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Circumradius of Triangle Formula

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Circumradius of Triangle is the radius of a circumcircle touching each of the vertices of the Triangle. Check FAQs

r c = \frac{S a \cdot S b \cdot S c}{\sqrt{(S a + S b + S c) \cdot (S b - S a + S c) \cdot (S a - S b + S c) \cdot (S a + S b - S c)}}

r_c - Circumradius of Triangle?S_a - Side A of Triangle?S_b - Side B of Triangle?S_c - Side C of Triangle?

Circumradius of Triangle Example

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Here is how the Circumradius of Triangle equation looks like with Values.

Here is how the Circumradius of Triangle equation looks like with Units.

Here is how the Circumradius of Triangle equation looks like.

10.7705 = \frac{10 \cdot 14 \cdot 20}{\sqrt{(10 + 14 + 20) \cdot (14 - 10 + 20) \cdot (10 - 14 + 20) \cdot (10 + 14 - 20)}}

10.7705m = \frac{10m \cdot 14m \cdot 20m}{\sqrt{(10m + 14m + 20m) \cdot (14m - 10m + 20m) \cdot (10m - 14m + 20m) \cdot (10m + 14m - 20m)}}

10.7705 = \frac{10 \cdot 14 \cdot 20}{\sqrt{(10 + 14 + 20) \cdot (14 - 10 + 20) \cdot (10 - 14 + 20) \cdot (10 + 14 - 20)}}

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Circumradius of Triangle Solution

Follow our step by step solution on how to calculate Circumradius of Triangle?

FIRST Step Consider the formula

r c = \frac{S a \cdot S b \cdot S c}{\sqrt{(S a + S b + S c) \cdot (S b - S a + S c) \cdot (S a - S b + S c) \cdot (S a + S b - S c)}}

Next Step Substitute values of Variables

∴

r c = \frac{10m \cdot 14m \cdot 20m}{\sqrt{(10m + 14m + 20m) \cdot (14m - 10m + 20m) \cdot (10m - 14m + 20m) \cdot (10m + 14m - 20m)}}

Next Step Prepare to Evaluate

∴

r c = \frac{10 \cdot 14 \cdot 20}{\sqrt{(10 + 14 + 20) \cdot (14 - 10 + 20) \cdot (10 - 14 + 20) \cdot (10 + 14 - 20)}}

Next Step Evaluate

∴

r c = 10.7705054606916m

LAST Step Rounding Answer

∴

r c = 10.7705m

Circumradius of Triangle Formula Elements

Variables

Functions

Circumradius of Triangle

Circumradius of Triangle is the radius of a circumcircle touching each of the vertices of the Triangle.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumradius of Triangle

Side A of Triangle

The Side A of Triangle is the length of the side A, of the three sides of the triangle. In other words, the side A of the Triangle is the side opposite to the angle A.

Symbol: S_a

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Side A of Triangle

Side B of Triangle

The Side B of Triangle is the length of the side B of the three sides. In other words, the side Bof the Triangle is the side opposite to the angle B.

Symbol: S_b

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Side B of Triangle

Side C of Triangle

The Side C of Triangle is the length of the side C of the three sides. In other words, side C of the Triangle is the side opposite to angle C.

Symbol: S_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Side C of Triangle

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.

Syntax: sqrt(Number)

Other formulas in Radius of Triangle category

Go Exradius Opposite to Angle A of Triangle

r e(∠A) = \sqrt{\frac{(\frac{S a + S b + S c}{2}) \cdot (\frac{S a - S b + S c}{2}) \cdot (\frac{S a + S b - S c}{2})}{\frac{S b + S c - S a}{2}}}

Go Inradius of Triangle

r i = \frac{\sqrt{(S a + S b + S c) \cdot (S b + S c - S a) \cdot (S a - S b + S c) \cdot (S a + S b - S c)}}{2 \cdot (S a + S b + S c)}

How to Evaluate Circumradius of Triangle?

Circumradius of Triangle evaluator uses Circumradius of Triangle = (Side A of Triangle*Side B of Triangle*Side C of Triangle)/sqrt((Side A of Triangle+Side B of Triangle+Side C of Triangle)*(Side B of Triangle-Side A of Triangle+Side C of Triangle)*(Side A of Triangle-Side B of Triangle+Side C of Triangle)*(Side A of Triangle+Side B of Triangle-Side C of Triangle)) to evaluate the Circumradius of Triangle, The Circumradius of Triangle formula is defined as the length of the radius of the circumcircle of the triangle, calculated using three sides of the Triangle. Circumradius of Triangle is denoted by r_c symbol.

How to evaluate Circumradius of Triangle using this online evaluator? To use this online evaluator for Circumradius of Triangle, enter Side A of Triangle (S_a), Side B of Triangle (S_b) & Side C of Triangle (S_c) and hit the calculate button.

FAQs on Circumradius of Triangle

What is the formula to find Circumradius of Triangle?

The formula of Circumradius of Triangle is expressed as Circumradius of Triangle = (Side A of Triangle*Side B of Triangle*Side C of Triangle)/sqrt((Side A of Triangle+Side B of Triangle+Side C of Triangle)*(Side B of Triangle-Side A of Triangle+Side C of Triangle)*(Side A of Triangle-Side B of Triangle+Side C of Triangle)*(Side A of Triangle+Side B of Triangle-Side C of Triangle)). Here is an example- 10.77051 = (10*14*20)/sqrt((10+14+20)*(14-10+20)*(10-14+20)*(10+14-20)).

How to calculate Circumradius of Triangle?

With Side A of Triangle (S_a), Side B of Triangle (S_b) & Side C of Triangle (S_c) we can find Circumradius of Triangle using the formula - Circumradius of Triangle = (Side A of Triangle*Side B of Triangle*Side C of Triangle)/sqrt((Side A of Triangle+Side B of Triangle+Side C of Triangle)*(Side B of Triangle-Side A of Triangle+Side C of Triangle)*(Side A of Triangle-Side B of Triangle+Side C of Triangle)*(Side A of Triangle+Side B of Triangle-Side C of Triangle)). This formula also uses Square Root (sqrt) function(s).

Can the Circumradius of Triangle be negative?

No, the Circumradius of Triangle, measured in Length cannot be negative.

Which unit is used to measure Circumradius of Triangle?

Circumradius of Triangle is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Circumradius of Triangle can be measured.

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Circumradius of Triangle Formula

Circumradius of Triangle Example

Circumradius of Triangle Solution

Circumradius of Triangle Formula Elements

Other formulas in Radius of Triangle category

How to Evaluate Circumradius of Triangle?

FAQs on Circumradius of Triangle

Variable Name