Circumradius of Octagon given Inradius Calculator

✖The Inradius of Octagon is the radius of incircle of the Regular Octagon or the circle that contained by the Octagon with all edges touch the circle.ⓘ Inradius of Octagon [r_i]

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✖The Circumradius of Octagon is the radius of circumcircle of the Regular Octagon or the circle that contains the Octagon with all vertices lies on that circle.ⓘ Circumradius of Octagon given Inradius [r_c]

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Formula

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Circumradius of Octagon given Inradius

Formula

`"r"_{"c"} = sqrt(4-(2*sqrt(2)))*"r"_{"i"}`

Example

`"12.98871m"=sqrt(4-(2*sqrt(2)))*"12m"`

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Circumradius of Octagon given Inradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Circumradius of Octagon = sqrt(4-(2*sqrt(2)))*Inradius of Octagon
r_c = sqrt(4-(2*sqrt(2)))*r_i
This formula uses 1 Functions, 2 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Circumradius of Octagon - (Measured in Meter) - The Circumradius of Octagon is the radius of circumcircle of the Regular Octagon or the circle that contains the Octagon with all vertices lies on that circle.
Inradius of Octagon - (Measured in Meter) - The Inradius of Octagon is the radius of incircle of the Regular Octagon or the circle that contained by the Octagon with all edges touch the circle.

STEP 1: Convert Input(s) to Base Unit

Inradius of Octagon: 12 Meter --> 12 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = sqrt(4-(2*sqrt(2)))*r_i --> sqrt(4-(2*sqrt(2)))*12

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 Octagon

(Calculation completed in 00.004 seconds)

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< 8 Circumradius of Octagon Calculators

Circumradius of Octagon given Medium Diagonal

Go Circumradius of Octagon = sqrt(1-(1/sqrt(2)))*Medium Diagonal of Octagon

Circumradius of Octagon given Perimeter

Go Circumradius of Octagon = sqrt(4+(2*sqrt(2)))*Perimeter of Octagon/16

Circumradius of Octagon

Go Circumradius of Octagon = sqrt(1+(1/sqrt(2)))*Edge Length of Octagon

Circumradius of Octagon given Inradius

Go Circumradius of Octagon = sqrt(4-(2*sqrt(2)))*Inradius of Octagon

Circumradius of Octagon given Height

Go Circumradius of Octagon = sqrt(1-(1/sqrt(2)))*Height of Octagon

Circumradius of Octagon given Area

Go Circumradius of Octagon = sqrt(Area of Octagon/(2*sqrt(2)))

Circumradius of Octagon given Short Diagonal

Go Circumradius of Octagon = Short Diagonal of Octagon/(sqrt(2))

Circumradius of Octagon given Long Diagonal

Go Circumradius of Octagon = Long Diagonal of Octagon/2

Circumradius of Octagon given Inradius Formula

Circumradius of Octagon = sqrt(4-(2*sqrt(2)))*Inradius of Octagon
r_c = sqrt(4-(2*sqrt(2)))*r_i

What is an Octagon?

Octagon is a polygon in geometry, which has 8 sides and 8 angles. That means the number of vertices is 8 and the number of edges is 8. All the sides are joined with each other end-to-end to form a shape. These sides are in a straight line form; they are not curved or disjoint with each other. Each interior angle of a regular octagon is 135° and each exterior angle will be 45°.

How to Calculate Circumradius of Octagon given Inradius?

Circumradius of Octagon given Inradius calculator uses Circumradius of Octagon = sqrt(4-(2*sqrt(2)))*Inradius of Octagon to calculate the Circumradius of Octagon, The Circumradius of Octagon given Inradius formula is defined as the radius of circumcircle of the Regular Octagon or the circle that contains the Octagon with all vertices lies on that circle, and calculated using inradius of the Octagon. Circumradius of Octagon is denoted by r_c symbol.

How to calculate Circumradius of Octagon given Inradius using this online calculator? To use this online calculator for Circumradius of Octagon given Inradius, enter Inradius of Octagon (r_i) and hit the calculate button. Here is how the Circumradius of Octagon given Inradius calculation can be explained with given input values -> 12.98871 = sqrt(4-(2*sqrt(2)))*12.

FAQ

What is Circumradius of Octagon given Inradius?

The Circumradius of Octagon given Inradius formula is defined as the radius of circumcircle of the Regular Octagon or the circle that contains the Octagon with all vertices lies on that circle, and calculated using inradius of the Octagon and is represented as r_c = sqrt(4-(2*sqrt(2)))*r_i or Circumradius of Octagon = sqrt(4-(2*sqrt(2)))*Inradius of Octagon. The Inradius of Octagon is the radius of incircle of the Regular Octagon or the circle that contained by the Octagon with all edges touch the circle.

How to calculate Circumradius of Octagon given Inradius?

The Circumradius of Octagon given Inradius formula is defined as the radius of circumcircle of the Regular Octagon or the circle that contains the Octagon with all vertices lies on that circle, and calculated using inradius of the Octagon is calculated using Circumradius of Octagon = sqrt(4-(2*sqrt(2)))*Inradius of Octagon. To calculate Circumradius of Octagon given Inradius, you need Inradius of Octagon (r_i). With our tool, you need to enter the respective value for Inradius of Octagon 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 Octagon?

In this formula, Circumradius of Octagon uses Inradius of Octagon. We can use 7 other way(s) to calculate the same, which is/are as follows -

Circumradius of Octagon = sqrt(1+(1/sqrt(2)))*Edge Length of Octagon
Circumradius of Octagon = Long Diagonal of Octagon/2
Circumradius of Octagon = sqrt(1-(1/sqrt(2)))*Medium Diagonal of Octagon
Circumradius of Octagon = Short Diagonal of Octagon/(sqrt(2))
Circumradius of Octagon = sqrt(1-(1/sqrt(2)))*Height of Octagon
Circumradius of Octagon = sqrt(4+(2*sqrt(2)))*Perimeter of Octagon/16
Circumradius of Octagon = sqrt(Area of Octagon/(2*sqrt(2)))

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