Circumradius of Regular Polygon Calculator

✖The Edge Length of Regular Polygon is the length of one of the sides of the Regular Polygon.ⓘ Edge Length of Regular Polygon [l_e]			+10% -10%
✖The Number of Sides of Regular Polygon denotes the total number of sides of the Polygon. The number of sides is used to classify the types of polygons.ⓘ Number of Sides of Regular Polygon [N_S]			+10% -10%

✖The Circumradius of Regular Polygon is the radius of a circumcircle touching each of the Regular Polygon's vertices.ⓘ Circumradius of Regular Polygon [r_c]

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Circumradius of Regular Polygon Solution

STEP 0: Pre-Calculation Summary

Formula Used

Circumradius of Regular Polygon = Edge Length of Regular Polygon/(2*sin(pi/Number of Sides of Regular Polygon))
r_c = l_e/(2*sin(pi/N_S))
This formula uses 1 Constants, 1 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)

Variables Used

Circumradius of Regular Polygon - (Measured in Meter) - The Circumradius of Regular Polygon is the radius of a circumcircle touching each of the Regular Polygon's vertices.
Edge Length of Regular Polygon - (Measured in Meter) - The Edge Length of Regular Polygon is the length of one of the sides of the Regular Polygon.
Number of Sides of Regular Polygon - The Number of Sides of Regular Polygon denotes the total number of sides of the Polygon. The number of sides is used to classify the types of polygons.

STEP 1: Convert Input(s) to Base Unit

Edge Length of Regular Polygon: 10 Meter --> 10 Meter No Conversion Required
Number of Sides of Regular Polygon: 8 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = l_e/(2*sin(pi/N_S)) --> 10/(2*sin(pi/8))

Evaluating ... ...

r_c = 13.0656296487638

STEP 3: Convert Result to Output's Unit

13.0656296487638 Meter --> No Conversion Required

FINAL ANSWER

13.0656296487638 ≈ 13.06563 Meter <-- Circumradius of Regular Polygon

(Calculation completed in 00.004 seconds)

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< Circumradius of Regular Polygon Calculators

Circumradius of Regular Polygon given Area

LaTeX Go Circumradius of Regular Polygon = sqrt((2*Area of Regular Polygon)/(Number of Sides of Regular Polygon*sin((2*pi)/Number of Sides of Regular Polygon)))

Circumradius of Regular Polygon given Perimeter

LaTeX Go Circumradius of Regular Polygon = Perimeter of Regular Polygon/(2*Number of Sides of Regular Polygon*sin(pi/Number of Sides of Regular Polygon))

Circumradius of Regular Polygon

LaTeX Go Circumradius of Regular Polygon = Edge Length of Regular Polygon/(2*sin(pi/Number of Sides of Regular Polygon))

Circumradius of Regular Polygon given Inradius

LaTeX Go Circumradius of Regular Polygon = Inradius of Regular Polygon/cos(pi/Number of Sides of Regular Polygon)

Circumradius of Regular Polygon Formula

LaTeX Go

Circumradius of Regular Polygon = Edge Length of Regular Polygon/(2*sin(pi/Number of Sides of Regular Polygon))
r_c = l_e/(2*sin(pi/N_S))

What is Regular Polygon?

A Regular Polygon has sides of equal length and equal angles between each side. A regular n-sided polygon has rotational symmetry of order n and it is also known as a cyclic polygon. All the vertices of a regular polygon lie on the circumscribed circle.

How to Calculate Circumradius of Regular Polygon?

Circumradius of Regular Polygon calculator uses Circumradius of Regular Polygon = Edge Length of Regular Polygon/(2*sin(pi/Number of Sides of Regular Polygon)) to calculate the Circumradius of Regular Polygon, Circumradius of Regular Polygon formula is defined as the radius of a circumcircle touching each of the Regular Polygon's vertices. Circumradius of Regular Polygon is denoted by r_c symbol.

How to calculate Circumradius of Regular Polygon using this online calculator? To use this online calculator for Circumradius of Regular Polygon, enter Edge Length of Regular Polygon (l_e) & Number of Sides of Regular Polygon (N_S) and hit the calculate button. Here is how the Circumradius of Regular Polygon calculation can be explained with given input values -> 13.06563 = 10/(2*sin(pi/8)).

FAQ

What is Circumradius of Regular Polygon?

Circumradius of Regular Polygon formula is defined as the radius of a circumcircle touching each of the Regular Polygon's vertices and is represented as r_c = l_e/(2*sin(pi/N_S)) or Circumradius of Regular Polygon = Edge Length of Regular Polygon/(2*sin(pi/Number of Sides of Regular Polygon)). The Edge Length of Regular Polygon is the length of one of the sides of the Regular Polygon & The Number of Sides of Regular Polygon denotes the total number of sides of the Polygon. The number of sides is used to classify the types of polygons.

How to calculate Circumradius of Regular Polygon?

Circumradius of Regular Polygon formula is defined as the radius of a circumcircle touching each of the Regular Polygon's vertices is calculated using Circumradius of Regular Polygon = Edge Length of Regular Polygon/(2*sin(pi/Number of Sides of Regular Polygon)). To calculate Circumradius of Regular Polygon, you need Edge Length of Regular Polygon (l_e) & Number of Sides of Regular Polygon (N_S). With our tool, you need to enter the respective value for Edge Length of Regular Polygon & Number of Sides of Regular Polygon and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Circumradius of Regular Polygon?

In this formula, Circumradius of Regular Polygon uses Edge Length of Regular Polygon & Number of Sides of Regular Polygon. We can use 3 other way(s) to calculate the same, which is/are as follows -

Circumradius of Regular Polygon = Inradius of Regular Polygon/cos(pi/Number of Sides of Regular Polygon)
Circumradius of Regular Polygon = Perimeter of Regular Polygon/(2*Number of Sides of Regular Polygon*sin(pi/Number of Sides of Regular Polygon))
Circumradius of Regular Polygon = sqrt((2*Area of Regular Polygon)/(Number of Sides of Regular Polygon*sin((2*pi)/Number of Sides of Regular Polygon)))

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