Last updated: Jul 29, 2024

Dodecagon Calculator

Q: What are the angles in a dodecagon?

The interior angle α in a dodecagon has 150° . As there are twelve identical interior angles, the sum of all the interior angles of a dodecagon equals 1800° . We can also easily deduce that the exterior angle, β , has 30° , because it satisfies α + β = 180° . Note that these angles remain the same no matter the side length of the regular dodecagon!

Q: How many sides does a dodecagon have?

A dodecagon is a polygon with twelve sides as well as twelve vertices and twelve internal angles. This fact is encoded in the word itself, as dodeka is Greek for twelve .

Q: What is the area of a dodecagon with a 10 cm side?

The answer is approximately 1120 cm² . To get this result, use the formula area ≈ 11.196 × a² . We plug in a = 10 and obtain area ≈ 11.196 × 100 ≈ 1119.6 ≈ 1120 . This is an approximation of the precise formula that reads area = 2.5 × a² × √(5 + 2 × √5) .

Q: How do I find the sum of the interior angles of a dodecagon?

The interior angles of a dodecagon sum up to 1800° . To arrive at this result, recall that the formula for the sum of internal angles in a polygon with n sides reads n × 180° - 360° . Plugging in n = 12 , we obtain 12 × 180° - 360° = 2160° - 360° = 1800° . This is our answer.

Created by Anna Szczepanek, PhD

Anna Szczepanek

PhD, Jagiellonian University in Kraków, Poland

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Holds a Ph.D. degree in mathematics obtained at Jagiellonian University. An active researcher in the field of quantum information and a lecturer with 8+ years of teaching experience. Passionate about everything connected with maths in particular and science in general. Fond of coding, she has a keen eye for detail and perfectionistic leanings. A bookworm, an avid language learner, and a sluggish hiker. She is hopelessly addicted to coffee & chocolate – the darker and bitterer, the better. See full profile

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Reviewed by Luis Hoyos

Luis Hoyos

Luis Hoyos is a fresh graduate Mechanical Engineer with thermodynamics and fluids mechanics expertise. He's interested in learning new things and applying them to real-life problems. Luis also likes to build tools that make repetitive and boring tasks a breeze, like calculators (surprise?). When he's not creating calculators, he's in the process of building the size of the tissue attached to his bones, aka bodybuilding. He also loves being with his little cat and seeing her do crazy things. See full profile

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Table of contents

What's a dodecagon and its main formulas?What are the angles in a dodecagon?How to use this dodecagon calculator?Related Omni Calculator tools FAQs

Omni Calculator's dodecagon calculator is here to help you answer all the questions related to dodecagons! This tool can work out all the missing values based on just one piece of information, be it the dodecagon diagonal, side, area, perimeter, or incircle/circumcircle radius.

As is our custom in Omni, we also provide a short explanation of the dodecagon formulas implemented in the tool so that you can do the calculations by hand as well. Apart from that, we discuss in detail several of the most confusing problems related to dodecagons, including:

How do you calculate the sum of the interior angles of a dodecagon?
How many diagonals does a dodecagon have, and how do you get this result? (we give two ways!)

To make sure we're on the same page, let us start by recalling what a dodecagon is.

What's a dodecagon and its main formulas?

A dodecagon is a polygon with twelve sides. The name resembles words like pentagon or octagon, isn't it? This is because it follows the same principle: the prefix is a Greek numeral describing how many sides (or angles) our polygon has. Since dodeka is Greek for twelve, we can now play around with dodecagons.

If our dodecagon has all sides equal and all interior angles identical, we call it a regular dodecagon. This is exactly the shape you can see in the picture!

Once we've recalled what a dodecagon is, let's move on to the formulas! From now on, we consider a regular decagon with side length a. Since it has twelve sides, we bet you can guess the dodecagon perimeter formula:

Perimeter = 12 × a

The dodecagon area formula is more complicated, so we accompany it with an approximation:

Area = 3 × (2 + √3) ≈ 11.196 × a²

More information on how to calculate the area of a dodecagon awaits you in Omni's
dodecagon area calculator!

The formulas for the radius of the circumcircle R and the radius of the incircle r are the following:

R = ½ a × (√6 + √2) ≈ 1.932 × a

r = ½ a × (2 + √3) ≈ 1.866 × a

What are the angles in a dodecagon?

The interior angle α in a dodecagon has 150°. As there are twelve identical interior angles, the sum of all the interior angles of a dodecagon equals 1800°.

We can also easily deduce that the exterior angle, β, has 30°, because it satisfies α + β = 180°. Note that these angles remain the same no matter the side length of the regular dodecagon!

How to use this dodecagon calculator?

To use Omni's dodecagon calculator, simply input whatever data you have: side length, perimeter, area, incircle or circumcircle radius, or any of the diagonals... Our tool will immediately compute all the remaining values, and you'll have the complete set of parameters of the dodecagon.

Tip. Once you're done with dodecagons, you can play with other regular polygons: just tick the Try other regular polygons checkbox beneath the Polygon diagram section of our dodecagon calculator and set the number of sides to whatever value you like!

FAQs

How many sides does a dodecagon have?

A dodecagon is a polygon with twelve sides as well as twelve vertices and twelve internal angles. This fact is encoded in the word itself, as dodeka is Greek for twelve.

How many diagonals does a dodecagon have?

A dodecagon has 54 diagonals. To get this result:

Recall that a polygon with n sides has n(n - 3)/2 diagonals.
Plug in n = 12 and compute 12 × (12 - 3) / 2 = 54. This is our result.
If you forget the formula, compute in how many ways we can choose two out of twelve vertices: it is 12 × 11 / 2 = 66. However, this result includes both sides and diagonals.
Subtract twelve sides: 66 - 12 = 54, and that's it.

What is the area of a dodecagon with a 10 cm side?

The answer is approximately 1120 cm². To get this result, use the formula area ≈ 11.196 × a². We plug in a = 10 and obtain area ≈ 11.196 × 100 ≈ 1119.6 ≈ 1120. This is an approximation of the precise formula that reads area = 2.5 × a² × √(5 + 2 × √5).

How do I find the sum of the interior angles of a dodecagon?

The interior angles of a dodecagon sum up to 1800°. To arrive at this result, recall that the formula for the sum of internal angles in a polygon with n sides reads n × 180° - 360°. Plugging in n = 12, we obtain 12 × 180° - 360° = 2160° - 360° = 1800°. This is our answer.