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Polygon Perimeter Calculator | Find Perimeter From Side Length

Find the perimeter of any polygon — regular or irregular — from its side lengths, with interior angles for regular shapes. Enter the sides and get the total boundary length, ideal for fencing, framing and geometry.

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

info Perimeter Of Polygon Calculator

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info Educational

Includes the formula and step-by-step explanation so you understand the math, not just the answer.

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

lightbulb Worked example — edging for an octagonal garden bed

A gardener is building a regular octagonal raised bed with each side 3.5 ft long, and needs to buy metal edging for the perimeter plus the bed’s area for ordering soil.

Result: Perimeter = n × a = 8 × 3.5 = 28 ft. Apothem = a ÷ (2tan(π÷n)) = 3.5 ÷ (2 × tan(22.5°)) = 3.5 ÷ 0.8284 = 4.22 ft. Area = P × apothem ÷ 2 = 28 × 4.22 ÷ 2 = 59.1 ft². Each interior corner angle = (8−2) × 180 ÷ 8 = 135°.

What this means: 28 ft of edging covers the boundary with no waste calculation needed, and the 59 ft² area tells the gardener how much soil to order (about 2.2 cubic yards at 1 ft depth). The 135° interior angles matter if the bed corners are mitred rather than overlapped.

Formula & methodology

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

How polygon measurements are calculated

For a regular polygon, the perimeter is simply the side length multiplied by the number of sides. The apothem (centre to midpoint of a side) unlocks the area, and the interior angle helps with corner cuts.

  • Perimeter: P = n × a, where n is the side count and a is the side length.
  • Apothem = a ÷ (2 tan(π ÷ n)).
  • Area = P × apothem ÷ 2.
  • Interior angle = (n − 2) × 180° ÷ n.

Irregular polygons: the apothem and area formulas need a regular shape, but the perimeter is still the sum of every side — just add the individual lengths. Example: a regular hexagon with side 5 → perimeter 30, apothem 4.33, area 64.95, interior angles 120°.

Authoritative source: Wolfram MathWorld

Frequently asked questions

How do you find the perimeter of a polygon?
Enter the required values into the input fields and press the calculate button. The tool applies the formula P = n × a; apothem = a ÷ (2tan(π÷n)); A = P × apothem ÷ 2 and returns the result with a short explanation of each step, so you can check the working yourself.
What is an apothem?
The Perimeter Of Polygon Calculator is free, private, and accurate: it runs entirely in your browser (no uploads, no accounts), applies the standard calculation, and explains each step so you can verify the result. Calculates perimeter of polygon using P = n × a, live in your browser. There is no limit on usage, and it works on any device.
Does this work for irregular polygons?
Yes — the calculator accepts the side lengths of any polygon, regular or irregular, and sums them for the perimeter. For irregular shapes you enter each side length; for regular polygons you enter one side and the number of sides, and the tool multiplies. The distance-between-vertices mode also handles polygons defined by coordinates.
What is the interior angle of my polygon?
The interior angle sum of any n-sided polygon is (n − 2) × 180°. For a regular polygon, each interior angle is (n − 2) × 180° ÷ n: a regular hexagon has angles of 120° and a regular pentagon 108°. The calculator reports the per-angle value for regular polygons and the total angle sum for any polygon.
Can I mix units like feet and inches for the sides?
Convert everything to one unit first — 3 ft 6 in becomes 42 in or 3.5 ft — because the formulas add and multiply raw lengths. Mixing 3 ft with 6 in directly would treat them as 3 and 6 in the same unit, silently producing a wrong perimeter. Pick the smallest unit present to keep the numbers clean.
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.
How do I use the apothem result for a real project?
The apothem is the distance from the centre to the middle of a side, and it is the key to the area: area = perimeter × apothem ÷ 2. For a hexagonal patio with side 5 ft, the apothem of 4.33 ft gives 64.95 ft² — that is the number you use to order pavers or concrete.
Why does the calculator also show an interior angle?
The interior angle (n−2) × 180° ÷ n tells you each corner’s angle, which matters for cutting and joining. A hexagon’s 120° corners need 60° mitre cuts on each piece; an octagon’s 135° corners need 67.5° cuts. Without it, you’d be guessing the saw setting.
What is the smallest polygon this works for?
A triangle — three sides is the minimum for a closed polygon. With n = 3 the formulas still hold: a triangle with side 6 has perimeter 18, apothem 6 ÷ (2tan 60°) = 1.73, and area 18 × 1.73 ÷ 2 = 15.59. Below three sides there is no enclosed shape, so the calculation has no meaning.
How precise are the apothem and area results?
The formulas are exact for ideal regular polygons, and the arithmetic is carried at full double precision, so displayed results are correct to the shown decimals. The real-world limit is your measurement: a side measured to the nearest eighth of an inch carries about that much uncertainty into the area.

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