About

The hexagon is one of the most efficient shapes in nature and engineering, appearing in everything from honeycombs to structural bolts. In manufacturing and machining, confusing "Across Flats" (wrench size) with "Across Corners" (clearance diameter) can lead to scrapped parts and costly errors.

This Inscribed Hexagon Calculator simplifies these conversions. By entering just one dimension, it instantly calculates the area, perimeter, and the critical corresponding diameters. Whether you are a CNC operator checking stock sizes or a student studying geometry, this tool provides clear, visual answers distinguishing between the inscribed circle (flats) and circumscribed circle (corners).

Formulas

For a regular hexagon with side length a:

Area = 3√3 2 a² ≈ 2.598a²

Key relationships:

Across Corners (d): d = 2a (This is the diameter of the circumcircle).
Across Flats (f): f = √3 a ≈ 1.732a (This is the diameter of the incircle).

Reference Data

Side Length (a)	Across Flats (f)	Across Corners (d)	Area
1	1.732	2.000	2.598
5	8.660	10.000	64.952
10	17.321	20.000	259.808
15	25.981	30.000	584.567
20	34.641	40.000	1039.23
25	43.301	50.000	1623.80
50	86.603	100.000	6495.19
100	173.205	200.000	25980.76

Frequently Asked Questions

Across Flats is the distance between two parallel opposite sides (the way a wrench fits a bolt). Across Corners is the distance between two opposite vertices (the widest point of the hexagon).

If you have a round stock of diameter D, the largest hexagon you can machine from it has an 'Across Corners' dimension equal to D. The resulting 'Across Flats' size would be D × 0.866.

Hexagons provide 6 access points for a tool, requiring only a 60-degree rotation to engage, which is ideal for tight spaces. They are also mechanically robust and easy to manufacture.