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Regular Polygon Perimeter Calculator

Finding the perimeter of a regular polygon is straightforward once you know the side length and how many sides it has. Whether you're working with a triangle, square, hexagon, or any other regular polygon, the calculation follows the same principle. This calculator eliminates manual arithmetic and helps architects, engineers, students, and designers quickly determine total boundary length for planning and construction purposes.

Last updated: April 27, 2026

Creators Anna Szczepanek, PhD Mathematics

Reviewers Mateusz Mucha and Jasmine J. Mah

8,049 people find this calculator helpful

Perimeter Formula for Regular Polygons

A regular polygon has all sides of equal length and all angles equal. To find its perimeter, multiply the number of sides by the length of one side. For irregular polygons where sides vary, you sum all individual side lengths.

P = n × a

P — Perimeter of the polygon
n — Number of sides
a — Length of one side

How to Calculate Polygon Perimeter

The perimeter calculation depends on what information you have available:

Regular polygon: When all sides are identical, multiply the side length by the total number of sides. An octagon with 17-inch sides, for example, has a perimeter of 17 × 8 = 136 inches.
Irregular polygon: Add the lengths of every individual side together. If sides measure 5, 7, 6, and 8 units, the perimeter equals 26 units.
Polygon defined by coordinates: Calculate the distance between consecutive vertices using the distance formula, then sum all segments.

This approach works for any polygon—triangles, pentagons, decagons, or shapes with dozens of sides.

Common Polygon Types and Their Properties

Different polygons appear frequently in geometry, engineering, and design:

Triangle (3 sides): The simplest polygon; forms the basis for structural triangulation in bridges and buildings.
Square (4 sides): Equal sides and 90° angles; foundation of grid layouts and tile patterns.
Hexagon (6 sides): Appears in honeycombs, nuts, and bolts; efficient for space-filling tessellations.
Octagon (8 sides): Common in floor plans, stop signs, and architectural details.
Decagon (10 sides): Used in formal garden designs and mathematical demonstrations.

Practical Tips for Perimeter Calculations

Avoid common mistakes and work more efficiently when measuring and calculating polygon boundaries.

Verify measurement units before calculating — Ensure all side lengths use the same unit—converting 17 feet and 200 inches separately will produce nonsensical results. Convert everything to metres, feet, or centimetres first, then apply the formula.
Distinguish regular from irregular polygons — Regular polygons have one formula; irregular ones require summing individual sides. Misidentifying polygon type is the most frequent error. Check whether all sides and angles are genuinely equal before simplifying.
Account for rounding in coordinate-based calculations — When deriving side lengths from vertex coordinates, small rounding errors accumulate. Keep three to four decimal places during intermediate steps to minimise final error, especially with many-sided polygons.
Double-check your side count — Miscounting sides ruins the calculation. For unfamiliar shapes, sketch the polygon or count vertices twice independently before multiplying.

Real-World Applications

Perimeter calculations serve practical purposes across multiple fields:

Construction and landscaping: Determining fencing length, edging material, or concrete trim for irregular garden beds or building foundations.
Manufacturing: Computing the length of material needed to frame or seal polygon-shaped components in machinery or product design.
Urban planning: Calculating boundary lengths for park layouts, traffic islands, or building footprints in city design projects.
Textiles and crafts: Estimating binding, trim, or edging required for polygon-shaped quilts, rugs, or decorative items.
Mathematics and physics: Studying relationships between perimeter, area, and other geometric properties in academic research.

Frequently Asked Questions

What's the difference between perimeter and area of a polygon?

Perimeter measures the total distance around the outside edge of a shape, calculated by summing side lengths. Area measures the space enclosed inside the polygon, typically in square units. A rectangle might have a 20-metre perimeter but only 24 square metres of area. Both are essential for different purposes—perimeter for fencing or framing, area for flooring or land coverage.

Can you find a polygon's perimeter if you only know its area?

Generally no. Many polygons can have the same area but very different perimeters. A long, thin rectangle and a nearly square rectangle might enclose the same area yet require different amounts of fencing. Conversely, many shapes can share the same perimeter with different areas. You need either side lengths or vertex coordinates to calculate perimeter.

How do you find the perimeter of a regular polygon from its radius?

If you know the circumradius (radius from centre to vertex), you can derive the side length using trigonometry. For a regular polygon with n sides and circumradius R, the side length is 2R × sin(π/n). Once you have the side length, multiply by n to get the perimeter. This approach is common in geometric construction and design work where radii are easier to measure than individual sides.

Why is perimeter important for regular hexagons?

Hexagons tile perfectly without gaps, making them extremely efficient in nature and industry. Calculating perimeter helps determine material quantities for honeycomb structures, pipe fittings, architectural elements, and tessellated surfaces. Understanding hexagon perimeter also supports structural analysis—perimeter relates directly to the forces acting on polygon boundaries under stress.

What happens to perimeter when you scale a polygon?

Scaling changes perimeter proportionally. If you double all side lengths, the perimeter doubles. If you scale by a factor of 0.5, the perimeter halves. Area, however, scales with the square of the linear factor—doubling sides quadruples the area. This distinction is crucial in architecture and manufacturing when enlarging or reducing designs.

Can an irregular polygon have the same perimeter as a regular polygon with the same number of sides?

Yes. Perimeter depends only on the sum of side lengths, not their arrangement. An irregular triangle with sides 3, 4, and 5 units has a perimeter of 12, just like an equilateral triangle with sides of 4 units each. However, the two shapes enclose different areas and have different angle measurements, demonstrating that perimeter alone doesn't fully define a polygon's shape.

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