When holding a guitar in your hand, you'll notice that the back of the guitar neck has a round shape, making it more comfortable to place your palm. But did you know that the front of most guitar necks, the guitar fretboard side, is also convex?
The fretboard side is much flatter than the back of the neck, having a small convex arc across its width. The measure of that arc is called the fingerboard radius (or the fretboard radius).
Is Fingerboard Radius Important?
Some guitarists think that the fingerboard radius has little to do with playability because one can barely feel the subtle difference between different radii. However, most believe that it's very important because a rounder radius makes playing chords, especially barre chords, more comfortable; while a flatter radius is better for single-note playing, and string bending.
Different Types of Radius
Since the invention of the electric guitar, straight-radius fretboards, which feature the same radius, down the entire length of the fretboard, have been used and are still the industry standard. However, some manufacturers created compound radius fretboards where the radius changes along the length of the fingerboard, the area closer to the nut being rounder with the area closer to the body being flatter. This was created as the best-of-both-worlds design to provide hand comfort for chords near the nut while allowing greater speed and cleaner string bending further up the neck.

Common Sizes
Most classical guitars, banjos, and some acoustic guitars have flat fingerboards. However, the electric guitar offers multiple fretboard radius options for all manner of applications, especially on custom guitars.
The most common Fender radius is the modern 9.5” radius, which was adopted in the 1980s. The next is 7.25”, which originated in the early 1950s when the manufacturer first started making electric guitars.
PRS guitars are mostly 10'', while Gibsons have a 12'' radius ever since. In the 1980s, Ibanez, Charvel, and Jackson adopted a 16'' radius.