Case 1
- Side length
- 6
173.823376
Open with these valuesOctagon Area Calculator
173.823376units²
Result: 173.823376 units²A regular octagon is a square with its four corners sliced off at 45°, and that cut is where the √2 comes from: area = 2(1+√2)s², about 4.828 times the side squared. A side of 6 gives 173.82 square units. Enter the side, not the width across the flats.
Worked examples
Case 2
- Side length
- 1
4.828427
Open with these valuesCase 3
- Side length
- 10
482.842712
Open with these valuesHow it's calculated
A = 2 × (1 + √2) × s²
- StepMeasure one side — in a regular octagon all eight are equal.
- StepEnter it in any length unit; do not enter the flat-to-flat width.
- ResultRead the area in the square of that unit.
Reference table
| Side | Perimeter, apothem, circumradius | Area |
|---|---|---|
| 0.5 | 4, 0.603553, 0.653281 | 1.207107 |
| 1 | 8, 1.207107, 1.306563 | 4.828427 |
| 2.5 | 20, 3.017767, 3.266407 | 30.177670 |
| 6 | 48, 7.242641, 7.839378 | 173.823376 |
| 10 | 80, 12.071068, 13.065630 | 482.842712 |
Questions
How do I calculate the area of a regular octagon?
Multiply 2 × (1 + √2) — about 4.828 — by the side length squared. For a side of 6 that is 4.828 × 36 ≈ 173.823376 square units. The (1 + √2) factor comes from treating the octagon as a square with its corners cut off.
Do I enter the side or the width across the flats?
The side, meaning one of the eight equal edges. The flat-to-flat width is twice the apothem and about 2.414 times the side, so entering it would inflate the area by nearly six times.
What is the difference between the apothem and the circumradius?
The apothem is the distance from the centre to the middle of a side, ((1+√2)/2) × s, and is the radius of the largest circle that fits inside. The circumradius is the distance from the centre to a corner, (√(4+2√2)/2) × s, the radius of the smallest circle around it. For a side of 6 they are about 7.242641 and 7.839378.
How do I find the perimeter of an octagon?
A regular octagon has eight equal sides, so the perimeter is simply 8 × s. For a side of 6 it is 48 — the length of edging or trim you would run all the way around.
What units does the octagon calculator use?
Any length unit you like. Enter the side in centimetres and the area comes back in square centimetres; enter it in inches and you get square inches.
Sources and last check
Information, not professional advice.