Apothem of Regular Polygon Calculator
The Apothem of Regular Polygon Calculator finds the apothem — the distance from the center to the midpoint of a side — of a regular polygon, then uses it to compute the perimeter and area. The formula used is: Apothem = s / (2×tan(π/n)); Area = (perimeter × apothem) / 2 = (n×s×apothem)/2.
Formula
Apothem = s / (2×tan(π/n)); Area = (perimeter × apothem) / 2 = (n×s×apothem)/2
- The Apothem of Regular Polygon Calculator updates instantly as you change the number of sides or side length.
- Formula: Apothem = s / (2×tan(π/n)); Area = (perimeter × apothem) / 2 = (n×s×apothem)/2
- Input definitions: • Number of Sides (n): how many equal sides the regular polygon has (minimum 3) • Side Length (s): the length of one side, in your chosen unit
- The apothem is the perpendicular distance from the center to the midpoint of any side, which equals the inradius of the polygon.
- As the number of sides grows, the polygon approaches a circle and the apothem approaches the radius.
- All outputs share the unit you use for side length (area is in those units squared).
Example Calculation
Inputs
- Number of Sides: 6
- Side Length (cm): 5
For a regular hexagon (6 sides) with side length 5: apothem = 5 / (2×tan(π/6)) ≈ 4.33, perimeter = 30, and area = (30 × 4.33) / 2 ≈ 64.95.
Frequently asked questions
What is the apothem of a polygon?
It is the distance from the center of a regular polygon to the midpoint of one of its sides — the same as the polygon's inradius.
How is the apothem calculated?
Apothem = s / (2 × tan(π/n)), where s is the side length and n is the number of sides.
How does the apothem give the area?
Area = (perimeter × apothem) / 2. Since perimeter = n × s, the area equals (n × s × apothem) / 2.
Does this work for any regular polygon?
Yes, for any regular polygon with at least 3 sides where every side and angle is equal.
What units does the result use?
The apothem and perimeter use the same unit as the side length, and the area uses that unit squared.
Can I use this for planning and budgeting?
Yes. Run best-case, expected, and worst-case inputs to compare outcomes and make safer planning decisions.
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