Inradius of N-gon Calculator

✖Edge Length of N-gon is the length of the line segment joining two adjacent vertices of N-gon.ⓘ Edge Length of N-gon [l_e]			+10% -10%
✖Number of Sides of N-gon is the number of line segments required to make a N-gon.ⓘ Number of Sides of N-gon [N_Sides]			+10% -10%

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

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Formula

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Inradius of N-gon

Formula

`"r"_{"i"} = "l"_{"e"}/(2*tan(pi/"N"_{"Sides"}))`

Example

`"12.07107m"="10m"/(2*tan(pi/"8"))`

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Inradius of N-gon Solution

STEP 0: Pre-Calculation Summary

Formula Used

Inradius of N-gon = Edge Length of N-gon/(2*tan(pi/Number of Sides of N-gon))
r_i = l_e/(2*tan(pi/N_Sides))
This formula uses 1 Constants, 1 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)

Variables Used

Inradius of N-gon - (Measured in Meter) - Inradius of N-gon is defined as the radius of the circle which is inscribed inside the N-gon.
Edge Length of N-gon - (Measured in Meter) - Edge Length of N-gon is the length of the line segment joining two adjacent vertices of N-gon.
Number of Sides of N-gon - Number of Sides of N-gon is the number of line segments required to make a N-gon.

STEP 1: Convert Input(s) to Base Unit

Edge Length of N-gon: 10 Meter --> 10 Meter No Conversion Required
Number of Sides of N-gon: 8 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = l_e/(2*tan(pi/N_Sides)) --> 10/(2*tan(pi/8))

Evaluating ... ...

r_i = 12.0710678118655

STEP 3: Convert Result to Output's Unit

12.0710678118655 Meter --> No Conversion Required

FINAL ANSWER

12.0710678118655 ≈ 12.07107 Meter <-- Inradius of N-gon

(Calculation completed in 00.004 seconds)

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St Joseph's College (SJC), Bengaluru

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< 2 Radius of N-gon Calculators

Circumradius of N-gon

Go Circumradius of N-gon = Edge Length of N-gon/(2*sin(pi/Number of Sides of N-gon))

Inradius of N-gon

Go Inradius of N-gon = Edge Length of N-gon/(2*tan(pi/Number of Sides of N-gon))

Inradius of N-gon Formula

Inradius of N-gon = Edge Length of N-gon/(2*tan(pi/Number of Sides of N-gon))
r_i = l_e/(2*tan(pi/N_Sides))

What is N-gon?

N-gon is a polygon with N sides and N vertices. An n-gon, can be either convex or concave. A convex polygon has none of its interior angles greater than 180°. On the contrary, a concave polygon has one or more of its interior angles greater than 180°. A polygon is called regular when its sides are equal and also its interior angles are equal.

How to Calculate Inradius of N-gon?

Inradius of N-gon calculator uses Inradius of N-gon = Edge Length of N-gon/(2*tan(pi/Number of Sides of N-gon)) to calculate the Inradius of N-gon, The Inradius of N-gon formula is defined as the radius of the circle which is inscribed inside the N-gon. Inradius of N-gon is denoted by r_i symbol.

How to calculate Inradius of N-gon using this online calculator? To use this online calculator for Inradius of N-gon, enter Edge Length of N-gon (l_e) & Number of Sides of N-gon (N_Sides) and hit the calculate button. Here is how the Inradius of N-gon calculation can be explained with given input values -> 12.07107 = 10/(2*tan(pi/8)).

FAQ

What is Inradius of N-gon?

The Inradius of N-gon formula is defined as the radius of the circle which is inscribed inside the N-gon and is represented as r_i = l_e/(2*tan(pi/N_Sides)) or Inradius of N-gon = Edge Length of N-gon/(2*tan(pi/Number of Sides of N-gon)). Edge Length of N-gon is the length of the line segment joining two adjacent vertices of N-gon & Number of Sides of N-gon is the number of line segments required to make a N-gon.

How to calculate Inradius of N-gon?

The Inradius of N-gon formula is defined as the radius of the circle which is inscribed inside the N-gon is calculated using Inradius of N-gon = Edge Length of N-gon/(2*tan(pi/Number of Sides of N-gon)). To calculate Inradius of N-gon, you need Edge Length of N-gon (l_e) & Number of Sides of N-gon (N_Sides). With our tool, you need to enter the respective value for Edge Length of N-gon & Number of Sides of N-gon and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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