Tell the tool what you know — the side length, the long diagonal, the circumradius, the inradius (apothem) or the area — and it derives every other property of a regular octagon: area, perimeter, long diagonal, flat-to-flat width, circumradius and inradius. A regular octagon is an eight-sided polygon with all sides and all interior angles (135° each) equal, used everywhere from stop signs to floor tiles and umbrellas.
How it works
From whichever value you enter, the calculator first solves for the side length, then applies the standard regular-octagon constants. With side s:
- Area = 2(1 + √2) · s² ≈ 4.8284 · s²
- Perimeter = 8 · s
- Width (flat-to-flat) = (1 + √2) · s ≈ 2.4142 · s = 2 × inradius
- Long diagonal (vertex to vertex) = √(4 + 2√2) · s ≈ 2.6131 · s = 2 × circumradius
- Circumradius = √(4 + 2√2)/2 · s ≈ 1.3066 · s
- Inradius (apothem) = (1 + √2)/2 · s ≈ 1.2071 · s
When you give the area instead of the side, it inverts the area formula: s = √(area ÷ 4.8284).
Example
Enter a side length of 10 units:
- Area = 4.8284 × 100 = 482.843 square units
- Perimeter = 8 × 10 = 80 units
- Width = 2.4142 × 10 = 24.142 units
- Long diagonal = 2.6131 × 10 = 26.131 units
- Inradius = 12.071 units, circumradius = 13.066 units
| Side | Area | Perimeter | Width | Long diagonal |
|---|---|---|---|---|
| 5 | 120.71 | 40 | 12.07 | 13.07 |
| 10 | 482.84 | 80 | 24.14 | 26.13 |
| 20 | 1931.37 | 160 | 48.28 | 52.26 |
Values are unitless — read them in whatever unit you entered the side in (mm, cm, m, in). All calculations stay in your browser and nothing is uploaded.