Octagon area calculator
Find the area and perimeter of a regular octagon from the length of one side. Change the units to work in metres, feet, inches and more.
Calculate your octagon’s area
For a regular octagon, keep eight sides selected and enter the length of one side. All eight sides and angles must be equal.
- Perimeter / boundary
- Square metres
- Square feet
- Acres
- Hectares
Results are rounded to 10 significant figures. Changing units converts your existing dimensions and coordinates, preserving the physical size.
Tap or click anywhere along an edge to add a point, then drag it. Drawing grid: x = 0–20, y = 0–13. For larger or more precise plots, type coordinates. Keyboard users can edit every corner in the coordinate field.
A little help with measuring
Use matching units for every dimension. A radius is half the diameter; an ellipse uses two radii. A perpendicular height is measured at 90° to the base.
For an irregular plot, enter each corner in order around its boundary. Concave shapes work too. For holes or curved boundaries, calculate separate pieces and add or subtract their areas using the everyday calculator.
Side lengths alone don’t determine the area of an irregular polygon. Custom mode therefore uses corner coordinates. This calculator measures flat, two-dimensional shapes; it does not calculate 3D surface areas.
Regular octagon area formula
A regular octagon has eight equal sides and eight equal interior angles. With side length s, its area is A = 2 × (1 + √2) × s². Its perimeter is P = 8 × s.
Worked example: a four-metre side
If each side is 4 m, A = 2 × (1 + √2) × 4² ≈ 77.254834 m². The perimeter is 8 × 4 = 32 m. The square unit matters: an area in square metres is not a length in metres.
What if my octagon is irregular?
Eight side lengths alone do not determine its area. Choose Custom outline above and enter the corner coordinates in boundary order, or draw the outline on the grid. It supports concave shapes, but edges must not cross and holes are not supported.
Why this formula works
Split a regular octagon into eight matching triangles from its centre. Their combined area is half the perimeter times the apothem (the perpendicular distance from centre to a side). The apothem is s ÷ [2 tan(π ÷ 8)], giving the formula above.
For triangles, circles, rectangles and other polygons, visit the full area calculator. Explore more number and time tools or take a break with today’s Sudoku.