Inradius 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%

✖Inradius of Triangle is defined as the radius of the circle which is inscribed inside the Triangle.ⓘ Inradius of Triangle [r_i]

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Formula

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Inradius of Triangle

Formula

`"r"_{"i"} = sqrt(("S"_{"a"}+"S"_{"b"}+"S"_{"c"})*("S"_{"b"}+"S"_{"c"}-"S"_{"a"})*("S"_{"a"}-"S"_{"b"}+"S"_{"c"})*("S"_{"a"}+"S"_{"b"}-"S"_{"c"}))/(2*("S"_{"a"}+"S"_{"b"}+"S"_{"c"}))`

Example

`"2.954196m"=sqrt(("10m"+"14m"+"20m")*("14m"+"20m"-"10m")*("10m"-"14m"+"20m")*("10m"+"14m"-"20m"))/(2*("10m"+"14m"+"20m"))`

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Inradius of Triangle Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
r_i = sqrt((S_a+S_b+S_c)*(S_b+S_c-S_a)*(S_a-S_b+S_c)*(S_a+S_b-S_c))/(2*(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

Inradius of Triangle - (Measured in Meter) - Inradius of Triangle is defined as the radius of the circle which is inscribed inside 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_i = sqrt((S_a+S_b+S_c)*(S_b+S_c-S_a)*(S_a-S_b+S_c)*(S_a+S_b-S_c))/(2*(S_a+S_b+S_c)) --> sqrt((10+14+20)*(14+20-10)*(10-14+20)*(10+14-20))/(2*(10+14+20))

Evaluating ... ...

r_i = 2.95419578350399

STEP 3: Convert Result to Output's Unit

2.95419578350399 Meter --> No Conversion Required

FINAL ANSWER

2.95419578350399 ≈ 2.954196 Meter <-- Inradius of Triangle

(Calculation completed in 00.004 seconds)

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

Credits

Created by Dhruv Walia

Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

Dhruv Walia has created this Calculator and 1100+ more calculators!

Verified by Nikhil

Mumbai University (DJSCE), Mumbai

Nikhil has verified this Calculator and 300+ 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

Inradius 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 Incircle of a Triangle ?

The Incircle or inscribed circle of a triangle is the largest circle contained in the triangle. It touches the three sides. The center of the incircle is a triangle center called the triangle's Incenter. Incenter is the point of intersection of all the 3 internal angular bisectors of the triangle.

How to Calculate Inradius of Triangle?

Inradius of Triangle calculator uses 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)) to calculate the Inradius of Triangle, The Inradius of Triangle formula is defined as the radius of the circle which is inscribed inside the Triangle. Inradius of Triangle is denoted by r_i symbol.

How to calculate Inradius of Triangle using this online calculator? To use this online calculator for Inradius 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 Inradius of Triangle calculation can be explained with given input values -> 2.954196 = sqrt((10+14+20)*(14+20-10)*(10-14+20)*(10+14-20))/(2*(10+14+20)).

FAQ

What is Inradius of Triangle?

The Inradius of Triangle formula is defined as the radius of the circle which is inscribed inside the Triangle and is represented as r_i = sqrt((S_a+S_b+S_c)*(S_b+S_c-S_a)*(S_a-S_b+S_c)*(S_a+S_b-S_c))/(2*(S_a+S_b+S_c)) or 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)). 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 Inradius of Triangle?

The Inradius of Triangle formula is defined as the radius of the circle which is inscribed inside the Triangle is calculated using 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)). To calculate Inradius 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 Inradius of Triangle?

In this formula, Inradius 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 -

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)
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)

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