Circumradius of Triangle Calculator

✖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.ⓘ Side A of Triangle [S_a]			+10% -10%
✖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.ⓘ Side B of Triangle [S_b]			+10% -10%
✖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.ⓘ Side C of Triangle [S_c]			+10% -10%

✖Circumradius of Triangle is the radius of a circumcircle touching each of the vertices of the Triangle.ⓘ Circumradius of Triangle [r_c]

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Formula

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Circumradius of Triangle

Formula

`"r"_{"c"} = ("S"_{"a"}*"S"_{"b"}*"S"_{"c"})/sqrt(("S"_{"a"}+"S"_{"b"}+"S"_{"c"})*("S"_{"b"}-"S"_{"a"}+"S"_{"c"})*("S"_{"a"}-"S"_{"b"}+"S"_{"c"})*("S"_{"a"}+"S"_{"b"}-"S"_{"c"}))`

Example

`"10.77051m"=("10m"*"14m"*"20m")/sqrt(("10m"+"14m"+"20m")*("14m"-"10m"+"20m")*("10m"-"14m"+"20m")*("10m"+"14m"-"20m"))`

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Circumradius of Triangle Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
r_c = (S_a*S_b*S_c)/sqrt((S_a+S_b+S_c)*(S_b-S_a+S_c)*(S_a-S_b+S_c)*(S_a+S_b-S_c))
This formula uses 1 Functions, 4 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 Triangle - (Measured in Meter) - Circumradius of Triangle is the radius of a circumcircle touching each of the vertices of the Triangle.
Side A of Triangle - (Measured in Meter) - 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.
Side B of Triangle - (Measured in Meter) - 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.
Side C of Triangle - (Measured in Meter) - 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.

STEP 1: Convert Input(s) to Base Unit

Side A of Triangle: 10 Meter --> 10 Meter No Conversion Required
Side B of Triangle: 14 Meter --> 14 Meter No Conversion Required
Side C of Triangle: 20 Meter --> 20 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = (S_a*S_b*S_c)/sqrt((S_a+S_b+S_c)*(S_b-S_a+S_c)*(S_a-S_b+S_c)*(S_a+S_b-S_c)) --> (10*14*20)/sqrt((10+14+20)*(14-10+20)*(10-14+20)*(10+14-20))

Evaluating ... ...

r_c = 10.7705054606916

STEP 3: Convert Result to Output's Unit

10.7705054606916 Meter --> No Conversion Required

FINAL ANSWER

10.7705054606916 ≈ 10.77051 Meter <-- Circumradius of Triangle

(Calculation completed in 00.021 seconds)

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Home » Math » Geometry » 2D Geometry » Triangle » Triangle » Radius of Triangle » Circumradius of Triangle

Credits

Created by Venkata Sai Prasanna Aradhyula

Birla Institute of Technology & Science (BITS), Hyderabad

Venkata Sai Prasanna Aradhyula has created this Calculator and 10+ more calculators!

Verified by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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

< 7 Radius of Triangle Calculators

Circumradius of Triangle

Go 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))

Inradius of Triangle

Go Inradius of Triangle = sqrt((Side A of Triangle+Side B of Triangle+Side C of Triangle)*(Side B of Triangle+Side C of Triangle-Side A 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))/(2*(Side A of Triangle+Side B of Triangle+Side C of Triangle))

Exradius Opposite to Angle A of Triangle

Go Exradius Opposite to ∠A of Triangle = sqrt(( ((Side A of Triangle+Side B of Triangle+Side C of Triangle)/2)* ((Side A of Triangle-Side B of Triangle+Side C of Triangle)/2)* ((Side A of Triangle+Side B of Triangle-Side C of Triangle)/2))/ ((Side B of Triangle+Side C of Triangle-Side A of Triangle)/2))

Inradius of Triangle by Heron's Formula

Go Inradius of Triangle = sqrt(((Semiperimeter of Triangle-Side C of Triangle)*(Semiperimeter of Triangle-Side B of Triangle)*(Semiperimeter of Triangle-Side A of Triangle))/Semiperimeter of Triangle)

Circumradius of Triangle given Three Exradii and Inradius

Go Circumradius of Triangle = (Exradius Opposite to ∠A of Triangle+Exradius Opposite to ∠B of Triangle+Exradius Opposite to ∠C of Triangle-Inradius of Triangle)/4

Inradius of Triangle given Three Exradii

Go Inradius of Triangle = 1/(1/Exradius Opposite to ∠A of Triangle+1/Exradius Opposite to ∠B of Triangle+1/Exradius Opposite to ∠C of Triangle)

Circumradius of Triangle given One Side and its Opposite Angle

Go Circumradius of Triangle = Side A of Triangle/(2*sin(Angle A of Triangle))

< 3 Radius of Triangle Calculators

Circumradius of Triangle

Inradius of Triangle

Exradius Opposite to Angle A of Triangle

Circumradius of Triangle Formula

What is a Triangle?

A Triangle is a type of polygon, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.

What is a Circumcircle ?

Circumcircle is the circle that passes through all vertices (corner points) of a triangle. The center of the circumcircle is called the circumcenter, and the circle's radius is called the circumradius. The circumcenter of a triangle is defined as the point where the perpendicular bisectors of the sides of that particular triangle intersect.

How to Calculate Circumradius of Triangle?

Circumradius of Triangle calculator 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 calculate 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 calculate Circumradius of Triangle using this online calculator? To use this online calculator 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. Here is how the Circumradius of Triangle calculation can be explained with given input values -> 10.77051 = (10*14*20)/sqrt((10+14+20)*(14-10+20)*(10-14+20)*(10+14-20)).

FAQ

What is 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 and is represented as r_c = (S_a*S_b*S_c)/sqrt((S_a+S_b+S_c)*(S_b-S_a+S_c)*(S_a-S_b+S_c)*(S_a+S_b-S_c)) or 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)). 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, 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 & 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.

How to calculate 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 is calculated using 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 calculate Circumradius of Triangle, you need Side A of Triangle (S_a), Side B of Triangle (S_b) & Side C of Triangle (S_c). With our tool, you need to enter the respective value for Side A of Triangle, Side B of Triangle & Side C of Triangle 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 Triangle?

In this formula, Circumradius of Triangle uses Side A of Triangle, Side B of Triangle & Side C of Triangle. We can use 2 other way(s) to calculate the same, which is/are as follows -

Circumradius of Triangle = Side A of Triangle/(2*sin(Angle A of Triangle))
Circumradius of Triangle = (Exradius Opposite to ∠A of Triangle+Exradius Opposite to ∠B of Triangle+Exradius Opposite to ∠C of Triangle-Inradius of Triangle)/4

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