Example 1
- n = 3
180
What is the angle sum in a triangle? 180°. (n − 2)×180 at n = 3.
Sum of polygon angles
Type the number of sides n. The sum of interior angles is (n − 2)×180°. A triangle, n = 3, gives 180°. A quadrilateral, n = 4, gives 360°. A hexagon, n = 6, gives 720°.
The calculator computes the sum of all interior angles, not one angle. n = 2 gives 0. n = 1 gives −180, because that is (n − 2)×180.
Results
Enter data and click Calculate.
How it works
A convex polygon splits into n − 2 triangles. Each triangle brings 180°, so the sum is (n − 2)×180°. n = 3 leaves one triangle, 180°. n = 4 leaves two, 360°. n = 6 leaves four, 720°.
The field is the side count n. This is not one angle and not the number of diagonals. A pentagon, n = 5, gives 540°. The result is 540, with no degree sign in the result field.
n = 2 gives 0. n = 1 gives −180. The formula does not stop. On paper that drawing is not a polygon. A fractional n also passes.
The number of diagonals is on the neighbouring page and from the same n counts strokes. The third angle in a triangle from two known angles is another calculator: there 180 − α − β, not (n − 2)×180.
The header units switch does not multiply anything. 4 stays 360 whatever the label says.
n = 3 gives 180. n = 4 gives 360. n = 6 gives 720. That is the whole card: one n and a sum in degrees. Angle sum uses the number of sides.
Formula
S = (n − 2) × 180°
How to use
- Type the number of sides, for example 4.
- Click Calculate. The angle sum is 360°.
- n = 3 gives 180°. n = 6 gives 720°.
- n = 2 gives 0. n = 1 gives −180, because that is the formula.
- The number of diagonals from the same n lives on the neighbouring card.
n = 4 gives 360°
The sum of polygon angles is (n − 2)×180°. n = 3 gives 180°. n = 4 gives 360°. n = 6 gives 720°.
- angles
- The interior sum. 3 gives 180. 4 gives 360. 6 gives 720.
- sides
- Field n. 5 gives 540. 2 gives 0, because n − 2 is zero.
- polygon
- A figure with n sides. Here a sum of degrees, not the number of diagonals.
Examples
Example 2
- n = 4
360
What is the angle sum in a quadrilateral? 360°.
Example 3
- n = 6
720
What is the angle sum in a hexagon? 720°.
Related calculators
Common questions
What is the angle sum at n = 3?
180°. One triangle in the split.
What does the sum of polygon angles mean?
The sum of interior angles. (n − 2)×180°. n = 4 gives 360°.
What about n = 4 and n = 6?
360° and 720°.
What about n = 5?
540°. Three triangles in the split.
Is this one angle?
No. The whole sum. One angle of a regular polygon is that sum over n, not this card.
What about n = 2?
0. (2 − 2)×180 = 0. On paper that is not a polygon.
How is this different from the third angle in a triangle?
Here from n. There from two known angles: 180 − α − β.
How is this different from the number of diagonals?
Degrees here. There n(n − 3)/2 strokes.
Does n have to be an integer?
School wants an integer. The calculator will also multiply 4.5.
Does a comma in 6.0 work?
Yes. 6 and 6.0 give 720.
Knowledge sources
The calculator computes the same formula as the definition below.
Page updated in 2026.