Dodecagon Calculator — Regular 12-Sided Polygon
Enter the side length of a regular dodecagon and instantly get its area, perimeter, interior and exterior angles, circumradius, apothem, and long diagonal.
A = 3(2 + √3) × s²
- 1
Square the side
5² = 25 - 2
Multiply by 3(2+√3)
3(2+√3) × 25 = 279.9038Area factor 3(2+√3) ≈ 11.196 comes from the 12 isoceles triangles at the centre.
How does this calculator work?
A regular dodecagon with side s has area 3(2+√3)s² ≈ 11.196s², perimeter 12s, interior angle 150°, circumradius s(√6+√2)/2 ≈ 1.932s, and apothem s(2+√3)/2 ≈ 1.866s. Enter the side length to get all properties at once.
Formula
How this is calculated
A regular dodecagon has 12 equal sides and 12 equal angles. Its interior angle is (12−2)×180°/12 = 150°, and each exterior angle is 360°/12 = 30°. The area formula A = 3(2+√3)s² comes from dividing the dodecagon into 12 isoceles triangles meeting at the centre: each triangle has a central angle of 30° and two sides equal to the circumradius R, giving an area of ½R²sin(30°) per triangle, which simplifies to 3(2+√3)s² when R is replaced by its expression in terms of s.
The circumradius R (distance from centre to a vertex) equals s/(2·sin(π/12)) = s(√6+√2)/2 ≈ 1.932s. The apothem a (distance from centre to the midpoint of a side, also called the inradius) equals s/(2·tan(π/12)) = s(2+√3)/2 ≈ 1.866s. Area can also be computed from the apothem as A = ½ × perimeter × a = 6s × a, confirming the formula.
The long diagonal (the one that passes through the centre) connects two opposite vertices and equals 2R = s(√6+√2) ≈ 3.864s. A dodecagon also has shorter diagonals of five other distinct lengths; only the longest is shown here.
Frequently asked questions
A dodecagon is a polygon with 12 sides. A regular dodecagon has all 12 sides equal in length and all 12 interior angles equal to 150°. It is the highest-order regular polygon that tiles the plane in combination with other shapes (used in Islamic geometric art and some floor tiling patterns).
The circumradius R is the radius of the circle passing through all 12 vertices (circumscribed circle). The apothem a is the radius of the circle tangent to all 12 sides (inscribed circle, or incircle). For a dodecagon, R ≈ 1.932s and a ≈ 1.866s — they are close because 12 is a large number of sides (a circle has R = a).
A dodecagon has n(n−3)/2 = 12×9/2 = 54 diagonals. They fall into 5 distinct length groups plus the long diameter. The longest diagonal (passing through the centre) equals s(√6+√2) ≈ 3.864s.
Also known as
TG we-Calculate Editorial Team. (2026). Dodecagon Calculator — Regular 12-Sided Polygon [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/dodecagon-calculator
TG we-Calculate Editorial Team. "Dodecagon Calculator — Regular 12-Sided Polygon." TG we-Calculate. 2026. https://we-calculate.com/calculator/dodecagon-calculator.
TG we-Calculate Editorial Team, "Dodecagon Calculator — Regular 12-Sided Polygon," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/dodecagon-calculator
@misc{wecalculate_dodecagon_calculator, title = {Dodecagon Calculator — Regular 12-Sided Polygon}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/dodecagon-calculator}}, year = {2026}, note = {TG we-Calculate} }
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