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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
rc=P2⋅NS⋅sin(πNS)
rc - Circumradius of Regular Polygon?P - Perimeter of Regular Polygon?NS - Number of Sides of Regular Polygon?π - Archimedes' constant?

Circumradius of Regular Polygon given Perimeter Example

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

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

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

13.0656Edit=80Edit2⋅8Edit⋅sin(3.14168Edit)
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Circumradius of Regular Polygon given Perimeter Solution

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

FIRST Step Consider the formula
rc=P2⋅NS⋅sin(πNS)
Next Step Substitute values of Variables
∴ rc=80m2⋅8⋅sin(π8)
Next Step Substitute values of Constants
∴ rc=80m2⋅8⋅sin(3.14168)
Next Step Prepare to Evaluate
∴ rc=802⋅8⋅sin(3.14168)
Next Step Evaluate
∴rc=13.0656296487638m
LAST Step Rounding Answer
∴rc=13.0656m

Circumradius of Regular Polygon given Perimeter 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: rc
Measurement: LengthUnit: m
Note: Value should be greater than 0.
Formulas to find Circumradius of Regular PolygonOpen Variable
Perimeter of Regular Polygon
The Perimeter of Regular Polygon is the total distance around the edge of the Regular Polygon.
Symbol: P
Measurement: LengthUnit: m
Note: Value should be greater than 0.
Formulas to find Perimeter of Regular PolygonOpen Variable
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: NS
Measurement: NAUnit: Unitless
Note: Value should be greater than 0.
Formulas to find Number of Sides of Regular PolygonOpen Variable
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
rc=le2⋅sin(πNS)
​Go Circumradius of Regular Polygon given Inradius
rc=ricos(πNS)
​Go Circumradius of Regular Polygon given Area
rc=2⋅ANS⋅sin(2⋅πNS)

How to Evaluate Circumradius of Regular Polygon given Perimeter?

Circumradius of Regular Polygon given Perimeter evaluator uses Circumradius of Regular Polygon = Perimeter of Regular Polygon/(2*Number of Sides of Regular Polygon*sin(pi/Number of Sides of Regular Polygon)) to evaluate the Circumradius of Regular Polygon, The Circumradius of Regular Polygon given Perimeter formula can be defined as the radius of a circumcircle touching each of the Regular Polygon's vertices, calculated using its perimeter. Circumradius of Regular Polygon is denoted by rc symbol.

How to evaluate Circumradius of Regular Polygon given Perimeter using this online evaluator? To use this online evaluator for Circumradius of Regular Polygon given Perimeter, enter Perimeter of Regular Polygon (P) & Number of Sides of Regular Polygon (NS) and hit the calculate button.

FAQs on Circumradius of Regular Polygon given Perimeter

What is the formula to find Circumradius of Regular Polygon given Perimeter?
The formula of Circumradius of Regular Polygon given Perimeter is expressed as Circumradius of Regular Polygon = Perimeter of Regular Polygon/(2*Number of Sides of Regular Polygon*sin(pi/Number of Sides of Regular Polygon)). Here is an example- 13.06563 = 80/(2*8*sin(pi/8)).
How to calculate Circumradius of Regular Polygon given Perimeter?
With Perimeter of Regular Polygon (P) & Number of Sides of Regular Polygon (NS) we can find Circumradius of Regular Polygon given Perimeter using the formula - Circumradius of Regular Polygon = Perimeter of Regular Polygon/(2*Number of Sides of Regular Polygon*sin(pi/Number of Sides of Regular Polygon)). This formula also uses Archimedes' constant and Sine 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=Edge Length of Regular Polygon/(2*sin(pi/Number of Sides of Regular Polygon))OpenImg
  • Circumradius of Regular Polygon=Inradius of Regular Polygon/cos(pi/Number of Sides of Regular Polygon)OpenImg
  • 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)))OpenImg
Can the Circumradius of Regular Polygon given Perimeter be negative?
No, the Circumradius of Regular Polygon given Perimeter, measured in Length cannot be negative.
Which unit is used to measure Circumradius of Regular Polygon given Perimeter?
Circumradius of Regular Polygon given Perimeter 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 given Perimeter can be measured.
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