Perimeter of Regular Octagon Calculator
Enter the side length of a regular octagon, or its apothem, circumradius or area, to find its perimeter.
Updated
Perimeter of Regular Octagon Calculator
Our Perimeter of Regular Octagon Calculator finds the total length around a eight-sided shape with equal sides and equal angles. Enter the side length, or switch to the apothem, the circumradius or the area, and it shows the perimeter with the working, the other octagon measurements and the perimeter in other units.
Quick answer
The perimeter of a regular octagon is P = 8 × s: a 6 cm side gives 48 cm.
- From the apothem: P = 16(√2 − 1) × a ≈ 6.627417 × a
- From the circumradius: P = 8√(2 − √2) × R ≈ 6.122935 × R
- From the area: P ≈ 3.640719 × √A
- Side from the perimeter: s = P ÷ 8
What Is a Regular Octagon?
A regular octagon is a polygon with eight equal sides and eight equal interior angles of 135°, like a stop sign. Its perimeter is the distance all the way around it: the sum of the eight sides. Because the sides are equal, one side is all you need.
Perimeter of a Regular Octagon Formula
+ s + s + s + s
P = 8 × s
- Measure one side. All eight sides are equal, say 6 cm.
- Multiply by 8. 8 × 6 = 48.
- Keep the unit. The perimeter is 48 cm, in the same unit as the side.
A perimeter is a length, so it is never in square units. Square units (cm², m²) are for the area of a regular octagon.
Octagon Perimeter Examples
| Side | Perimeter |
|---|---|
| 4 cm | 32 cm |
| 7.5 mm | 60 mm |
| 10 m | 80 m |
| 12 in | 96 in |
| 2.3 km | 18.4 km |
Doubling the side doubles the perimeter. (The area, by contrast, goes up four times.)
Perimeter From the Apothem
The apothem a runs from the centre to the middle of a side. In a regular octagon a = s(1 + √2) ÷ 2 ≈ 1.207107 × s, so the side is s = 2a(√2 − 1):
P = 16(√2 − 1) × a
P ≈ 6.627417 × a
a = 5 m: P ≈ 33.137 m
Twice the apothem is the width across the flats, w = s(1 + √2). So if you measured straight across from one side to the opposite side, P = 8(√2 − 1) × w ≈ 3.313708 × w.
Perimeter From the Circumradius
The circumradius R runs from the centre to a corner. Lines from the centre to every corner split a regular octagon into eight isosceles triangles with a 45° angle at the centre, so the side is s = 2R × sin 22.5° = R√(2 − √2):
P ≈ 6.122935 × R
R = 4 cm: P ≈ 24.49 cm
The octagon perimeter is a little shorter than the circle around it: about 6.122935 × R against 2π × R ≈ 6.283185 × R.
Perimeter From the Area
The area of a regular octagon is A = 2(1 + √2) × s² ≈ 4.828427 × s². Undo that to get the side, then multiply by 8:
A = 60 cm²: s ≈ 3.525 cm
P ≈ 8 × 3.525 ≈ 28.20 cm
In one step, P ≈ 3.640719 × √A. For the square root, the Square Root Calculator gives as many digits as you need.
Side Length From the Perimeter
Work backwards by dividing the perimeter by 8:
60 m ÷ 8 = 7.5 m
So 60 m of edging goes round a regular octagon with 7.5 m sides.
Common Mistakes
- Multiplying by 6. An octagon has 8 sides, so the factor is 8.
- Using square units. Perimeter is a length: 48 cm, not 48 cm².
- Mixing units. Convert every side to one unit before adding.
- Using 8 × s on an irregular octagon. If the sides differ, add all eight lengths.
- Using the apothem or radius as the side. Both are longer than a side (about 1.207 × s and 1.307 × s), so convert them first.
- Mixing up the two widths. Across the flats is s(1 + √2); corner to corner is the long diagonal, 2R. They give different perimeters.
Key Terms
- Perimeter
- Total length around the shape, P.
- Side
- Any of the eight equal edges, s.
- Apothem
- Centre to the middle of a side, a.
- Circumradius
- Centre to a corner, R.
- Width
- Across the flats, 2a = s(1 + √2).
How to Use the Perimeter of Regular Octagon Calculator
- Choose what you know. Pick Side, Apothem, Radius (the circumradius) or Area. Side is the usual choice; the others work the side out first.
- Enter the value. Type it, such as 6, and pick a unit if you want one (mm, cm, m, km, in, ft, yd or mi). Decimals and fractions such as 3/4 work.
- Read and copy the result. The perimeter appears as you type, with a drawing, the working, the side, apothem, circumradius, width, both diagonals, area and the perimeter in other units. Press Copy to copy it, or Clear or Esc to start again.
Example: an octagonal garden bed has 12 ft sides. Enter 12 and pick ft. The perimeter is 96 ft (29.2608 m), which is the length of edging you need.
Who Can Use This Calculator?
Frequently Asked Questions (FAQs)
How do you find the perimeter of a regular octagon?
Multiply the side length by 8. A regular octagon with 6 cm sides has a perimeter of 8 × 6 = 48 cm.
What is the formula for the perimeter of a regular octagon?
P = 8 × s, where s is the length of one side. It is the eight equal sides added together.
How do you find the perimeter of an octagon with the apothem?
Use P = 16(√2 − 1) × a, about 6.627417 × a. An apothem of 5 m gives a side of about 4.142 m and a perimeter of about 33.137 m.
How do you find the perimeter of an octagon from the radius?
Use P = 8√(2 − √2) × R, about 6.122935 × R, where R runs from the centre to a corner. A 4 cm radius gives a side of about 3.061 cm and a perimeter of about 24.49 cm.
How do you find the perimeter of an octagon from its area?
Find the side with s = √(A ÷ 4.828427), then multiply by 8. An area of 60 cm² gives a side of about 3.525 cm and a perimeter of about 28.20 cm.
How do you find the side of a regular octagon from its perimeter?
Divide the perimeter by 8. A perimeter of 60 m gives sides of 7.5 m.
What units is the perimeter of an octagon in?
The same length unit as the side, such as cm, m or ft. Perimeter is never in square units; those are for area.
Does P = 8 × s work for any octagon?
No. It only works for a regular octagon, where all eight sides are equal. For an irregular octagon, add the eight side lengths.
Is the Perimeter of Regular Octagon Calculator free?
Yes. It is completely free, needs no sign-up, and can be used as many times as you like.
Try our Perimeter of Regular Octagon Calculator to find the perimeter of any regular octagon from its side, apothem, circumradius or area, in any units.