How to Calculate the Square Footage of a Regular Heptagon
A regular heptagon is a seven-sided polygon with all sides and all angles equal. Seven-sided shapes are uncommon, which is exactly why they are worth a dedicated calculator: custom gazebos, decorative garden beds, and some architectural deck features use seven sides, and most general area tools skip them. The good news is that because the shape is regular, a single side length is enough to find the entire area.
The regular heptagon formula
For a regular heptagon with side length s:
Area = (7 × s²) ⁄ (4 × tan(π ⁄ 7))
The term tan(π ⁄ 7) comes from dividing the heptagon into seven identical triangles that meet at the center. You do not need to work the trigonometry by hand — enter one side length above and the calculator evaluates it for you.
Measuring a heptagon
Since every side is equal, you only need to measure one of them accurately. Pick the side that is easiest to reach, lay the tape flat from corner to corner, and read the length. If you measure two or three sides and they differ noticeably, the shape is not a true regular heptagon — in that case it is better to divide it into triangles and measure those individually.
Worked example
For a heptagonal gazebo floor with sides of 10 feet:
Area = (7 × 10²) ⁄ (4 × tan(π ⁄ 7)) = 700 ⁄ (4 × 0.4816) ≈ 363.39 square feet.
For decking boards on a floor this size, a 10–15% waste allowance is wise because the angled perimeter generates many mitre cuts, suggesting a purchase covering roughly 400–418 square feet.
Where seven-sided shapes appear
- Gazebos and pavilions: Seven-sided gazebos give an unusual, eye-catching footprint.
- Decorative garden beds: A heptagonal raised bed stands out in a formal garden.
- Architectural features: Bay windows, towers and feature floors occasionally use seven facets.
Related shape calculators
For other regular polygons, see the hexagon (6 sides), pentagon (5 sides), octagon (8 sides) and decagon (10 sides) calculators. For an irregular many-sided plot, divide it into triangles and use the irregular triangle calculator.