Calculate regular dodecagon (12-sided polygon) properties: perimeter, area, diagonals, interior/exterior angles, apothem, inradius, circumradius. Presets, properties table, and polygon visual.
A regular dodecagon is a twelve-sided polygon with all sides equal and all interior angles equal. It appears in everyday life as the shape of many clock faces, some coins (UK pound coin), and stop-sign-style designs. Each interior angle of a regular dodecagon measures 150°, and the sum of all interior angles is 1800°. The area of a regular dodecagon with side length s is 3(2 + √3)s², which is approximately 11.196s². The number of diagonals is 54. This calculator takes the side length as primary input (or you can specify the circumradius, inradius/apothem, or area and it will derive the side length). It outputs the perimeter, area, apothem (inradius), circumradius, diagonal lengths, interior and exterior angles, and more. A polygon visual draws the dodecagon with labeled vertices, and a properties comparison table shows how the dodecagon compares to other regular polygons from triangle to icosagon. Check the example with realistic values before reporting.
Dodecagon formulas involve trigonometric expressions with π/12 (sin 15° and tan 15°), making manual computation tedious. This calculator derives all properties from any single measurement and includes a polygon comparison table so you can see how the dodecagon relates to other regular polygons. It is useful for geometry students, tile pattern designers, and anyone working with 12-fold symmetry.
Interior angle = (n−2)×180°/n = 150° (n=12) Area = 3(2+√3)s² ≈ 11.196s² Perimeter = 12s Apothem = s/(2 tan(π/12)) Circumradius = s/(2 sin(π/12)) Diagonals = n(n−3)/2 = 54
Result: Area ≈ 279.9, Perimeter = 60
A regular dodecagon with side 5: Area = 3(2+√3)×25 ≈ 279.9, Perimeter = 60, Apothem ≈ 9.33, Circumradius ≈ 9.66.
The regular dodecagon appears more often than you might expect. The UK one-pound coin (minted since 2017) has a 12-sided shape for security and tactile recognition. Many clock faces approximate a dodecagonal layout with 12 hour markers. In architecture, 12-fold rosettes are common in Gothic cathedral rose windows. The dodecagon also tiles the plane in combination with triangles and squares (the "3-4-6-12" Archimedean tiling).
A regular dodecagon has 12 lines of symmetry and rotational symmetry of order 12 (30° increments). Its interior angle of 150° means three dodecagons cannot meet at a vertex (3×150° = 450° > 360°), so regular dodecagons alone cannot tile the plane. Its area formula 3(2+√3)s² ≈ 11.196s² makes it very close to a circle (for comparison, a circle of the same circumradius has area πR²). As n increases, the n-gon area approaches πR², and the dodecagon is already 98.86% of the circular area.
A dodecagon has 54 diagonals with 5 distinct diagonal lengths (spanning 2, 3, 4, 5, and 6 vertices). The longest diagonal (spanning 6 vertices) equals the diameter (2R). These diagonals intersect to create intricate star patterns — the most famous being the Star of David pattern formed by two overlapping hexagons inscribed in the dodecagon. This rich diagonal structure is exploited in Islamic geometric art and quilt patterns.
A dodecagon has 12 sides. The prefix "dodeca-" comes from the Greek word for twelve.
Each interior angle is 150°. The sum of all interior angles is 1800°.
A dodecagon has 54 diagonals, calculated as n(n−3)/2 = 12×9/2 = 54. Use this as a practical reminder before finalizing the result.
The apothem is the distance from the center to the midpoint of a side. For a regular dodecagon, apothem = s/(2 tan(π/12)).
Area = 3(2+√3)s², or equivalently (1/2) × perimeter × apothem = (1/2) × 12s × apothem. Keep this note short and outcome-focused for reuse.
Clock faces, some coins (old UK three-pence, current £1 coin shape), architectural elements, and tile patterns. Apply this check where your workflow is most sensitive.