Circumradius of Square given Inradius Calculator

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

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✖The Circumradius of Square is the radius of the circumcircle of the Square or the circle which contains the square with all the vertices of the Square lying on the circle.ⓘ Circumradius of Square given Inradius [r_c]

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Formula

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Circumradius of Square given Inradius

Formula

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

Example

`"7.071068m"=sqrt(2)*"5m"`

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Circumradius of Square given Inradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Circumradius of Square = sqrt(2)*Inradius of Square
r_c = 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 Square - (Measured in Meter) - The Circumradius of Square is the radius of the circumcircle of the Square or the circle which contains the square with all the vertices of the Square lying on the circle.
Inradius of Square - (Measured in Meter) - The Inradius of Square is the radius of incircle of the Square or the circle which contained by the Square with all the edges of the Square touch the circle.

STEP 1: Convert Input(s) to Base Unit

Inradius of Square: 5 Meter --> 5 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = sqrt(2)*r_i --> sqrt(2)*5

Evaluating ... ...

r_c = 7.07106781186548

STEP 3: Convert Result to Output's Unit

7.07106781186548 Meter --> No Conversion Required

FINAL ANSWER

7.07106781186548 ≈ 7.071068 Meter <-- Circumradius of Square

(Calculation completed in 00.004 seconds)

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Created by Payal Priya

Birsa Institute of Technology (BIT), Sindri

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< 7 Circumradius of Square Calculators

Circumradius of Square given Diameter of Incircle

Go Circumradius of Square = Diameter of Incircle of Square/(sqrt(2))

Circumradius of Square given Perimeter

Go Circumradius of Square = Perimeter of Square/(4*sqrt(2))

Circumradius of Square

Go Circumradius of Square = Edge Length of Square/(sqrt(2))

Circumradius of Square given Inradius

Go Circumradius of Square = sqrt(2)*Inradius of Square

Circumradius of Square given Area

Go Circumradius of Square = sqrt(Area of Square/2)

Circumradius of Square given Diameter of Circumcircle

Go Circumradius of Square = Diameter of Circumcircle of Square/2

Circumradius of Square given Diagonal

Go Circumradius of Square = Diagonal of Square/2

Circumradius of Square given Inradius Formula

Circumradius of Square = sqrt(2)*Inradius of Square
r_c = sqrt(2)*r_i

What is a Square?

A Square is a quadrilateral with all the sides are equal and all the angles are equal. To be precise, all the angles will be 90^°. In other words, a four sided regular polygon is called Square. This is a fundamental shape in geometry.

What is circumradius and how it is calculated when inradius is given?

In geometry, the circumscribed circle or circumcircle of a square is a circle that passes through all the vertices of the square. The center of this circle is called the circumcenter and its radius is called the circumradius. To calculate it, R = √2r
Where R is the radius of the circumscribed circle and r is the radius of the inscribed circle.

How to Calculate Circumradius of Square given Inradius?

Circumradius of Square given Inradius calculator uses Circumradius of Square = sqrt(2)*Inradius of Square to calculate the Circumradius of Square, The Circumradius of Square given Inradius formula is defined as the radius of the circumcircle of the Square or the circle which contains the square with all the vertices of the Square lying on the circle, and calculated using inradius. Circumradius of Square is denoted by r_c symbol.

How to calculate Circumradius of Square given Inradius using this online calculator? To use this online calculator for Circumradius of Square given Inradius, enter Inradius of Square (r_i) and hit the calculate button. Here is how the Circumradius of Square given Inradius calculation can be explained with given input values -> 7.071068 = sqrt(2)*5.

FAQ

What is Circumradius of Square given Inradius?

The Circumradius of Square given Inradius formula is defined as the radius of the circumcircle of the Square or the circle which contains the square with all the vertices of the Square lying on the circle, and calculated using inradius and is represented as r_c = sqrt(2)*r_i or Circumradius of Square = sqrt(2)*Inradius of Square. The Inradius of Square is the radius of incircle of the Square or the circle which contained by the Square with all the edges of the Square touch the circle.

How to calculate Circumradius of Square given Inradius?

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

In this formula, Circumradius of Square uses Inradius of Square. We can use 6 other way(s) to calculate the same, which is/are as follows -

Circumradius of Square = Edge Length of Square/(sqrt(2))
Circumradius of Square = Perimeter of Square/(4*sqrt(2))
Circumradius of Square = sqrt(Area of Square/2)
Circumradius of Square = Diagonal of Square/2
Circumradius of Square = Diameter of Circumcircle of Square/2
Circumradius of Square = Diameter of Incircle of Square/(sqrt(2))

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