5 Sided Shape Angle Calculator

Solve regular and irregular five-sided angle problems confidently. Review steps and compare angle distributions visually. Use one page for quick checks and printable reports.

This Physics-focused tool helps evaluate regular and irregular five-sided angle sets, useful for path changes, frame layouts, sensor geometry, and motion-turn checks.

Calculator Form

Use regular mode for standard pentagon values, missing-angle mode to solve one blank interior angle, and full-check mode to validate a complete five-angle set.

Calculation Mode

Output Unit

Decimal Precision

Interior Angle 1

Interior Angle 2

Interior Angle 3

Interior Angle 4

Interior Angle 5

Input rule: This tool is designed for convex five-sided shapes. Interior angles must be greater than 0 and less than 180. The full interior sum must equal 540°.

Example Data Table

Scenario	Mode	Input Angles	Main Result
Standard pentagon panel	Regular pentagon summary	No manual angle entry needed	Interior 108°, exterior 72°, central 72°
Irregular frame check	Solve one missing interior angle	100°, 110°, 95°, 120°, blank	Missing interior angle = 115°
Sensor mount validation	Check full five-angle set	108°, 108°, 108°, 108°, 108°	Valid regular five-sided shape

Formula Used

1) Interior Angle Sum

For any n-sided polygon, the interior-angle sum is: S = (n - 2) × 180°. For a five-sided shape, S = (5 - 2) × 180° = 540°.

2) Missing Interior Angle

If four interior angles are known, the missing one is: Missing Angle = 540° - (A1 + A2 + A3 + A4).

3) Exterior Angle at Each Vertex

For a convex shape, the exterior angle at a vertex is: Exterior = 180° - Interior. The exterior-angle total should be 360°.

4) Regular Five-Sided Shape

In a regular five-sided shape, all interior angles are equal: 540° / 5 = 108°. Each exterior angle is 360° / 5 = 72°. The central angle is also 72°.

How to Use This Calculator

Choose a calculation mode based on your task.
Select degrees or radians for the final display.
Set the rounding precision you want.
For missing-angle mode, enter four interior angles and leave one blank.
For full-check mode, enter all five interior angles.
Click the calculate button to show the result above the form.
Review the summary cards, result table, and Plotly graph.
Use the CSV or PDF buttons to save the result.

FAQs

1) What is the interior-angle sum of a five-sided shape?

The interior-angle sum is always 540° for any simple five-sided polygon. This value comes from the polygon sum formula, not from side length.

2) What is each interior angle in a regular five-sided shape?

Each interior angle is 108°. A regular shape divides the 540° total equally across five identical vertices.

3) What is each exterior angle in a regular five-sided shape?

Each exterior angle is 72°. You can get it by dividing 360° by five or by subtracting 108° from 180°.

4) Can this tool solve one missing interior angle?

Yes. Enter four interior angles, leave one blank, and the calculator finds the missing value using the 540° total.

5) Why does the calculator offer radians?

Radians are useful in physics, simulation, and trigonometric modeling. The calculator converts degree results into radians for easier equation work.

6) Does this work for concave five-sided shapes?

This version is designed for convex checks. It expects each interior angle to stay between 0° and 180° for direct exterior-angle calculation.

7) What does the graph help me see?

The graph shows how interior and exterior angles are distributed across the five vertices. That makes irregularity easier to spot quickly.

8) Can I save the results for reports?

Yes. Use the CSV button for spreadsheets and the PDF button for printable summaries when documenting design checks or classroom work.