Height 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 Height of Octagon is the vertical distance from the bottom edge to the top edge of the Regular Octagon.ⓘ Height of Octagon given Circumradius [h]

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Formula

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Height of Octagon given Circumradius

Formula

`"h" = ((2*"r"_{"c"})/(sqrt(4+(2*sqrt(2)))))*(1+sqrt(2))`

Example

`"24.02087m"=((2*"13m")/(sqrt(4+(2*sqrt(2)))))*(1+sqrt(2))`

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Height of Octagon given Circumradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Height of Octagon = ((2*Circumradius of Octagon)/(sqrt(4+(2*sqrt(2)))))*(1+sqrt(2))
h = ((2*r_c)/(sqrt(4+(2*sqrt(2)))))*(1+sqrt(2))
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

Height of Octagon - (Measured in Meter) - The Height of Octagon is the vertical distance from the bottom edge to the top edge of the Regular Octagon.
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

h = ((2*r_c)/(sqrt(4+(2*sqrt(2)))))*(1+sqrt(2)) --> ((2*13)/(sqrt(4+(2*sqrt(2)))))*(1+sqrt(2))

Evaluating ... ...

h = 24.0208678452935

STEP 3: Convert Result to Output's Unit

24.0208678452935 Meter --> No Conversion Required

FINAL ANSWER

24.0208678452935 ≈ 24.02087 Meter <-- Height of Octagon

(Calculation completed in 00.004 seconds)

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< 8 Height of Octagon Calculators

Height of Octagon given Circumradius

Go Height of Octagon = ((2*Circumradius of Octagon)/(sqrt(4+(2*sqrt(2)))))*(1+sqrt(2))

Height of Octagon given Short Diagonal

Go Height of Octagon = sqrt(1+(1/(sqrt(2))))*Short Diagonal of Octagon

Height of Octagon given Long Diagonal

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

Height of Octagon given Area

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

Height of Octagon given Perimeter

Go Height of Octagon = (1+sqrt(2))*Perimeter of Octagon/8

Height of Octagon

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

Height of Octagon given Medium Diagonal

Go Height of Octagon = Medium Diagonal of Octagon*1

Height of Octagon given Inradius

Go Height of Octagon = 2*Inradius of Octagon

Height of Octagon given Circumradius Formula

Height of Octagon = ((2*Circumradius of Octagon)/(sqrt(4+(2*sqrt(2)))))*(1+sqrt(2))
h = ((2*r_c)/(sqrt(4+(2*sqrt(2)))))*(1+sqrt(2))

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 Height of Octagon given Circumradius?

Height of Octagon given Circumradius calculator uses Height of Octagon = ((2*Circumradius of Octagon)/(sqrt(4+(2*sqrt(2)))))*(1+sqrt(2)) to calculate the Height of Octagon, The Height of Octagon given Circumradius formula is defined as the vertical distance from the bottom edge to the top edge of the Regular Octagon, and calculated using the circumradius of the Octagon. Height of Octagon is denoted by h symbol.

How to calculate Height of Octagon given Circumradius using this online calculator? To use this online calculator for Height of Octagon given Circumradius, enter Circumradius of Octagon (r_c) and hit the calculate button. Here is how the Height of Octagon given Circumradius calculation can be explained with given input values -> 24.02087 = ((2*13)/(sqrt(4+(2*sqrt(2)))))*(1+sqrt(2)).

FAQ

What is Height of Octagon given Circumradius?

The Height of Octagon given Circumradius formula is defined as the vertical distance from the bottom edge to the top edge of the Regular Octagon, and calculated using the circumradius of the Octagon and is represented as h = ((2*r_c)/(sqrt(4+(2*sqrt(2)))))*(1+sqrt(2)) or Height of Octagon = ((2*Circumradius of Octagon)/(sqrt(4+(2*sqrt(2)))))*(1+sqrt(2)). 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 Height of Octagon given Circumradius?

The Height of Octagon given Circumradius formula is defined as the vertical distance from the bottom edge to the top edge of the Regular Octagon, and calculated using the circumradius of the Octagon is calculated using Height of Octagon = ((2*Circumradius of Octagon)/(sqrt(4+(2*sqrt(2)))))*(1+sqrt(2)). To calculate Height 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 Height of Octagon?

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

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

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