Inradius of Regular Polygon given Circumradius Calculator

✖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]			+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%

✖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 given Circumradius [r_i]

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Inradius of Regular Polygon given Circumradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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.
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

Circumradius of Regular Polygon: 13 Meter --> 13 Meter No Conversion Required
Number of Sides of Regular Polygon: 8 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = r_c*cos(pi/N_S) --> 13*cos(pi/8)

Evaluating ... ...

r_i = 12.0104339226467

STEP 3: Convert Result to Output's Unit

12.0104339226467 Meter --> No Conversion Required

FINAL ANSWER

12.0104339226467 ≈ 12.01043 Meter <-- Inradius of Regular Polygon

(Calculation completed in 00.020 seconds)

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< Inradius of Regular Polygon Calculators

Inradius of Regular Polygon given Area

LaTeX Go Inradius of Regular Polygon = sqrt(Area of Regular Polygon/(Number of Sides of Regular Polygon*tan(pi/Number of Sides of Regular Polygon)))

Inradius of Regular Polygon given Perimeter

LaTeX Go Inradius of Regular Polygon = Perimeter of Regular Polygon/(2*Number of Sides of Regular Polygon*tan(pi/Number of Sides of Regular Polygon))

Inradius of Regular Polygon

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

Inradius of Regular Polygon given Circumradius

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

Inradius of Regular Polygon given Circumradius Formula

LaTeX Go

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

Inradius of Regular Polygon given Circumradius calculator uses Inradius of Regular Polygon = Circumradius of Regular Polygon*cos(pi/Number of Sides of Regular Polygon) to calculate the Inradius of Regular Polygon, Inradius of Regular Polygon given Circumradius formula can be defined as the line connecting the center of the polygon to the midpoint of one of the Regular Polygon's sides, calculated using its circumradius. Inradius of Regular Polygon is denoted by r_i symbol.

How to calculate Inradius of Regular Polygon given Circumradius using this online calculator? To use this online calculator for Inradius of Regular Polygon given Circumradius, enter Circumradius of Regular Polygon (r_c) & Number of Sides of Regular Polygon (N_S) and hit the calculate button. Here is how the Inradius of Regular Polygon given Circumradius calculation can be explained with given input values -> 12.01043 = 13*cos(pi/8).

FAQ

What is Inradius of Regular Polygon given Circumradius?

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

Inradius of Regular Polygon given Circumradius formula can be defined as the line connecting the center of the polygon to the midpoint of one of the Regular Polygon's sides, calculated using its circumradius is calculated using Inradius of Regular Polygon = Circumradius of Regular Polygon*cos(pi/Number of Sides of Regular Polygon). To calculate Inradius of Regular Polygon given Circumradius, you need Circumradius of Regular Polygon (r_c) & Number of Sides of Regular Polygon (N_S). With our tool, you need to enter the respective value for Circumradius 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 Inradius of Regular Polygon?

In this formula, Inradius of Regular Polygon uses Circumradius 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 -

Inradius of Regular Polygon = (Edge Length of Regular Polygon)/(2*tan(pi/Number of Sides of Regular Polygon))
Inradius of Regular Polygon = sqrt(Area of Regular Polygon/(Number of Sides of Regular Polygon*tan(pi/Number of Sides of Regular Polygon)))
Inradius of Regular Polygon = Perimeter of Regular Polygon/(2*Number of Sides of Regular Polygon*tan(pi/Number of Sides of Regular Polygon))

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