Interior Angles Calculator

Measure polygon interior angle sums quickly today online. Compare regular, exterior, and central angle measures. Enter sides or known angles for dependable geometry results.

Enter Polygon Details

Each angle, exterior angle, central angle, and diagonals are calculated.

Enter all known angles except one to solve the missing value.

Formula Used

Interior angle sum: S = (n - 2) × 180°

Each regular interior angle: A = S ÷ n

Each exterior angle: E = 360° ÷ n

Central angle: C = 360° ÷ n

Diagonal count: D = n(n - 3) ÷ 2

Missing angle: M = S - sum of known angles

Here, n means the number of polygon sides.

How to Use This Calculator

  1. Enter the number of sides. Use at least three sides.
  2. Select degrees, radians, or gradians.
  3. Enter known interior angles when solving a missing angle.
  4. Leave the known angle box empty for regular polygon values.
  5. Select decimal places for rounded results.
  6. Press the calculate button.
  7. Review the result above the form.
  8. Use CSV or PDF buttons to save the result.

Example Data Table

Sides Polygon Interior Sum Regular Interior Angle Exterior Angle Diagonals
3 Triangle 180° 60° 120° 0
4 Quadrilateral 360° 90° 90° 2
5 Pentagon 540° 108° 72° 5
6 Hexagon 720° 120° 60° 9
8 Octagon 1080° 135° 45° 20

Interior Angles Calculator Guide

An interior angle sits inside a polygon. It is formed where two sides meet. This calculator helps you study that angle with less guesswork. You can enter the number of sides for any polygon. You can also enter known angles when one value is missing.

Why Interior Angles Matter

Interior angles explain the shape of triangles, squares, pentagons, and larger polygons. They help students solve geometry homework. They also help designers check layouts, tiles, frames, panels, and simple drafting plans. A correct angle sum prevents wrong shapes and uneven joints.

What This Tool Calculates

The tool finds the interior angle sum. It also finds one angle of a regular polygon. It gives the exterior angle, central angle, and diagonal count. When you provide a list of known angles, it compares their total with the required polygon sum. If one angle is missing, the tool shows the needed value.

Regular And Irregular Polygons

A regular polygon has equal sides and equal interior angles. Its single interior angle is easy to find after the total sum is known. An irregular polygon may have different angles. For those shapes, the total still follows the same formula, but each angle can be different.

Helpful Geometry Checks

Use the result as a check before submitting work. If the entered known angles are greater than the required sum, the shape is not possible with those values. If the remaining angle is positive, the missing value can complete the polygon. The calculator also shows whether a regular polygon angle is convex.

Practical Uses

Interior angle work appears in school geometry, pattern making, architecture, woodworking, and game design. Regular polygon values support wheels, icons, signs, tables, and floor patterns. Missing angle checks are useful when diagrams hide one value. The calculator keeps each step visible, so the method is easier to learn and repeat.

Best Input Tips

Choose a side count of at least three. For regular polygons, leave the known angle box empty. For missing angle work, type angles with commas. Use the same unit shown in your problem. Degrees are most common. Radians and gradians help when advanced courses require alternate angle units. Review the step summary before downloading your report safely.

FAQs

What is an interior angle?

An interior angle is the angle inside a polygon where two sides meet. Every polygon has one interior angle at each vertex.

How do I find the interior angle sum?

Use S = (n - 2) × 180°. The variable n means the number of sides in the polygon.

Can this calculator solve a missing angle?

Yes. Enter all known interior angles except one. The calculator subtracts their sum from the required polygon angle sum.

Does it work for irregular polygons?

Yes. The total interior angle sum works for both regular and irregular polygons with the same side count.

What is a regular polygon angle?

It is one interior angle of a polygon with equal sides and equal angles. The calculator divides the total sum by sides.

What angle units are supported?

The calculator supports degrees, radians, and gradians. Enter known angles using the same selected unit.

Why is the exterior angle included?

The exterior angle helps check regular polygon results. For a regular polygon, each exterior angle equals 360° divided by sides.

Can I download my result?

Yes. After calculation, use the CSV or PDF buttons shown in the result area above the form.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.