CalcaTools

Perimeter Of Polygon Calculator

Calculates perimeter of polygon using P = n × a, live in your browser.

Last updated: July 2026 · Free · No sign-up required

Results

Enter values above and click Calculate to see your result instantly.

What the Perimeter Of Polygon Calculator does

Every result on this page comes from a real formula — P = n × a; apothem = a ÷ (2tan(π÷n)); A = P × apothem ÷ 2 — computed live in your browser the moment you press the button.

Scroll past the calculator for a quick-reference table, a step-by-step methodology with a fully worked example, and answers to the questions people most often ask about perimeter of polygon calculator.

Quick reference

Polygon (side 5)PerimeterArea
Triangle (3)1510.83
Square (4)2025
Hexagon (6)3064.95
Octagon (8)40120.71

functions Shows the working, not just the answer

For students and teachers, the final number is only half the value. Every math tool here exposes the formula it applied, the intermediate steps, and the rounding rule, so you can follow along, check your homework, or use the answer in a proof or report with confidence.

calculate Accurate to the spec

Calculations use 64-bit floating point with sensible rounding for the domain (currency to 2 decimals, percentages to 4 decimals, algebra to 6 significant figures). Where exact rational arithmetic matters — fractions, factorials, simplification — we use a dedicated BigNumber path so 1/3 + 1/6 returns ½, not 0.49999.

school Free for classroom use

Educators are welcome to link to any math calculator on CalcaTools from a class site, Google Classroom, or worksheet. The pages are mobile-friendly, free, ad-supported (so we can keep them free) and have no sign-up wall — students just click and use them in class or at home.

tips_and_updates Pair with the spoke articles

Below the calculator we link a small set of plain-English explainer pages — "What is a percentage?", "Why does PEMDAS matter?", and so on. They cover the underlying concept in 4–6 short paragraphs. Read those before the calculator if the topic is new, or after if you want the extra context.

Interpretation guide

OutputMeaning
PerimeterTotal edge length — fencing/trim needed
ApothemCentre to edge midpoint — key to area
Interior angle(n−2)×180÷n — corner angle for cuts

Formula & methodology

Formula: P = n × a; apothem = a ÷ (2tan(π÷n)); A = P × apothem ÷ 2

  1. Enter the number of sides n (3 or more) and the side length a.
  2. Perimeter is simply n × a.
  3. The apothem a÷(2tan(π÷n)) and area P×apothem÷2 are computed for the same shape.
  4. The interior angle (n−2)×180÷n helps with mitre cuts.

Example: a hexagon with side 5 → P = 30, apothem 4.33, area 64.95, corners 120°.

Frequently asked questions

How do you find the perimeter of a polygon?
For a regular polygon, multiply the number of sides by the side length: a hexagon with 5-unit sides has P = 30. Irregular polygons need each side added individually.
What is an apothem?
The distance from the centre to the midpoint of a side. It is the “radius” used in the area formula A = perimeter × apothem ÷ 2.
Does this work for irregular polygons?
The perimeter formula n × a assumes equal sides. For irregular shapes, sum the individual side lengths — area then needs coordinates or triangulation.
What is the interior angle of my polygon?
(n − 2) × 180 ÷ n degrees: 60° for triangles, 90° for squares, 120° for hexagons, 135° for octagons. The tool reports it for your n.
Is this polygon calculator free?
Yes — free, no sign-up, instant results in your browser.
What's the fastest way to get a square's perimeter?
Multiply one side by 4 — a 15 ft side means 60 ft of fence line. Working backwards from area: side = √area, so a 225 sq ft square patio has 15 ft sides and a 60 ft perimeter. The same shortcut generalizes to any regular polygon: perimeter = side × number of sides.