Calculator Form
Choose a method, enter values, and press calculate. The result appears above this form under the page header.
Plotly Graph
The chart updates after calculation and visualizes the entered or derived angle values.
Formula used
1) Sum of interior angles: For any simple polygon with n sides, the total is (n - 2) × 180°.
2) Each interior angle of a regular polygon: Divide the total sum by the number of sides, so ((n - 2) × 180°) ÷ n.
3) Interior from exterior: A straight line measures 180°, so Interior angle = 180° - Exterior angle.
4) Missing interior angle: Subtract the sum of known interior angles from the polygon total. The remainder is the missing angle or remaining angle total.
How to use this calculator
- Select the calculation mode that matches your problem.
- Enter the number of sides when the method requires polygon size.
- Provide the total sum, exterior angle, or known angles as needed.
- Choose how many decimal places you want in the output.
- Click the calculate button to show the result above the form.
- Review the step-by-step working and the chart for validation.
- Use the export buttons to save the result as CSV or PDF.
Example data table
| Polygon | Sides | Total Interior Sum (°) | Each Interior Angle (Regular) (°) | Each Exterior Angle (°) |
|---|---|---|---|---|
| Triangle | 3 | 180 | 60 | 120 |
| Quadrilateral | 4 | 360 | 90 | 90 |
| Pentagon | 5 | 540 | 108 | 72 |
| Hexagon | 6 | 720 | 120 | 60 |
| Octagon | 8 | 1080 | 135 | 45 |
Frequently asked questions
1) What is an interior angle?
An interior angle is the angle formed inside a polygon where two sides meet. Every polygon has one interior angle at each vertex, and their total depends on the number of sides.
2) How do I find the sum of interior angles?
Use the formula (n - 2) × 180°, where n is the number of polygon sides. This gives the total of all interior angles for any simple polygon.
3) How do I find one interior angle of a regular polygon?
First find the total interior angle sum. Then divide that value by the number of sides. Because all angles are equal in a regular polygon, the result is the measure of each interior angle.
4) What is the relation between interior and exterior angles?
An interior angle and its adjacent exterior angle form a straight line. Their measures add to 180°, so you can find one by subtracting the other from 180°.
5) Can this calculator solve a missing interior angle?
Yes. Enter the polygon side count and the known interior angles. The calculator subtracts the known total from the polygon sum and returns the missing angle or the remaining angle total.
6) Why does my entered total sum show a warning?
If your entered sum does not match the standard polygon sum formula, the calculator shows a warning. That usually means the side count, angle total, or polygon assumption needs checking.
7) Does this work for irregular polygons?
Yes, for total-sum and missing-angle analysis. Irregular polygons still follow the same total interior angle formula, although individual angles are not all equal like a regular polygon.
8) What can I export from this page?
You can export the calculated result summary as a CSV file or save the result block as a PDF. This is useful for homework, worksheets, project notes, and quick records.