Geometry

Interior Angle Sum Calculator

Calculate the sum of interior angles of any polygon with this easy-to-use online tool. Just enter the number of sides and get instant results with visualization.

Calculate Interior Angle Sum

Enter the number of sides of your polygon to calculate the sum of its interior angles.

Polygon Visualization

Formula for Interior Angle Sum

The sum of the interior angles of a polygon is given by the formula:

$$ Sum = (n - 2) \times 180^\circ $$

Where n is the number of sides.

For a polygon with sides, the sum of the interior angles is: °.

Learn About Interior Angles of Polygons

In geometry, a polygon is a closed shape with straight sides. The interior angles are the angles inside the polygon at each vertex. The sum of these angles depends on the number of sides the polygon has. For example, a triangle (3 sides) has an interior angle sum of 180°, and a quadrilateral (4 sides) has 360°. This calculator helps you find this sum for any polygon. The formula (n-2) × 180° is derived by dividing the polygon into triangles. Each triangle contributes 180° to the total sum.

  • Triangle (3 sides): 180°
  • Quadrilateral (4 sides): 360°
  • Pentagon (5 sides): 540°
  • Hexagon (6 sides): 720°

Source: Wikipedia - Interior Angle

Frequently Asked Questions

What is the Interior Angle Sum Calculator?
The Interior Angle Sum Calculator is an online Geometry calculator. You enter your values, and it returns the answer with the steps shown so you can follow along.
How accurate is the Interior Angle Sum Calculator?
The solver uses a math engine that avoids the floating-point rounding errors you get from most hardware calculators. For typical homework and professional calculations, the results will match what you would get by hand.
Can I use the Interior Angle Sum Calculator for professional Geometry projects?
Yes. The math behind it is standard Geometry, so the results are reliable for professional use. That said, always double-check that your inputs are in the right format before relying on the output.
Why use the Interior Angle Sum Calculator instead of calculating by hand?
Manual calculation is slow and error-prone, especially with multiple steps. This tool does the arithmetic for you and shows each step, so you can catch mistakes before they carry forward.
How do I format my inputs for the Interior Angle Sum Calculator?
Type your numbers into the input fields. Leave out units and symbols unless a field specifically asks for them. The solver handles the rest.

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