Geometry
Polygon Area Calculator
Specify the side length and number of sides to get a regular polygon’s area, perimeter, apothem, circumradius, and interior/exterior angles.
Enter the number of sides and a side length to get area, perimeter, apothem, and interior/exterior angles.
Regular polygon formulas
Perimeter = n·s Apothem = s / [2·tan(π/n)] Area = ½ · Perimeter · Apothem
n is the number of sides (≥3) and s is the side length. Interior angle = (n − 2)·180° / n while the exterior angle is 360° / n.
How to use
- Enter how many equal sides the polygon has (triangle = 3, hexagon = 6, etc.).
- Provide the side length using any unit.
- Review area, perimeter, apothem, circumradius, and the interior/exterior angles.
Example
Input: n = 8, side length = 5 cm
Output: Area ≈ 120.7 cm², Perimeter = 40 cm, Apothem ≈ 4.14 cm, Interior angle = 135°
Student-friendly breakdown
This walkthrough emphasizes the most searched ideas for Polygon Area Calculator: Polygon Area Calculator. Start with the formula above, then follow the guided steps to double-check your work. For quick revision, highlight the givens, plug into the equation, and finish by verifying your units.
Need more support? Use the links below to open the long-form guide, browse additional examples, or hop into adjacent calculators within the same topic — each one is a quick way to double-check your work or handle a related question without starting from scratch.
Deep dive & study plan
Polygon Area Calculator: Area, perimeter, apothem, and angles for any regular polygon. It's built around regular polygon, area, perimeter, so you can go from a raw question to a checked answer without switching tools.
The math behind it: n is the number of sides (≥3) and s is the side length. Interior angle = (n − 2)·180° / n while the exterior angle is 360° / n. The core relationship is Perimeter = n·s Apothem = s / [2·tan(π/n)] Area = ½ · Perimeter · Apothem, shown above the calculator so you can see exactly how your inputs turn into the result.
To use it well: (1) Enter how many equal sides the polygon has (triangle = 3, hexagon = 6, etc.). (2) Provide the side length using any unit. (3) Review area, perimeter, apothem, circumradius, and the interior/exterior angles. Keep your units consistent as you go, and re-run a case you already know the answer to — it's the fastest way to catch a typo before it throws off a result you're relying on.
Worked example: entering n = 8, side length = 5 cm returns Area ≈ 120.7 cm², Perimeter = 40 cm, Apothem ≈ 4.14 cm, Interior angle = 135°. Try swapping in your own numbers next, especially a case you're unsure about, before you use this for something that matters.
Quick retention checklist
- Speak the formula aloud (or annotate it) so the relationships stick.
- Write each step in your own words and compare with the numbered list above.
- Swap in new numbers for the Example to make sure the calculator (and your logic) handles edge cases.
- Check at least one related calculator below — it's the fastest way to confirm your numbers still line up from a different angle.
FAQ & notes
Does this work for irregular polygons?
No. The formulas assume every side and angle is identical. For irregular polygons use coordinate-based area methods instead.
Can I enter radius instead of side length?
This tool expects side length. Convert radius to side length first using s = 2r · sin(π/n) if needed.
What formula does the Polygon Area Calculator use?
n is the number of sides (≥3) and s is the side length. Interior angle = (n − 2)·180° / n while the exterior angle is 360° / n.
How do I use the Polygon Area Calculator?
Enter how many equal sides the polygon has (triangle = 3, hexagon = 6, etc.). Provide the side length using any unit. Review area, perimeter, apothem, circumradius, and the interior/exterior angles.