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A regular polygon's area depends on more than just its side length — it also needs the apothem (the distance from the center to the midpoint of a side), which itself depends on how many sides the polygon has.
This calculator finds a regular polygon's area, perimeter, and apothem from its number of sides and side length.
How it works
Enter the number of sides and the side length. The calculator finds the apothem using a tangent-based formula, then uses the apothem and perimeter together to find the total area.
- Enter number of sides.
- Enter side length.
- Click Calculate to see your results.
Examples
Regular hexagon, side 5
A regular hexagon with side length 5 has a perimeter of 30, an apothem of about 4.33, and an area of about 64.95.
Who should use it
- Finding the area of a regular polygon-shaped floor, garden bed, or design element.
- Checking regular polygon geometry coursework.
Industry applications
- Geometry education
- Architecture, design, and construction (regular polygon layouts)
Advantages
- Calculates area, perimeter, and apothem together from just two inputs.
- Works for any number of sides, from triangles up to very high side counts.
Limitations
- Only valid for regular polygons — irregular polygons need a different calculation approach entirely.
Common mistakes to avoid
- Applying this tool's formulas to an irregular polygon, where they don't hold — regularity (equal sides and angles) is a strict requirement.
- Confusing the apothem with the circumradius (distance from center to a vertex, not a side's midpoint) — they're related but different measurements.
Best practices
- Confirm your polygon is actually regular (equal sides and angles) before relying on this calculator's area and apothem results.
Tips
- As the number of sides increases, a regular polygon's shape approaches a circle, and its area approaches πr² — a useful sanity check when working with very high side counts.