Area Calculator
Area and perimeter for ten shapes, with the formula and the working.
Geometry Calculators
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Regular Polygon Calculator
Area, angles and radii of any regular polygon.
Regular Polygon Calculator tool
Three or more.
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Area
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Perimeter
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Interior angle
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Apothem
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Circumradius
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About the Regular Polygon Calculator
Regular Polygon Calculator gives every measurement of an equal-sided, equal-angled polygon from the number of sides and one side length. The area comes from the perimeter times the apothem over two, which is the general formula every regular polygon obeys and which reduces to the familiar ones for a square or a triangle.
The apothem is the distance from the centre to the middle of a side, and the circumradius the distance to a corner. Both are needed in practice: the apothem for fitting a shape inside a space, the circumradius for setting one out from a centre point. For a regular hexagon the circumradius equals the side length exactly, which is why hexagons tile so conveniently.
The interior angle formula is worth knowing on its own: (n-2) times 180, divided by n. It follows from the fact that any polygon can be cut into n-2 triangles, each contributing 180 degrees. The exterior angles are simpler still -- they always sum to 360, whatever the number of sides.
The page shows its working, not just its answer. Where there is a formula it is printed with your own numbers substituted in, so you can check the result rather than take it on trust -- which is the difference between a calculator you can use for something that matters and one you cannot.
Everything runs inside your browser. What you type is never uploaded, never logged and never stored, and the calculator keeps working if your connection drops after the page has loaded.
Looking for something this does not cover? FreeToolsZone.org is more free browser-based tools, organised by job, and it is worth a look if regular polygon calculator is only part of what you are working on.
How to use the Regular Polygon Calculator
- Choose measurement inThe fields below change to match what you pick, so only the figures that matter to your case are asked for.
- Enter number of sides and side lengthDecimals are fine, and thousands separators are accepted and ignored.
- Read the area, perimeter and interior angleThe figures update as you type. The Calculate button is there if you would rather press something, but nothing waits for it.
- Copy or check the resultCopy the summary with the copy button, or open the table to check it row by row and read the formula with your own numbers in it.
Features
- Shows area, perimeter, interior angle, apothem and circumradius together, so you are not running it twice
- A results table you can read across
- Prints the formula with your own figures substituted in
- Updates as you type, with no button to press and no page reload
- Copy the result in one click
- Free, no sign-up, and it runs entirely in your browser
Who uses this tool
The regular polygon calculator is used by writers, developers, students, marketers and anyone else who needs the job done once without installing software. Common cases include:
- Finding the area of a hexagonal or octagonal space
- Setting out a regular shape from a centre point
- Getting the interior angle for a mitre cut
- Working out how many sides a given angle implies
Frequently asked questions
What is the apothem?
The perpendicular distance from the centre of the polygon to the middle of any side. It is the inradius, and it is what the area formula needs.
What angle do I cut for a mitre?
Half the exterior angle. For a hexagonal frame the exterior angle is 60 degrees, so each mitre is 30.
Does this work for irregular polygons?
No. It assumes all sides and angles are equal. For an irregular shape, split it into triangles and add their areas.
Related tools
If the regular polygon calculator is not quite what you need, these other free tools solve closely related problems, and there are 16 more in geometry calculators.
Triangle Calculator
Triangle sides, angles, area and type from any three facts.
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Circle Calculator
Radius, diameter, circumference and area of a circle.
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Perimeter Calculator
Perimeter of rectangles, circles, triangles and polygons.
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Angle Converter
Convert angles between every common unit.
Geometry Calculators
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Checked and rebuilt on 2026-10-14. The method this calculator uses is described in the section above, and corrections go through the contact page.