Fret Calculator
Calculate exact fret positions for guitars, bass, and other stringed instruments. Get precise measurements for luthiery and instrument building.
Calculate Your Fret Calculator
What is a Fret Calculator?
A fret calculator is a tool used by luthiers, guitar makers, and other stringed instrument builders to determine the precise placement of frets on the fingerboard of a stringed instrument. The accuracy of fret placement is crucial for proper intonation—ensuring that notes played at different positions along the neck are in tune with each other.
The Science Behind Fret Placement
Fret placement follows the principles of the 12-tone equal temperament system, which divides an octave into 12 equal semitones. Each fret represents one semitone, and the placement is calculated using a logarithmic formula rather than equal distances.
The standard formula for calculating the distance from the nut to a specific fret is:
Distance = Scale Length × (1 - 1/2^(n/12))Where:
- Scale Length: The vibrating length of the open string (from nut to bridge)
- n: The fret number
Common Scale Lengths
Different instruments and manufacturers use various scale lengths:
- Electric Guitars: 24.75" (Gibson), 25.5" (Fender)
- Acoustic Guitars: Typically 25.4" to 25.5"
- Bass Guitars: 30" to 36"
- Ukulele: Soprano: 13", Concert: 15", Tenor: 17", Baritone: 19"
- Mandolin: Typically around 14"
- Banjo: Typically 26" to 28"
Applications of Fret Calculations
Accurate fret calculations are essential for:
- Building new instruments with proper intonation
- Replacing fingerboards on existing instruments
- Adding or replacing individual frets
- Designing fretless instruments with position markers
- Educational purposes to understand string instrument design
Important Considerations
While mathematical precision is important, instrument makers often make small adjustments to account for factors such as:
- Action height: Higher strings require slightly sharper intonation
- String gauge: Thicker strings have different elasticity properties
- String material: Different materials stretch differently when pressed
- Temperature and humidity: Environmental conditions can affect wood and string tension
This calculator provides the theoretical positions based on the mathematical formula. Skilled luthiers might make minor adjustments based on experience and the specific characteristics of the instrument being built.
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Frequently Asked Questions
A fret calculator helps determine the exact placement of frets on stringed instruments like guitars, bass, ukuleles, and others. It uses mathematical formulas based on the 12-tone equal temperament system to ensure that when a string is pressed against a fret, it produces the correct note with proper intonation.
Fret spacing is calculated using the formula: Distance from nut = Scale Length × (1 - 1/2^(n/12)), where n is the fret number. This formula ensures that each fret produces exactly one semitone higher in pitch than the previous fret. The distances between consecutive frets get progressively smaller as you move up the neck toward the bridge.
Scale length is the theoretical vibrating length of an open string, measured from the nut to the bridge. It's a fundamental parameter in instrument design that affects playability, string tension, and tone. Longer scale lengths (like Fender's 25.5") typically have more tension and brighter tone, while shorter scale lengths (like Gibson's 24.75") have less tension and warmer tone. Scale length is the baseline measurement used to calculate all fret positions.
The mathematical proportion of fret spacing (following the 12-tone equal temperament) is the same across instruments, but the actual distances vary based on the instrument's scale length. A bass guitar with a 34" scale length will have larger distances between frets than a guitar with a 25.5" scale length, but the mathematical relationship between frets is identical.
Frets aren't evenly spaced because musical pitch follows a logarithmic scale rather than a linear one. To raise a note's pitch by one semitone, you need to increase its frequency by a factor of 2^(1/12) (approximately 1.059). This means that each consecutive fret spacing must be about 94.4% of the previous spacing to maintain correct intonation across the entire fingerboard.
Compensated scale length is an adjustment made to account for the fact that pressing a string increases its tension slightly, which can make fretted notes play sharp. To counteract this, the bridge saddles are often placed slightly farther from the nut than the theoretical scale length would suggest. This compensation varies by string gauge and action height, so many instruments have individual adjustable saddles for each string.
Yes, fret calculations are still useful for fretless instruments like fretless bass guitars or violin family instruments. They can be used to place position markers (often small dots on the side of the fingerboard) that guide the player's finger placement. For fretless instruments, compensated calculations are especially important since the player's finger directly determines the vibrating length of the string.
Fret placements should be extremely accurate—ideally within 0.1mm or less—for proper intonation. Even small errors can compound and become noticeable, especially in higher positions. Professional luthiers use specialized tools like precise fret saws and positioning templates to ensure accuracy. For DIY instrument makers, this calculator can provide the measurements needed, but proper tools and techniques are essential for implementation.
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