Solve area from side length or radius. See perimeter, apothem, interior angle, and export tools. Simple layout keeps every step clear on every screen.
| Polygon | Sides (n) | Side Length | Formula | Area |
|---|---|---|---|---|
| Equilateral Triangle | 3 | 6 | n × s² / [4 × tan(π / n)] | 15.5885 square units |
| Regular Hexagon | 6 | 8 | n × s² / [4 × tan(π / n)] | 166.2769 square units |
| Regular Octagon | 8 | 5 | n × s² / [4 × tan(π / n)] | 120.7107 square units |
Using side length: A = n × s² / [4 × tan(π / n)]
Using perimeter and apothem: A = (P × a) / 2
Using circumradius: A = n × R² × sin(2π / n) / 2
Here, n is the number of sides, s is side length, P is perimeter, a is apothem, and R is circumradius.
Regular polygons have equal sides and equal angles. That symmetry makes area calculations predictable. Architects, students, estimators, and designers use these shapes often. Common examples include equilateral triangles, squares, pentagons, hexagons, and octagons. This calculator helps you find regular polygon area from side length, apothem, circumradius, or perimeter with apothem. It also returns perimeter, interior angle, exterior angle, central angle, and supporting dimensions. That saves time during geometry homework, layout planning, and quick measurement checks.
In real work, you do not always start with the same measurement. A floor plan may show side length. A technical sketch may list apothem. A circular layout may provide circumradius. Some geometry problems give perimeter with apothem. This tool handles each case in one place. You can switch methods and compare outputs fast. That makes it easier to verify results, catch entry mistakes, and understand how each formula connects to the same regular polygon.
The most common formula is A = n × s² / [4 × tan(π / n)]. Here, n is the number of sides and s is side length. Another useful formula is A = (P × a) / 2. In this form, P is perimeter and a is apothem. When circumradius is known, area can be found with A = n × R² × sin(2π / n) / 2. Because all formulas describe the same shape, the calculator converts values and shows matching geometry measures.
Accuracy improves when you pick the correct method and enter exact measurements. Round only after the final result when possible. Small rounding differences in side length or radius can change area noticeably, especially for polygons with many sides. For large values of n, a regular polygon begins to resemble a circle, but it is still not the same figure. Keep the side count correct. A wrong n value changes every angle, every length relationship, and the final area.
After calculation, review the result table carefully. Check that units stay consistent across every measurement. Area is always shown in square units. Perimeter and side length use linear units. Angles appear in degrees. The example data table can help you test the calculator with known values. You can also export the final output as CSV or PDF. That is useful for reports, classroom work, shop drawings, quotations, or project notes.
A regular polygon has equal side lengths and equal interior angles. Examples include an equilateral triangle, square, regular pentagon, and regular hexagon.
The best formula depends on your known measurement. Side length works well for textbooks. Perimeter with apothem works well for design and drafting problems.
You also need the number of sides. The apothem alone is not enough because different regular polygons can share the same apothem.
Enter any unit label you want, such as cm, m, in, or ft. The calculator displays area in square units automatically.
The side count controls every angle and length relationship. A pentagon, hexagon, and octagon with similar measurements still have different areas.
The apothem runs from the center to the midpoint of a side. The circumradius runs from the center to a vertex.
Yes. The formulas still work for large values of n. As the side count increases, the shape looks more like a circle.
Yes. After calculation, use the CSV or PDF buttons to save the output for homework, records, estimates, or project files.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.