Polygon Angle Calculator
Enter the number of sides to get each interior angle of a regular polygon and the sum of all interior angles — and see why every extra side adds exactly 180°.
Each angle and the total at once
Enter the number of sides and the polygon angle calculator returns each interior angle of a regular polygon and the sum of all interior angles together.
Use whole sides
A polygon needs a whole number of at least 3 sides — a triangle is 3, a square 4, a hexagon 6. Fractions and counts below 3 are not polygons.
What does the polygon angle calculator do?
Interior angles from the side count
The polygon angle calculator turns a single number — how many sides a shape has — into two geometric facts. The first is the sum of the interior angles, the total of the angles at every corner, which depends only on the side count. The second is each interior angle of a regular polygon, the equal angle at every corner when all sides and angles match. A triangle's angles always add to 180°, a quadrilateral's to 360°, and each extra side adds another 180° to the total. It is the number behind tiling patterns, drafting regular shapes, and any design where corners must fit together cleanly.
Enter the number of sides to get each interior angle of a regular polygon and the sum of all interior angles instantly.
The sum of the interior angles is (n − 2) × 180°, where n is the number of sides. Each interior angle of a regular polygon is that sum divided equally among the n corners.
Each = (n − 2) × 180° / nTake a regular hexagon with 6 sides. The sum of its interior angles is (6 − 2) × 180° = 720°. Sharing that equally among the six corners gives 720° ÷ 6 = 120° for each interior angle. The same two steps work for any polygon: subtract 2 from the side count, multiply by 180° for the total, then divide by the side count for each angle of a regular shape.
The formula is exact, but a couple of practical points are worth keeping in mind.
Regular polygons and simple shapes only
The sum of the interior angles, (n − 2) × 180°, holds for any simple polygon — one whose sides do not cross — whether its angles are equal or not. The per-angle figure, however, assumes a regular polygon where every side and every angle is identical; an irregular polygon shares the same total but distributes it unevenly among the corners. The calculator also needs a whole number of at least 3 sides: there is no polygon with fewer than three sides or with a fractional side count.