Polygon Vertex Calculator

Build vertex lists from sides, radius, center, and rotation. Download tables and check key measures. Use this page for clean polygon coordinate analysis work.

Enter Polygon Details

Example Data Table

Polygon Sides Input Type Input Value Center Rotation Key Output
Triangle 3 Circumradius 5 (0, 0) 3 vertices with equal spacing
Hexagon 6 Circumradius 10 (0, 0) 30° 6 vertices, side length 10
Octagon 8 Apothem 12 (2, -1) 15° 8 vertices with shifted center

Formula Used

This calculator builds a regular polygon from one size input and a center point.

  • Angle step: 2π / n
  • Vertex angle: rotation + i × angle step
  • X coordinate: centerX + R × cos(angle)
  • Y coordinate: centerY + R × sin(angle)
  • Side length from circumradius: 2R × sin(π / n)
  • Apothem: R × cos(π / n)
  • Perimeter: n × side length
  • Area: (Perimeter × Apothem) / 2
  • Interior angle: ((n - 2) × 180) / n
  • Diagonals: n(n - 3) / 2

When you enter side length or apothem, the page first converts that value into circumradius. Then it generates every vertex in order.

How to Use This Calculator

  1. Enter the number of sides for the regular polygon.
  2. Select the size mode. Use circumradius, side length, or apothem.
  3. Type the numeric size value.
  4. Set the center coordinates for the polygon.
  5. Enter the rotation angle in degrees.
  6. Choose clockwise or counterclockwise ordering.
  7. Set the decimal precision and optional vertex label prefix.
  8. Press the calculate button to view the result summary and vertex table.
  9. Use the CSV and PDF buttons to export the vertex data.

Polygon Vertex Calculator Guide

Why Vertex Coordinates Matter

A polygon vertex calculator helps you map exact corner points. This is useful in geometry, drafting, coding, and classroom practice. Regular polygons follow a repeating structure. That makes them perfect for coordinate generation, angle checks, and shape analysis.

What This Tool Calculates

This page calculates regular polygon vertices from a chosen size input. You can start with circumradius, side length, or apothem. The calculator also uses a custom center point and a rotation value. That means you can place the shape anywhere on the plane.

After submission, the tool returns each vertex coordinate in order. It also shows side length, perimeter, area, interior angle, exterior angle, and diagonal count. These values support coordinate geometry work and polygon design tasks.

Why Rotation and Center Inputs Help

Many basic tools only draw a shape around the origin. This calculator does more. You can shift the polygon to any center location. You can also rotate the figure to match a layout, diagram, or graphing need. That saves time when you build models or verify points.

Useful for Math and Applied Work

Students can use this calculator to study regular polygons and angle patterns. Teachers can create clean examples for lessons. Developers can generate vertex lists for canvas work, SVG paths, or game objects. Engineers and designers can check layout symmetry before deeper modeling.

Better Data Handling

The export options make the tool practical. Use CSV when you need spreadsheet analysis. Use PDF when you need a clean record for a report or worksheet. The example table also helps new users understand valid inputs before they calculate.

Clear and Reliable Results

A good polygon vertex calculator should be simple and exact. This page keeps the workflow direct. You enter the inputs once. The result appears above the form. Then you can review every coordinate and key measure in one place. That supports fast, accurate polygon analysis.

FAQs

1. What does this polygon vertex calculator compute?

It computes the vertex coordinates of a regular polygon. It also returns side length, apothem, perimeter, area, diagonal count, and angle measures from the values you enter.

2. Can I use side length instead of radius?

Yes. Choose the side length option in the form. The calculator converts that value into circumradius first, then generates all vertex points from the converted radius.

3. What is the difference between circumradius and apothem?

Circumradius runs from the center to a vertex. Apothem runs from the center to the midpoint of a side. Both are useful for defining a regular polygon.

4. Why does rotation change the coordinates?

Rotation turns the polygon around its center. The side lengths stay the same, but every vertex shifts to a new coordinate position based on the entered angle.

5. Can I move the polygon away from the origin?

Yes. Enter any center X and center Y values. The calculator uses those values as the polygon center and places every vertex around that point.

6. What does clockwise or counterclockwise mean here?

It controls the order of the listed vertices. Counterclockwise follows the standard positive angle direction. Clockwise reverses the order around the same polygon.

7. What is the diagonal formula for a polygon?

The diagonal count for a polygon is n(n - 3) / 2. This works for any simple polygon with three or more sides.

8. Can I export the calculated vertex table?

Yes. Use the CSV button for spreadsheet data or the PDF button for a portable file. Both export the vertex table shown in the result section.

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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.