Fretboard Radius Matcher

What this tool is for

Recover a circular radius from measured chord width and center sagitta, with error sensitivity. Geometry tools apply explicit models to named measurements. A coordinate or angle must still be checked against a physical drawing, real hardware, tolerances, and material behavior.

Use it when you can describe the current state and need a defensible next check. It is not a shortcut around inspection: preserve the starting state, change one variable, and verify the result under the same conditions.

Before you begin

Use a straight chord of known width and measure perpendicular center sagitta without pressing a flexible surface. Repeat the reading and keep all values in one unit.

• Use a stable, tuned instrument unless the page specifically investigates tuning.
• Name the physical reference, unit, and test condition beside every important number.
• Keep the original measurements so any reversible change can be returned to baseline.

Input guide

Nominal radius for comparison

supplies a measured geometric quantity whose datum and resolution should be written down.

Measured chord width

supplies a measured geometric quantity whose datum and resolution should be written down.

Measured center depth / sagitta

provides a measured or counted input; confirm the allowed range and repeat the reading before relying on it.

Input and display unit

sets the interpretation and display unit; do not mix units elsewhere in the same run.

Measurement mode

classifies an observed condition; choose “unknown” or “not tested” instead of guessing when available.

Optional compound end radius

supplies a measured geometric quantity whose datum and resolution should be written down.

Input labels describe evidence, not targets. A placeholder demonstrates format only; it is never a recommendation for a particular guitar.

How the result should be read

Trust a cluster of repeated readings more than a rounded label. Compare with a known radius gauge and observe whether the board is compound or worn.

Read priorities from top to bottom, but stop as soon as new evidence contradicts an earlier assumption. Save or print the result ticket with the entered conditions so another person can reproduce the decision.

Method and logic

For chord c and sagitta h, circular radius R=c²/(8h)+h/2. The tool also perturbs h to show how small depth errors change a large radius estimate.

The page keeps calculation and diagnostic claims deliberately bounded. Display rounding improves readability, while the underlying logic uses entered values; descriptive branches report relative tendencies and the evidence needed to confirm them.

Worked example

A 2.000-inch chord with roughly 0.0418-inch sagitta returns close to a 12-inch radius. A small sagitta error noticeably changes the answer, demonstrating measurement sensitivity.

The example demonstrates reasoning, not a universal setup specification. Substitute real measurements and repeat the final test before accepting the next action.

Assumptions and limitations

The equation assumes a circular arc and an accurate chord. Fret crowns, compound boards, fall-away, tool tilt, string grooves, and surface wear violate that simple model.

Instrument design, service history, measurement error, and player technique can outweigh a calculator or checklist. Where manufacturer instructions exist for the exact hardware, use those instructions and record the revision consulted.

Safety and stop conditions

Stop for abnormal resistance, cracking, heat, odor, electrical sensation, moving wood or joints, a measurement that cannot be repeated, or any step that would remove material without a confirmed cause. Secure strings and stored mechanical energy before hardware work. Refer structural, fret-cutting, mains-powered, or uncertain repairs to a qualified technician.

Related workflow

• Saddle Radius Planner — Calculate relative saddle-center targets from radius, string spread, action, and gauge.
• Geometry Measurement Definitions — Name every datum before entering a number.
• Guitar Setup Measurement Points — Use repeatable setup datums.

Open the related page that answers the next unresolved question; do not run every tool as if every system needs adjustment.