Inradius of Octagon given Circumradius Calculator

✖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 [r_c]

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✖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 given Circumradius [r_i]

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Formula

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Inradius of Octagon given Circumradius

Formula

`"r"_{"i"} = (sqrt(2+sqrt(2))/2)*"r"_{"c"}`

Example

`"12.01043m"=(sqrt(2+sqrt(2))/2)*"13m"`

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Inradius of Octagon given Circumradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Inradius of Octagon = (sqrt(2+sqrt(2))/2)*Circumradius of Octagon
r_i = (sqrt(2+sqrt(2))/2)*r_c
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

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.
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.

STEP 1: Convert Input(s) to Base Unit

Circumradius of Octagon: 13 Meter --> 13 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = (sqrt(2+sqrt(2))/2)*r_c --> (sqrt(2+sqrt(2))/2)*13

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 Octagon

(Calculation completed in 00.004 seconds)

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< 9 Inradius of Octagon Calculators

Inradius of Octagon given Long Diagonal

Go Inradius of Octagon = ((sqrt(2+sqrt(2)))/4)*Long Diagonal of Octagon

Inradius of Octagon given Short Diagonal

Go Inradius of Octagon = sqrt((2+sqrt(2))/8)*Short Diagonal of Octagon

Inradius of Octagon given Circumradius

Go Inradius of Octagon = (sqrt(2+sqrt(2))/2)*Circumradius of Octagon

Inradius of Octagon given Area

Go Inradius of Octagon = sqrt(((1+sqrt(2))/8)*Area of Octagon)

Inradius of Octagon

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

Inradius of Octagon given Perimeter

Go Inradius of Octagon = (1+sqrt(2))*Perimeter of Octagon/16

Inradius of Octagon given Medium Diagonal

Go Inradius of Octagon = Medium Diagonal of Octagon/2

Inradius of Octagon given Height

Go Inradius of Octagon = Height of Octagon/2

Inradius of Octagon given Width

Go Inradius of Octagon = Width of Octagon/2

Inradius of Octagon given Circumradius Formula

Inradius of Octagon = (sqrt(2+sqrt(2))/2)*Circumradius of Octagon
r_i = (sqrt(2+sqrt(2))/2)*r_c

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 Inradius of Octagon given Circumradius?

Inradius of Octagon given Circumradius calculator uses Inradius of Octagon = (sqrt(2+sqrt(2))/2)*Circumradius of Octagon to calculate the Inradius of Octagon, The Inradius of Octagon given Circumradius formula is defined as the radius of incircle of the Regular Octagon or the circle that contained by the Octagon with all edges touch the circle, and calculated using circumradius of the Octagon. Inradius of Octagon is denoted by r_i symbol.

How to calculate Inradius of Octagon given Circumradius using this online calculator? To use this online calculator for Inradius of Octagon given Circumradius, enter Circumradius of Octagon (r_c) and hit the calculate button. Here is how the Inradius of Octagon given Circumradius calculation can be explained with given input values -> 12.01043 = (sqrt(2+sqrt(2))/2)*13.

FAQ

What is Inradius of Octagon given Circumradius?

The Inradius of Octagon given Circumradius formula is defined as the radius of incircle of the Regular Octagon or the circle that contained by the Octagon with all edges touch the circle, and calculated using circumradius of the Octagon and is represented as r_i = (sqrt(2+sqrt(2))/2)*r_c or Inradius of Octagon = (sqrt(2+sqrt(2))/2)*Circumradius of Octagon. 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.

How to calculate Inradius of Octagon given Circumradius?

The Inradius of Octagon given Circumradius formula is defined as the radius of incircle of the Regular Octagon or the circle that contained by the Octagon with all edges touch the circle, and calculated using circumradius of the Octagon is calculated using Inradius of Octagon = (sqrt(2+sqrt(2))/2)*Circumradius of Octagon. To calculate Inradius of Octagon given Circumradius, you need Circumradius of Octagon (r_c). With our tool, you need to enter the respective value for Circumradius 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 Inradius of Octagon?

In this formula, Inradius of Octagon uses Circumradius of Octagon. We can use 8 other way(s) to calculate the same, which is/are as follows -

Inradius of Octagon = ((1+sqrt(2))/2)*Edge Length of Octagon
Inradius of Octagon = ((sqrt(2+sqrt(2)))/4)*Long Diagonal of Octagon
Inradius of Octagon = Medium Diagonal of Octagon/2
Inradius of Octagon = sqrt((2+sqrt(2))/8)*Short Diagonal of Octagon
Inradius of Octagon = Height of Octagon/2
Inradius of Octagon = (1+sqrt(2))*Perimeter of Octagon/16
Inradius of Octagon = sqrt(((1+sqrt(2))/8)*Area of Octagon)
Inradius of Octagon = Width of Octagon/2

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