The octagon is a favorite deck and gazebo shape — eight equal sides, lots of edge, and a distinctive footprint. Its area comes from one tidy formula, and turning that into decking is a matter of coverage plus a healthy waste factor for all those 45° cuts. This guide covers both.
What’s in this guide
The octagon area formula
Worked example: a deck
An octagonal deck built with 6 ft sides:
| Step | Value |
|---|---|
| Square the side | 6² = 36 |
| Multiply by 4.828 | 36 × 4.828 = 173.8 sq ft |
This formula assumes all eight sides are equal. For an irregular octagon, split it into triangles and rectangles and add.
Octagon area by side length
| Side length | Area (4.828 × s²) | Width across flats |
|---|---|---|
| 4 ft | 77.3 sq ft | 9.7 ft |
| 6 ft | 173.8 sq ft | 14.5 ft |
| 8 ft | 309.0 sq ft | 19.3 ft |
| 10 ft | 482.8 sq ft | 24.1 ft |
| 12 ft | 695.3 sq ft | 29.0 ft |
Estimating deck boards
Board coverage depends on width and gap. A common 5½-inch board with a small gap covers roughly 0.5 sq ft per linear foot:
| Step | Value |
|---|---|
| Deck area | 173.8 sq ft |
| Linear feet of board | 173.8 ÷ 0.5 = ~348 lin ft |
| + 15% (angled cuts) | ~400 lin ft |
| 6 ft boards needed | 400 ÷ 6 ≈ 67 boards |
Eight angled edges mean many mitered ends. Lean toward 15% waste, more for diagonal or picture-frame board layouts.
Measuring an octagon
- Measure one straight side — on a regular octagon all eight are equal.
- If you only have the width across the flats, divide it by 2.414 to get the side length.
- Square the side and multiply by 4.828 for the area.
- Add a waste factor of 10–15% before ordering decking.
Common mistakes
The width across the flats is about 2.4× the side length. Don't plug it in as s.
An octagon's angled edges waste more decking than a rectangle. Use 15%.
If the octagon isn't perfectly regular, the 4.828 shortcut is off — decompose into triangles instead.
Key takeaways
- Octagon area = 2(1 + √2) s² ≈ 4.828 s².
- Width across flats ≈ side × 2.414.
- Decking waste runs 10–15% for the angled cuts.
- Irregular octagon? Split into triangles and add.
Related calculators & guides
Frequently asked questions
- How do I calculate the square footage of an octagon deck?
- For a regular octagon, use area = 2 × (1 + √2) × side², which simplifies to about 4.828 × side². A deck with 6 ft sides is 4.828 × 36 = 173.8 sq ft.
- What is the area formula for a regular octagon?
- Area = 2(1 + √2) s², where s is the side length. The constant 2(1 + √2) equals approximately 4.8284.
- How many deck boards do I need for an octagon deck?
- Divide the deck area by the coverage of one board. A 5.5-inch-wide board with a 6-inch on-center spacing covers about 0.5 sq ft per linear foot, so divide area by 0.5 and add 10–15% for the angled cuts an octagon requires.
- How do I measure an octagon deck?
- Measure the length of one straight side (all eight are equal on a regular octagon). If you know the width across the flats instead, the side length is that width ÷ 2.414.