Regular Octagon Calculator
Enter one known value for a regular octagon (all sides and angles equal), and this calculator will compute the rest.
What is an octagon?
An octagon is a polygon with eight sides. In geometry, calculators usually focus on the regular octagon, where each side has the same length and every interior angle is equal. Regular octagons are common in architecture, stop signs, decorative tiling, furniture design, and layout planning.
Because all the sides and angles are related, you only need one measurement to calculate many others: side length, perimeter, area, apothem, circumradius, and widths across flats/corners. That is exactly what this octagon calculator does.
Octagon formulas used by this calculator
For a regular octagon with side length s:
- Perimeter: P = 8s
- Area: A = 2(1 + √2)s²
- Apothem: a = s / (2tan(π/8))
- Circumradius: R = s / (2sin(π/8))
- Width across flats: 2a
- Width across corners: 2R
If your known value is not side length, the calculator first converts your input to s and then computes the rest.
How to use the octagon calculator
Step-by-step
- Choose the type of value you already know (side, perimeter, area, apothem, or circumradius).
- Enter a positive number in the input field.
- Optionally add a unit label (like cm, m, or in).
- Click Calculate to see all octagon dimensions.
The calculator validates your input and gives a clear result panel with all related dimensions.
Worked examples
Example 1: Given side length
Suppose side length is 10 cm. Then perimeter is 80 cm, and the area is approximately 482.84 cm². The apothem and circumradius are also computed automatically.
Example 2: Given area
If area is 500 m², the side length is found using s = √(A / (2(1 + √2))). From there, perimeter and other measures are immediate.
Where octagon calculations are useful
- Construction: measuring framing, decks, gazebos, and paving layouts.
- Interior design: custom rugs, ceiling details, and table tops.
- Manufacturing: machined parts, decorative plates, and tooling profiles.
- Education: learning polygon geometry and trigonometric relationships.
Common mistakes to avoid
- Using formulas for an irregular octagon (this tool is for regular octagons only).
- Mixing units (e.g., entering inches but interpreting output as centimeters).
- Entering negative or zero values.
- Confusing apothem with circumradius. The apothem reaches the midpoint of a side; the circumradius reaches a vertex.
Quick FAQ
Can I use this for an irregular octagon?
No. Irregular octagons need additional measurements and different methods.
Why does one number determine everything?
In a regular octagon, all sides and angles follow fixed geometric ratios. So one valid dimension uniquely defines the shape.
What if I only know diameter-like measurements?
If you know width across corners, divide by 2 to get circumradius. If you know width across flats, divide by 2 to get apothem, then use the calculator.