a compromise in which every interval except the octave is slightly out of tune with the pure ratio, by a fixed and small amount, in exchange for every key sounding identical. A fretted instrument essentially has to take that deal, because a fret serves all six strings at once and cannot be in a different place for each of them.

Compensation Is a Separate Job

Fret positions are calculated from a theoretical scale length, and a real instrument does not quite honour it. Pressing a string down to a fret stretches it slightly, which raises its pitch, and the effect grows with string gauge and action height. Left uncorrected, a perfectly fretted neck plays progressively sharp as you go up it.

The correction is compensation: the saddle is moved a small distance further from the nut than the theoretical scale length, so the speaking length is a fraction longer and the stretch is cancelled. Thicker strings need more of it, which is why an electric guitar bridge has six individually adjustable saddles set in a staircase rather than one straight line.

The important point for this page is that compensation is a setup operation carried out on a built instrument by ear and by tuner, not a number to fold into the fret positions. The frets go where the geometry says. The saddle goes where the intonation check says. Confusing the two produces an instrument that is wrong in both directions at once.

Practical Notes for Building or Checking a Neck

Always measure each fret slot from the nut, using the cumulative figures in the table. Measuring one gap at a time from the last fret means every small error is inherited by every fret above it, and by the twelfth you can easily be a millimetre out. Fret slot width also matters: the calculated position is the centre of the fret, so a slot cut on the wrong side of a marked line puts the fret half a slot width off.

Zero frets and nut placement are a related complication. If an instrument has a zero fret, the scale length is measured from the zero fret, not from the nut behind it. And a conventional nut is often set a fraction beyond the theoretical position as a form of nut compensation, which again is a setup decision rather than part of the fret geometry.

If you want to check the pitch consequences of a position, the note frequency converter turns a note name into a frequency in equal temperament, and the music interval calculator handles the semitone arithmetic between two notes. For string behaviour rather than fret geometry, the guitar string tension calculator relates gauge, pitch and scale length, and the harmonic series calculator covers the overtones that make natural harmonics land where they do.

Common Mistakes to Avoid

• Measuring each fret from the previous one — cumulative error is the single most common cause of a neck that plays sharp at the top.
• Using 18 instead of 17.817 — the round number puts the twelfth fret about 0.09 inches short on a standard electric scale.
• Adding compensation into the fret positions — compensation belongs at the saddle, set by ear on a finished instrument.
• Measuring scale length from the nut on a zero-fret instrument — the zero fret is the reference, not the nut behind it.
• Ignoring slot width — the calculated figure is the centre of the fret, so cut to the line, not beside it.

Related Free Tools From Arb Digital

Work with pitch using the note frequency converter, the music scale generator and the chord calculator, look at string physics with the guitar string tension calculator, and convert measurements with the length converter. More sit in the free online tools hub.

Frequently Asked Questions