Fretboard Calculator – Calculator City

Scale Length

The vibrating length of the string, from nut to bridge saddle.

Please enter a valid, positive scale length.

Units

Select the measurement unit for your scale length.

Number of Frets

Enter the total number of frets for the fingerboard (typically 12 to 24).

Please enter a valid number of frets (1-36).

What is a Fretboard Calculator?

A fretboard calculator is an essential tool for luthiers, guitar technicians, and DIY instrument builders used to determine the precise placement of frets on the neck of a stringed instrument like a guitar, bass, mandolin, or ukulele. The accuracy of fret placement is critical for ensuring the instrument plays in tune across the entire neck, a concept known as intonation.

This calculator uses a mathematical formula based on the principle of the equal-tempered scale, which divides an octave into twelve equal semitones. By inputting the instrument’s scale length (the distance from the nut to the bridge), the calculator provides the exact measurement from the nut to the crown of each fret.

Fretboard Calculator Formula and Explanation

The placement of frets on modern instruments is governed by a constant derived from the twelfth root of two (¹²√2), which is approximately 1.059463. This constant ensures that each fret raises the pitch by one semitone, and that 12 frets perfectly span one octave.

Alternatively, a simpler constant, 17.817, is often used. This number is derived from 1 / (1 – 1 / ¹²√2). The formula to calculate the distance from the nut to any given fret (n) is:

Distance(n) = ScaleLength – (ScaleLength / (2^n/12))

A more iterative approach, often called the “Rule of 17.817,” calculates the position of each fret based on the remaining string length:

Position of 1st Fret = Scale Length / 17.817
Position of 2nd Fret = (Scale Length – Position of 1st Fret) / 17.817 + Position of 1st Fret
…and so on for each subsequent fret.

Variables Table

Formula Variables
Variable	Meaning	Unit (Auto-Inferred)	Typical Range
ScaleLength	The total vibrating length of the open string.	in or mm	24″ – 26″ (Guitar), 30″ – 36″ (Bass)
n	The fret number you are calculating for.	Unitless Integer	1 – 24
Distance(n)	The resulting distance from the nut to the center of fret ‘n’.	in or mm	Varies by fret number

Practical Examples

Example 1: Standard Electric Guitar (Fender-style)

Inputs:
- Scale Length: 25.5 inches
- Number of Frets: 22
Results:
- 1st Fret Position: 1.431 inches from the nut
- 12th Fret Position: 12.75 inches from the nut (exactly half the scale length)
- 22nd Fret Position: 18.291 inches from the nut

Example 2: Short Scale Bass Guitar

Inputs:
- Scale Length: 762 mm (approx. 30 inches)
- Number of Frets: 20
Results:
- 1st Fret Position: 42.768 mm from the nut
- 12th Fret Position: 381.000 mm from the nut
- 20th Fret Position: 526.969 mm from the nut

How to Use This Fretboard Calculator

Enter Scale Length: Input the vibrating string length of your instrument, measured from the fret-facing edge of the nut to the point where the string breaks over the bridge saddle. For tips on measuring, you can check this fret spacing guide.
Select Units: Choose whether your measurement is in inches or millimeters. The calculator will adapt all output to match.
Set Number of Frets: Enter how many frets your fingerboard will have. The table and chart will update accordingly.
Review the Results: The calculator instantly provides a table listing the distance from the nut to each fret, as well as the spacing between adjacent frets. The octave position (12th fret) is highlighted for quick verification.
Visualize the Spacing: Use the dynamic chart to get a visual sense of how the fret spacing decreases as you move up the neck.

Key Factors That Affect Fretboard Calculations

Scale Length: This is the most critical factor. A longer scale length results in wider spacing between frets and can increase string tension, often leading to a brighter tone. A shorter scale length makes the frets closer together, reducing tension and often producing a warmer tone.
Intonation Compensation: While the calculator provides the theoretical fret positions, real-world physics requires slight adjustments. The act of fretting a string sharpens the note slightly. To compensate, the bridge saddle is often moved back slightly, effectively lengthening the string. Our bridge placement tool can help with this.
Fret Wire Size: The calculations measure to the center of the fret slot. The final intonation point is the peak (crown) of the fretwire. While minor, the width of the fret crown can impact precise measurements.
Nut Position: All measurements are made from the fingerboard-side edge of the nut. An improperly placed or cut nut will throw off the entire fretboard’s intonation.
Multi-Scale Instruments (Fanned Frets): Some instruments use different scale lengths for the bass and treble strings. This requires more complex calculations for each string, as the frets must be placed at an angle. For this, a more advanced 2D fretboard designer might be needed.
Measurement and Cutting Accuracy: The precision of your measurements and cuts is paramount. Even small, compounding errors can lead to noticeable intonation problems. Using a high-quality ruler and precise cutting tools is crucial.

Frequently Asked Questions (FAQ)

1. What is the “Rule of 18”?

The “Rule of 18” is a historical method for calculating fret placement. It’s a slightly less accurate approximation of the modern formula, using 18 as the divisor instead of 17.817. While it works reasonably well, the modern formula is more precise for perfect equal temperament.

2. Why is the 12th fret exactly at the midpoint of the scale length?

In equal temperament, the 12th note is the octave, which has exactly double the frequency of the open string. To achieve this, the string length must be halved. Therefore, the 12th fret is always positioned exactly halfway between the nut and the bridge saddle.

3. Does this calculator work for bass, mandolin, or ukulele?

Yes. The mathematical principle is the same for any fretted instrument that uses an equal-tempered scale. Simply enter the correct scale length and number of frets for your specific instrument. You can see various applications on this instrument calculator app.

4. How accurate do my cuts need to be?

Most luthiers aim for an accuracy of a few thousandths of an inch (or hundredths of a millimeter). Compounded errors are the biggest risk; measuring each fret slot from the nut, rather than from the previous fret, helps minimize this risk.

5. What is bridge compensation?

Bridge compensation is a slight adjustment to the string length at the saddle to correct for the sharpening effect of pressing a string down to a fret. This calculator does not include compensation, which varies by string gauge and action height. You can learn more about it with our fret scale instructions.

6. Why do the frets get closer together up the neck?

The fret positions are based on a ratio, not a fixed distance. Each fret must be placed at a specific fraction of the *remaining* string length. As the string length shortens with each fret, the distance to the next fret also becomes proportionally smaller.

7. Can I use this for a fanned-fret (multi-scale) guitar?

This calculator is designed for single scale length instruments. For a multi-scale design, you would need to run the calculation for your longest scale (bass side) and your shortest scale (treble side) separately and then connect the points to determine the angled fret slots.

8. How does humidity affect the fretboard?

Wood expands and contracts with changes in humidity. In high humidity, the wood can swell, and in low humidity, it can shrink. This can cause fret ends to protrude or sink, and can affect the neck’s straightness, impacting playability and intonation.