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Enter the number of sides and side length to quickly calculate the area of any regular polygon. Ideal for geometry students and engineering calculations.
Overview
Understand what the tool solves, how it works, and the boundaries of its data.
Enter the number of sides, n, and the length of one side, a. The calculator returns area and perimeter. It assumes a regular polygon: every side has the same length and every interior angle is equal. The side count must be at least three, and the side length must be positive.
The shape’s orientation does not affect these measurements. The calculator does not ask for vertex coordinates, separate edge lengths, or an apothem, so it cannot determine the area of an arbitrary irregular outline.
Area = n × a² ÷ (4 × tan(π ÷ n))
Perimeter = n × a
Here π/n is half the central angle between neighboring vertices. Dividing the polygon into n congruent triangles gives the area expression above; equivalently, area is half the perimeter times the apothem. The calculator uses the side-based form, so you do not need to find the apothem separately.
For a regular pentagon with side length 10 units, the perimeter is 50 units and the area is approximately 172.0477 square units. The result retains the unit implied by your input: inches produce square inches for area, feet produce square feet, and so on. No unit conversion is applied.
Guide
Follow the workflow and verify inputs and outputs with practical examples.
Enter a whole-number count of three or more. Although the field accepts numeric text, decimal values are read as an integer; enter an integer explicitly to avoid an unintended shape.
Use a positive length. Choose a unit such as inches, feet, centimeters, or meters for your own interpretation; the calculator does not attach or convert units.
Read the main area result and the additional perimeter result. Both are shown to four decimal places, so rounded display values may not preserve every digit in later calculations.
Use cases
See how the tool fits into real work and everyday tasks.
A student can compare the area and perimeter of regular shapes while changing the side count or side length, then verify the formula by hand.
A designer or craft planner can estimate material area for a regular tile or panel when all edges and angles are equal, while keeping the original measurement unit consistent.
A reviewer can enter a documented side count and edge length to cross-check a regular polygon’s stated area and perimeter before using those figures elsewhere.
Q&A
Find concise answers to common questions and confusing cases.
No. It calculates only a regular polygon from a single side length and side count. An irregular shape needs additional information, such as its vertices or a suitable decomposition.
No. It returns area and perimeter. The area formula accounts for the apothem mathematically, but the page does not display it as a separate result.
The calculator has no unit selector. Its numbers inherit your chosen input unit, and the area is in that unit squared. Keep units consistent when comparing results.
Notes
Review scope, result limitations, and important precautions before use.
The formula is exact for a regular polygon, while the displayed decimal is rounded to four places. If the real shape has unequal sides or angles, or if dimensions are estimates, this result may not describe it. Confirm that every input uses the same length unit before interpreting the area or perimeter.
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