Circumradius of Regular Polygon given Inradius Calculator

✖Inradius of Regular Polygon is the line connecting the center of the polygon to the midpoint of one of the Regular Polygon's sides. The inradius is also the radius of the incircle.ⓘ Inradius of Regular Polygon [r_i]			+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 given Inradius [r_c]

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Circumradius of Regular Polygon given Inradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Circumradius of Regular Polygon = Inradius of Regular Polygon/cos(pi/Number of Sides of Regular Polygon)
r_c = r_i/cos(pi/N_S)
This formula uses 1 Constants, 1 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(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.
Inradius of Regular Polygon - (Measured in Meter) - Inradius of Regular Polygon is the line connecting the center of the polygon to the midpoint of one of the Regular Polygon's sides. The inradius is also the radius of the incircle.
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

Inradius of Regular Polygon: 12 Meter --> 12 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 = r_i/cos(pi/N_S) --> 12/cos(pi/8)

Evaluating ... ...

r_c = 12.9887064035087

STEP 3: Convert Result to Output's Unit

12.9887064035087 Meter --> No Conversion Required

FINAL ANSWER

12.9887064035087 ≈ 12.98871 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 given Inradius Formula

LaTeX Go

Circumradius of Regular Polygon = Inradius of Regular Polygon/cos(pi/Number of Sides of Regular Polygon)
r_c = r_i/cos(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 given Inradius?

Circumradius of Regular Polygon given Inradius calculator uses Circumradius of Regular Polygon = Inradius of Regular Polygon/cos(pi/Number of Sides of Regular Polygon) to calculate the Circumradius of Regular Polygon, Circumradius of Regular Polygon given Inradius formula can be defined as the radius of a circumcircle touching each of the Regular Polygon's vertices, calculated using its inradius. Circumradius of Regular Polygon is denoted by r_c symbol.

How to calculate Circumradius of Regular Polygon given Inradius using this online calculator? To use this online calculator for Circumradius of Regular Polygon given Inradius, enter Inradius of Regular Polygon (r_i) & Number of Sides of Regular Polygon (N_S) and hit the calculate button. Here is how the Circumradius of Regular Polygon given Inradius calculation can be explained with given input values -> 12.98871 = 12/cos(pi/8).

FAQ

What is Circumradius of Regular Polygon given Inradius?

Circumradius of Regular Polygon given Inradius formula can be defined as the radius of a circumcircle touching each of the Regular Polygon's vertices, calculated using its inradius and is represented as r_c = r_i/cos(pi/N_S) or Circumradius of Regular Polygon = Inradius of Regular Polygon/cos(pi/Number of Sides of Regular Polygon). Inradius of Regular Polygon is the line connecting the center of the polygon to the midpoint of one of the Regular Polygon's sides. The inradius is also the radius of the incircle & 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 given Inradius?

Circumradius of Regular Polygon given Inradius formula can be defined as the radius of a circumcircle touching each of the Regular Polygon's vertices, calculated using its inradius is calculated using Circumradius of Regular Polygon = Inradius of Regular Polygon/cos(pi/Number of Sides of Regular Polygon). To calculate Circumradius of Regular Polygon given Inradius, you need Inradius of Regular Polygon (r_i) & Number of Sides of Regular Polygon (N_S). With our tool, you need to enter the respective value for Inradius 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 Inradius 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 = Edge Length of Regular Polygon/(2*sin(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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