Inradius of Octagon 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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Formula

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Inradius of Octagon

Formula

`"r"_{"i"} = ((1+sqrt(2))/2)*"l"_{"e"}`

Example

`"12.07107m"=((1+sqrt(2))/2)*"10m"`

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Inradius of Octagon Solution

STEP 0: Pre-Calculation Summary

Formula Used

Inradius of Octagon = ((1+sqrt(2))/2)*Edge Length of Octagon
r_i = ((1+sqrt(2))/2)*l_e
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.
Edge Length of Octagon - (Measured in Meter) - The Edge Length of Octagon is the length of any edge of the Regular Octagon.

STEP 1: Convert Input(s) to Base Unit

Edge Length of Octagon: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = ((1+sqrt(2))/2)*l_e --> ((1+sqrt(2))/2)*10

Evaluating ... ...

r_i = 12.0710678118655

STEP 3: Convert Result to Output's Unit

12.0710678118655 Meter --> No Conversion Required

FINAL ANSWER

12.0710678118655 ≈ 12.07107 Meter <-- Inradius of Octagon

(Calculation completed in 00.004 seconds)

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Created by Mona Gladys

St Joseph's College (SJC), Bengaluru

Mona Gladys has created this Calculator and 2000+ more calculators!

Verified by Shweta Patil

Walchand College of Engineering (WCE), Sangli

Shweta Patil has verified this Calculator and 1100+ more calculators!

< 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

< 5 Radius of Octagon Calculators

Circumradius of Octagon

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

Circumradius of Octagon given Height

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

Inradius of Octagon

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

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 Formula

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

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?

Inradius of Octagon calculator uses Inradius of Octagon = ((1+sqrt(2))/2)*Edge Length of Octagon to calculate the Inradius of Octagon, The Inradius of Octagon 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. Inradius of Octagon is denoted by r_i symbol.

How to calculate Inradius of Octagon using this online calculator? To use this online calculator for Inradius of Octagon, enter Edge Length of Octagon (l_e) and hit the calculate button. Here is how the Inradius of Octagon calculation can be explained with given input values -> 12.07107 = ((1+sqrt(2))/2)*10.

FAQ

What is Inradius of Octagon?

The Inradius of Octagon 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 is represented as r_i = ((1+sqrt(2))/2)*l_e or Inradius of Octagon = ((1+sqrt(2))/2)*Edge Length of Octagon. The Edge Length of Octagon is the length of any edge of the Regular Octagon.

How to calculate Inradius of Octagon?

The Inradius of Octagon 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 is calculated using Inradius of Octagon = ((1+sqrt(2))/2)*Edge Length of Octagon. To calculate Inradius of Octagon, you need Edge Length of Octagon (l_e). With our tool, you need to enter the respective value for Edge Length 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 Edge Length of Octagon. We can use 10 other way(s) to calculate the same, which is/are as follows -

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

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