What this calculator does
A regular octagon has eight equal sides and eight equal interior angles of 135° each, the shape behind a stop sign or an octagonal paver. As with any regular polygon, one measurement is enough to fix the whole shape, but that measurement could be the side length, the across-flats width (the distance between two opposite, parallel sides), or the across-corners width (the distance between two opposite corners).
This octagon calculator accepts any of those three, converts internally to the side length, and returns the area, perimeter and both width measurements together, so a stop-sign-shaped panel or paver measured by whichever dimension is easiest still gets a correct area.
The formula
From the side length s, area = 2(1+√2) × s². If the across-flats width is known instead, s = across-flats / (1+√2). If the across-corners width is known, s = across-corners / √(4+2√2). Perimeter is simply 8 × s once the side length is established.
| Term | Meaning |
|---|---|
| Side length | The length of one of the eight equal edges. |
| Across flats | The distance between two opposite, parallel sides, measured straight across. |
| Across corners | The distance between two opposite corners, the longest straight measurement across the octagon. |
The inputs explained
| Field | What to enter |
|---|---|
| Value | Enter the side length, across-flats or across-corners measure, whichever you already have. |
| This value is the | Select which measurement the value above represents. |
When to use it
An octagon paver, tile or gazebo base
An octagonal paver, tile or gazebo floor is normally cut to a side length, so the octagon calculator gives the area of material needed directly from that measurement.
A stop sign or octagonal panel measured across flats
A stop sign or bolt-pattern panel is often specified by its across-flats width, the distance a wrench or mounting bracket would actually span, rather than by the length of one angled edge.
Fitting an octagon inside a fixed circular opening
An octagon designed to fit snugly inside a round opening or frame is more naturally described by its across-corners width, the widest point that has to clear the opening.
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.
Octagon area across a range of side lengths
The area and perimeter of a regular octagon across a range of side lengths.
Does it matter whether the value 10 is the side, across flats or across corners?
The number 10 entered once as a side length, once as an across-flats measure and once as an across-corners measure, to show how the octagon calculator’s answer changes with what that number represents.
| The value 10 is the | Area | Side length |
|---|---|---|
| Side length | 482.843 | 10.000 |
| Across flats | 82.843 | 4.142 |
| Across corners | 70.711 | 3.827 |
Questions
What is a regular octagon?
A regular octagon is an eight-sided polygon with all eight sides equal in length and all eight interior angles equal, each measuring 135°.
What is the area formula for an octagon?
Area = 2(1+√2) × s², where s is the side length. The constant 2(1+√2) works out to roughly 4.828.
What is the difference between across flats and across corners on an octagon?
Across flats measures the shorter distance between two opposite, parallel sides. Across corners measures the longer distance between two opposite vertices. Across corners is always the larger of the two for the same octagon.
Why does a stop sign have eight sides?
An octagon’s shape is distinctive and legible from any angle at speed, which is why it was standardised for stop signs, though the geometry itself is the same regular-octagon maths used for any eight-sided design.
For a hexagon instead, see the hexagon calculator. For any number of sides at once, see the general regular polygon calculator.