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Circumradius of Regular Polygon Formula

GoCircumradius of Regular Polygon given Inradius Formula

GoCircumradius of Regular Polygon given Perimeter Formula

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The Circumradius of Regular Polygon is the radius of a circumcircle touching each of the Regular Polygon's vertices. Check FAQs

r c = \frac{l e}{2 \cdot \sin (\frac{π}{N S})}

r_c - Circumradius of Regular Polygon?l_e - Edge Length of Regular Polygon?N_S - Number of Sides of Regular Polygon?π - Archimedes' constant?

Circumradius of Regular Polygon Example

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Here is how the Circumradius of Regular Polygon equation looks like with Values.

Here is how the Circumradius of Regular Polygon equation looks like with Units.

Here is how the Circumradius of Regular Polygon equation looks like.

13.0656 = \frac{10}{2 \cdot \sin (\frac{3.1416}{8})}

13.0656m = \frac{10m}{2 \cdot \sin (\frac{3.1416}{8})}

13.0656 = \frac{10}{2 \cdot \sin (\frac{3.1416}{8})}

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Circumradius of Regular Polygon Solution

Follow our step by step solution on how to calculate Circumradius of Regular Polygon?

FIRST Step Consider the formula

r c = \frac{l e}{2 \cdot \sin (\frac{π}{N S})}

Next Step Substitute values of Variables

∴

r c = \frac{10m}{2 \cdot \sin (\frac{π}{8})}

Next Step Substitute values of Constants

∴

r c = \frac{10m}{2 \cdot \sin (\frac{3.1416}{8})}

Next Step Prepare to Evaluate

∴

r c = \frac{10}{2 \cdot \sin (\frac{3.1416}{8})}

Next Step Evaluate

∴

r c = 13.0656296487638m

LAST Step Rounding Answer

∴

r c = 13.0656m

Circumradius of Regular Polygon Formula Elements

Variables

Constants

Functions

Circumradius of Regular Polygon

The Circumradius of Regular Polygon is the radius of a circumcircle touching each of the Regular Polygon's vertices.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumradius of Regular Polygon

Edge Length of Regular Polygon

The Edge Length of Regular Polygon is the length of one of the sides of the Regular Polygon.

Symbol: l_e

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Edge Length of 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.

Symbol: N_S

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Sides of Regular Polygon

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: sin(Angle)

Other Formulas to find Circumradius of Regular Polygon

Go Circumradius of Regular Polygon given Inradius

r c = \frac{r i}{\cos (\frac{π}{N S})}

Go Circumradius of Regular Polygon given Perimeter

r c = \frac{P}{2 \cdot N S \cdot \sin (\frac{π}{N S})}

Go Circumradius of Regular Polygon given Area

r c = \sqrt{\frac{2 \cdot A}{N S \cdot \sin (\frac{2 \cdot π}{N S})}}

How to Evaluate Circumradius of Regular Polygon?

Circumradius of Regular Polygon evaluator uses Circumradius of Regular Polygon = Edge Length of Regular Polygon/(2*sin(pi/Number of Sides of Regular Polygon)) to evaluate 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 evaluate Circumradius of Regular Polygon using this online evaluator? To use this online evaluator 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.

FAQs on Circumradius of Regular Polygon

What is the formula to find Circumradius of Regular Polygon?

The formula of Circumradius of Regular Polygon is expressed as Circumradius of Regular Polygon = Edge Length of Regular Polygon/(2*sin(pi/Number of Sides of Regular Polygon)). Here is an example- 13.06563 = 10/(2*sin(pi/8)).

How to calculate Circumradius of Regular Polygon?

With Edge Length of Regular Polygon (l_e) & Number of Sides of Regular Polygon (N_S) we can find Circumradius of Regular Polygon using the formula - Circumradius of Regular Polygon = Edge Length of Regular Polygon/(2*sin(pi/Number of Sides of Regular Polygon)). This formula also uses Archimedes' constant and Sine (sin) function(s).

What are the other ways to Calculate Circumradius of Regular Polygon?

Here are the different ways to Calculate Circumradius of Regular Polygon-

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)))

Can the Circumradius of Regular Polygon be negative?

No, the Circumradius of Regular Polygon, measured in Length cannot be negative.

Which unit is used to measure Circumradius of Regular Polygon?

Circumradius of Regular Polygon is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Circumradius of Regular Polygon can be measured.

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Circumradius of Regular Polygon Formula

​GoCircumradius of Regular Polygon given Inradius Formula

​GoCircumradius of Regular Polygon given Perimeter Formula

Circumradius of Regular Polygon Example

Circumradius of Regular Polygon Solution

Circumradius of Regular Polygon Formula Elements

Other Formulas to find Circumradius of Regular Polygon

How to Evaluate Circumradius of Regular Polygon?

FAQs on Circumradius of Regular Polygon

Variable Name

GoCircumradius of Regular Polygon given Inradius Formula

GoCircumradius of Regular Polygon given Perimeter Formula