What this calculator does
A hexadecagon is a polygon with 16 sides. When every side and every angle is equal it is a regular hexadecagon, and that regularity is what lets the whole shape be worked out from a single measurement: the length of one side. Feed that in and every other dimension, area, perimeter, interior angle, apothem and circumradius, follows from fixed geometric ratios.
The shape turns up more than its name suggests: coins, architectural mouldings, stop-sign-style signage variants and some tiling patterns use 16 sides because it is close enough to a circle to look smooth while still being straightforward to cut or cast with straight edges. The calculator below is built specifically for the 16-sided case rather than a generic any-n-sides tool, so the numbers it shows are exact for a hexadecagon.
The formula
For a regular polygon with n sides and side length s, the interior angle is (n−2)×180/n, the perimeter is simply n×s, and the area is (n×s²) ÷ (4×tan(π/n)). With n fixed at 16, that interior angle works out to a constant 157.5° regardless of size, while area and perimeter scale with the side length you enter. The apothem (centre to the middle of a side) and circumradius (centre to a corner) are also derived from the same side length, using the standard regular-polygon trigonometric relationships.
| Term | Meaning |
|---|---|
| Side length (s) | The length of one of the 16 equal edges. |
| Interior angle | The angle inside the shape at each of its 16 corners, fixed at 157.5° for any regular hexadecagon. |
| Apothem | The distance from the centre of the shape to the midpoint of a side. |
| Circumradius | The distance from the centre of the shape to one of its corners. |
The inputs explained
| Field | What to enter |
|---|---|
| Side length | The length of one side of the regular 16-sided shape, in whatever unit you are measuring in. |
When to use it
Cutting or fabricating a 16-sided piece
Knowing the exact perimeter tells you how much edging or trim material is needed, and the interior angle tells you the exact mitre or bend angle at each corner.
Estimating material for a hexadecagonal surface
The area figure converts directly into how much sheet material, paving, glass or fabric is needed to cover a 16-sided panel or plot of that side length.
Comparing to other regular polygons
Because the interior angle climbs toward 180° as the number of sides increases, a hexadecagon at 157.5° sits noticeably closer to a circle than an octagon at 135°, which is worth knowing when choosing between shapes for a design.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How area and perimeter scale with side length
The area grows with the square of the side length while the perimeter grows in direct proportion to it.
| Side length | Area | Perimeter |
|---|---|---|
| 1 | 20.109 | 16.000 |
| 2 | 80.437 | 32.000 |
| 5 | 502.734 | 80.000 |
| 10 | 2,010.94 | 160.000 |
| 20 | 8,043.74 | 320.000 |
| 50 | 50,273.39 | 800.000 |
Questions
What is the interior angle of a 16-sided shape?
For a regular hexadecagon it is exactly 157.5°, from the formula (n−2)×180/n with n=16. This is fixed and does not depend on the size of the shape.
Is a hexadecagon the same as a 16 sided shape?
Yes. Hexadecagon is simply the geometric name for any 16-sided polygon; this calculator assumes the regular case, where all 16 sides and angles are equal.
How is the area calculated without a diagram?
The area of any regular polygon can be found purely from its side length and number of sides using area = (n×s²) ÷ (4×tan(π/n)). With n fixed at 16, that reduces to a single multiplication once s is known.
What if I know the across-corners distance instead of the side length?
This calculator is built around the side length as the single input. If you only have a across-corners or across-flats measurement, that can be converted to a side length using the circumradius or apothem relationship before entering it here.
For the equivalent working on an 8-sided shape, see the octagon calculator. For a 6-sided shape, see the hexagon calculator.