Regular Polygon Calculator
Find a regular polygon’s area, perimeter, apothem, circumradius and angles from side count and length. Choose global length units and compare dimensions.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Divide the regular polygon into equal isosceles triangles around its center. Trigonometry gives the apothem and circumradius from one half-triangle. Area is half the perimeter times the apothem.
P=ns; apothem=s/[2tan(π/n)]; R=s/[2sin(π/n)]; A=P×apothem/2; interior angle=180°(n−2)/n
Worked example
A regular hexagon with side 5 cm has perimeter 30 cm, apothem about 4.33012702 cm, circumradius 5 cm and area about 64.9519053 cm². Each interior angle is 120°.
Assumptions and input details
All sides and all interior angles must be equal; this does not calculate arbitrary irregular polygons. Use a whole side count from 3 to 1000 and positive side length. The equal-scale diagram is displayed up to 100 sides; larger polygons retain the computed dimensions and conversion table. A vertex on the right defines the drawing orientation. Area unit conversions square the length factor.
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
Find a circle’s diameter, circumference and area from its radius. Choose regional length units and see a labeled circle and conversion table.
Calculate triangle area from base and perpendicular height or from three side lengths. Mix regional units and follow the area formula with a diagram.
Calculate a circular arc, sector area and chord from radius and central angle. Mix angle and length units and view a sector diagram plus unit equivalents.
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