Regular Polygon Area Calculator
Area, perimeter, apothem and angles of any regular polygon — pentagon, hexagon, octagon and more.
In short
Area, perimeter, apothem and angles of any regular polygon — pentagon, hexagon, octagon and more.
Formula: A = n s² ÷ (4 tan(π/n)); apothem = s ÷ (2 tan(π/n)); circumradius = s ÷ (2 sin(π/n)); interior angle = (n − 2) × 180° ÷ n.
What this calculator does
Area, perimeter, apothem and angles of any regular polygon — pentagon, hexagon, octagon and more. Formula, worked example, sources, FAQs and limitations included.
You enter number of sides n, side length s and unit (labels only — no conversion), and the regular polygon area calculator shows the answer along with the working, so you can check it or try other numbers.
The page shows the formula, a numeric worked example, and the assumptions that affect this math calculation.
Inputs and what they mean
- Number of sides n
- — 3 = triangle, 5 = pentagon, 6 = hexagon, 8 = octagon.
- Side length s
- — number value.
- Unit (labels only — no conversion)
- — choice value.
How to use it
- Enter each value in the unit shown next to the box (use the unit converter first if your numbers are in other units).
- Check the breakdown to see every intermediate step.
- Read the limitations before relying on the result.
Formula
Source: Wolfram MathWorld, Regular Polygon.
Regular means every side and every angle is equal.
A = n s² ÷ (4 tan(π/n)); apothem = s ÷ (2 tan(π/n)); circumradius = s ÷ (2 sin(π/n)); interior angle = (n − 2) × 180° ÷ n.
Inputs used: Number of sides n, Side length s, Unit (labels only — no conversion).
Worked example
Regular hexagon, side 2
- tan(π/6) ≈ 0.57735.
- Area = 24 ÷ (4 × 0.57735) ≈ 10.3923 cm².
Reading the result
The headline figure is the main answer. Any breakdown underneath shows the parts that make it up, so you can check the working and see what changes when you adjust an input.
Limitations and assumptions
- Regular convex polygons only.
- Star polygons are not supported.
- Exact mathematical relationships, rounded for display. Check units and rounding before using a result in graded, engineering or financial work.
- The result depends on the values you enter for this regular polygon area calculator; it does not supply missing rates, rules, prices, dates, or assumptions for you.
Reference: Wolfram MathWorld
Last reviewed:
Common questions
Does this work for irregular shapes?
No. All sides and angles must be equal.
What is the apothem?
The distance from the centre to the midpoint of a side; area also equals perimeter × apothem ÷ 2.
Which n gives an octagon?
Enter 8. A pentagon is 5 and a hexagon is 6.
How do I use the Regular Polygon Area Calculator?
Enter the required values for Number of sides n, Side length s, Unit (labels only — no conversion). The calculator applies the formula on this page and shows the main result with any supporting breakdown so you can check the arithmetic.
What formula does the Regular Polygon Area Calculator use?
A = n s² ÷ (4 tan(π/n)); apothem = s ÷ (2 tan(π/n)); circumradius = s ÷ (2 sin(π/n)); interior angle = (n − 2) × 180° ÷ n. The visible formula section above lists the calculation path and the edge cases the page handles, so the result can be checked without relying on the form alone.
Can the Regular Polygon Area Calculator be used for exact decisions?
Use it as a calculation aid, not as a substitute for checking the underlying rule, contract, policy, or professional advice that applies to your situation. When a result depends on local rules, personal details, prices, or dates, enter those values yourself and confirm them before acting.
Sources
Method based on Wolfram MathWorld.
Cite this page
Free Calculator. (2026, November 3). Regular Polygon Area Calculator. https://freecalculator.tech/tools/regular-polygon-area-calculator
"Regular Polygon Area Calculator." Free Calculator, 3 Nov. 2026, https://freecalculator.tech/tools/regular-polygon-area-calculator.
Regular Polygon Area Calculator — Free Calculator, https://freecalculator.tech/tools/regular-polygon-area-calculator
Related tools
Calculate percentages, proportions, and percentage change with a clear formula breakdown.
Calculate a value after a percentage increase and see the exact increase amount.
Calculate a value after a percentage decrease and see the exact reduction.