Perimeter of Regular Polygon given Number of Sides and 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%

✖The Perimeter of Regular Polygon is the total distance around the edge of the Regular Polygon.ⓘ Perimeter of Regular Polygon given Number of Sides and Circumradius [P]

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Formula

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Perimeter of Regular Polygon given Number of Sides and Circumradius

Formula

`"P" = 2*"r"_{"c"}*"N"_{"S"}*sin(pi/"N"_{"S"})`

Example

`"79.59815m"=2*"13m"*"8"*sin(pi/"8")`

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Perimeter of Regular Polygon given Number of Sides and Circumradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Perimeter of Regular Polygon = 2*Circumradius of Regular Polygon*Number of Sides of Regular Polygon*sin(pi/Number of Sides of Regular Polygon)
P = 2*r_c*N_S*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

Perimeter of Regular Polygon - (Measured in Meter) - The Perimeter of Regular Polygon is the total distance around the edge of the Regular Polygon.
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

P = 2*r_c*N_S*sin(pi/N_S) --> 2*13*8*sin(pi/8)

Evaluating ... ...

P = 79.5981539319387

STEP 3: Convert Result to Output's Unit

79.5981539319387 Meter --> No Conversion Required

FINAL ANSWER

79.5981539319387 ≈ 79.59815 Meter <-- Perimeter of Regular Polygon

(Calculation completed in 00.004 seconds)

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< 5 Perimeter of Regular Polygon Calculators

Perimeter of Regular Polygon given Number of Sides and Circumradius

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

Perimeter of Regular Polygon given Number of Sides and Inradius

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

Perimeter of Regular Polygon given Circumradius and Area

Go Perimeter of Regular Polygon = (2*Area of Regular Polygon)/sqrt(Circumradius of Regular Polygon^2-Edge Length of Regular Polygon^2/4)

Perimeter of Regular Polygon

Go Perimeter of Regular Polygon = Number of Sides of Regular Polygon*Edge Length of Regular Polygon

Perimeter of Regular Polygon given Inradius and Area

Go Perimeter of Regular Polygon = (2*Area of Regular Polygon)/Inradius of Regular Polygon

Perimeter of Regular Polygon given Number of Sides and Circumradius Formula

Perimeter of Regular Polygon = 2*Circumradius of Regular Polygon*Number of Sides of Regular Polygon*sin(pi/Number of Sides of Regular Polygon)
P = 2*r_c*N_S*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 Perimeter of Regular Polygon given Number of Sides and Circumradius?

Perimeter of Regular Polygon given Number of Sides and Circumradius calculator uses Perimeter of Regular Polygon = 2*Circumradius of Regular Polygon*Number of Sides of Regular Polygon*sin(pi/Number of Sides of Regular Polygon) to calculate the Perimeter of Regular Polygon, Perimeter of Regular Polygon given Number of Sides and Circumradius formula can be defined as the total distance around the edge of the Regular Polygon, calculated using its circumradius and number of sides. Perimeter of Regular Polygon is denoted by P symbol.

How to calculate Perimeter of Regular Polygon given Number of Sides and Circumradius using this online calculator? To use this online calculator for Perimeter of Regular Polygon given Number of Sides and 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 Perimeter of Regular Polygon given Number of Sides and Circumradius calculation can be explained with given input values -> 79.59815 = 2*13*8*sin(pi/8).

FAQ

What is Perimeter of Regular Polygon given Number of Sides and Circumradius?

Perimeter of Regular Polygon given Number of Sides and Circumradius formula can be defined as the total distance around the edge of the Regular Polygon, calculated using its circumradius and number of sides and is represented as P = 2*r_c*N_S*sin(pi/N_S) or Perimeter of Regular Polygon = 2*Circumradius of Regular Polygon*Number of Sides of Regular Polygon*sin(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 Perimeter of Regular Polygon given Number of Sides and Circumradius?

Perimeter of Regular Polygon given Number of Sides and Circumradius formula can be defined as the total distance around the edge of the Regular Polygon, calculated using its circumradius and number of sides is calculated using Perimeter of Regular Polygon = 2*Circumradius of Regular Polygon*Number of Sides of Regular Polygon*sin(pi/Number of Sides of Regular Polygon). To calculate Perimeter of Regular Polygon given Number of Sides and 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 Perimeter of Regular Polygon?

In this formula, Perimeter of Regular Polygon uses Circumradius of Regular Polygon & Number of Sides of Regular Polygon. We can use 4 other way(s) to calculate the same, which is/are as follows -

Perimeter of Regular Polygon = Number of Sides of Regular Polygon*Edge Length of Regular Polygon
Perimeter of Regular Polygon = (2*Area of Regular Polygon)/sqrt(Circumradius of Regular Polygon^2-Edge Length of Regular Polygon^2/4)
Perimeter of Regular Polygon = 2*Number of Sides of Regular Polygon*Inradius of Regular Polygon*tan(pi/Number of Sides of Regular Polygon)
Perimeter of Regular Polygon = (2*Area of Regular Polygon)/Inradius of Regular Polygon

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