Skip to main content
Book Consultation →
Shapes100% FreeInstant

Regular Polygon Calculator: Area, Perimeter and Angles

This free regular polygon calculator handles any polygon with equal sides and angles, such as a pentagon, hexagon or octagon. Enter the number of sides and the side length to get everything else.

By Debmedia Technologies LLP · Kolkata, India · Updated

What Is It and When Do You Need It?

Regular polygons appear in tiles, nuts and bolts, honeycombs and signs. Their area, angles and radii all follow from the number of sides and the side length.

Enter both values and read the whole set.

How to Use This Tool

  1. Enter the value or values asked for in the boxes.
  2. Choose the unit label if there is a choice.
  3. Press Calculate.
  4. Read every result in the table and copy what you need.

How the Calculation Works

Interior angle = (n − 2) × 180° ÷ n. Apothem = s ÷ (2 tan(π ÷ n)). Circumradius = s ÷ (2 sin(π ÷ n)). Perimeter = n × s. Area = ½ × perimeter × apothem. Diagonals = n(n − 3) ÷ 2.

Worked Example

A regular hexagon with side 2 has a perimeter of 12, an area of 10.3923, an apothem of 1.7321, a circumradius of 2, an interior angle of 120° and 9 diagonals.

Common Uses

  • Tiles and paving.
  • Nuts, bolts and gears.
  • Signs and logos.
  • Geometry homework.

Tips and Common Mistakes

  • A regular polygon with many sides looks like a circle.
  • The side length is for one side.
  • Use at least three sides.
  • Measure carefully: a small error in a length is squared in an area and cubed in a volume, so a 5 percent error in a side can become a 10 percent error in the area or a 15 percent error in the volume.
  • Round only at the end. If you copy a result into another calculation, copy the full number from the tool rather than a rounded one, so small errors do not build up.

Next, you may need the circle calculator, rhombus calculator, trapezoid calculator, rectangle calculator.

Everything runs in your browser. Nothing you type is uploaded, stored or sent to any outside service.

Frequently Asked Questions

A polygon with all sides equal and all angles equal, such as a square, a regular pentagon or a regular hexagon.
Area = n × s² ÷ (4 × tan(π ÷ n)), or half the perimeter times the apothem.
The distance from the centre to the middle of a side. The circumradius is the distance from the centre to a corner.
n × (n − 3) ÷ 2. A hexagon has 9.

Disclaimer: results are calculated in your browser from the numbers you enter. Check important results before you rely on them for money, health, safety or legal decisions.