Polygon Angle Calculator
The interior angles sum to (n − 2) × 180°, and in a regular polygon each one is that divided by n. Exterior angles always total 360°, whatever n is.
Your numbers
Interior angle
135°
Exterior angle
45°
Sum of angles
1,080°
Formula
Interior angle = (Number of sides − 2) × 180 ÷ Number of sides
A regular octagon has 135° interior angles. As sides increase, each interior angle approaches 180°.
What to enter
| Input | Default | Accepted range |
|---|---|---|
| Number of sidesHow many sides the polygon has, counting from three. | 8 | 3 ~ 1,000 |
Step by step
Quick reference table
Results when only Number of sides changes and everything else stays put.
| Number of sides | Interior angle (°) | Exterior angle (°) | Sum of angles (°) |
|---|---|---|---|
| 4 | 90 | 90 | 360 |
| 6 | 120 | 60 | 720 |
| 8 | 135 | 45 | 1,080 |
| 12 | 150 | 30 | 1,800 |
| 16 | 157.5 | 22.5 | 2,520 |
What each result means
| Result | At default values |
|---|---|
| Interior angle (°)The interior angle at one corner of a regular polygon. | 135 |
| Exterior angle (°)How far you turn at a corner; they always add to 360°. | 45 |
| Sum of angles (°)All interior angles added up — (sides − 2) × 180°. | 1,080 |
Common mistakes
A regular octagon has 135° interior angles. As sides increase, each interior angle approaches 180°.
Glossary
- Number of sides
- How many sides the polygon has, counting from three.
- Interior angle
- The interior angle at one corner of a regular polygon.
- Exterior angle
- How far you turn at a corner; they always add to 360°.
- Sum of angles
- All interior angles added up — (sides − 2) × 180°.
Frequently asked questions
Q. How is Polygon Angle Calculator calculated?
Interior angle = (Number of sides − 2) × 180 ÷ Number of sides — The interior angles sum to (n − 2) × 180°, and in a regular polygon each one is that divided by n. Exterior angles always total 360°, whatever n is.
Q. Can you walk through an example?
With Number of sides 8, the answer is Interior angle 135°.
Q. What do I need to enter?
Enter Number of sides. The result recalculates as you type, and an empty box counts as zero.
Q. How much does the answer move if I change a number?
Changing only Number of sides moves the answer to Number of sides 4 → Interior angle (°) 90 and Number of sides 16 → Interior angle (°) 157.5. The table below lays out five steps.
Q. How are the numbers rounded?
Money is shown to the nearest whole unit, percentages to one decimal place and everything else to two. What you see is rounded; the calculation itself carries the unrounded value forward.
Q. Anything to watch out for?
A regular octagon has 135° interior angles. As sides increase, each interior angle approaches 180°.
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