Height of Circular Segment Calculator

✖Radius of Circular Segment is the radius of the circle from which the Circular Segment is cut.ⓘ Radius of Circular Segment [r]			+10% -10%
✖Chord Length of Circular Segment is the length of the linear boundary edge of a Circular Segment.ⓘ Chord Length of Circular Segment [l_c]			+10% -10%

✖Height of Circular Segment is the perpendicular distance of the chord of the Circular Segment from the center of the circle of Circular Segment.ⓘ Height of Circular Segment [h]

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Height of Circular Segment Solution

STEP 0: Pre-Calculation Summary

Formula Used

Height of Circular Segment = Radius of Circular Segment-sqrt(Radius of Circular Segment^2-(Chord Length of Circular Segment/2)^2)
h = r-sqrt(r^2-(l_c/2)^2)
This formula uses 1 Functions, 3 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

Height of Circular Segment - (Measured in Meter) - Height of Circular Segment is the perpendicular distance of the chord of the Circular Segment from the center of the circle of Circular Segment.
Radius of Circular Segment - (Measured in Meter) - Radius of Circular Segment is the radius of the circle from which the Circular Segment is cut.
Chord Length of Circular Segment - (Measured in Meter) - Chord Length of Circular Segment is the length of the linear boundary edge of a Circular Segment.

STEP 1: Convert Input(s) to Base Unit

Radius of Circular Segment: 5 Meter --> 5 Meter No Conversion Required
Chord Length of Circular Segment: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h = r-sqrt(r^2-(l_c/2)^2) --> 5-sqrt(5^2-(10/2)^2)

Evaluating ... ...

h = 5

STEP 3: Convert Result to Output's Unit

5 Meter --> No Conversion Required

FINAL ANSWER

5 Meter <-- Height of Circular Segment

(Calculation completed in 00.004 seconds)

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Shri Madhwa Vadiraja Institute of Technology and Management (SMVITM), Udupi

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< Height of Circular Segment Calculators

Height of Circular Segment

LaTeX Go Height of Circular Segment = Radius of Circular Segment-sqrt(Radius of Circular Segment^2-(Chord Length of Circular Segment/2)^2)

Height of Circular Segment given Chord Length and Central Angle

LaTeX Go Height of Circular Segment = Chord Length of Circular Segment/2*cot(-3/4*Central Angle of Circular Segment)

Height of Circular Segment given Radius and Central Angle

LaTeX Go Height of Circular Segment = Radius of Circular Segment*(1-cos(Central Angle of Circular Segment/2))

Height of Circular Segment Formula

LaTeX Go

Height of Circular Segment = Radius of Circular Segment-sqrt(Radius of Circular Segment^2-(Chord Length of Circular Segment/2)^2)
h = r-sqrt(r^2-(l_c/2)^2)

What is a Circular Segment?

Circular Segment is basically a portion of a circle cut by using a chord. Geometrically a Circular Segment is the region bounded by a circular arc at a particular central angle and the chord joining both the end points of that arc.

What is a Circle?

A Circle is a basic two dimensional geometric shape which is defined as the collection of all points on a plane which are in a fixed distance from a fixed point. The fixed point is called the center of the Circle and the fixed distance is called the radius of the Circle. When two radii become collinear, that combined length is called the diameter of the Circle. That is, diameter is the length of the line segment inside the Circle which pass through the center and it will be two times the radius.

How to Calculate Height of Circular Segment?

Height of Circular Segment calculator uses Height of Circular Segment = Radius of Circular Segment-sqrt(Radius of Circular Segment^2-(Chord Length of Circular Segment/2)^2) to calculate the Height of Circular Segment, The Height of Circular Segment formula is defined as the maximum vertical distance of the Circular Segment when the chord of Circular Segment is the base. Height of Circular Segment is denoted by h symbol.

How to calculate Height of Circular Segment using this online calculator? To use this online calculator for Height of Circular Segment, enter Radius of Circular Segment (r) & Chord Length of Circular Segment (l_c) and hit the calculate button. Here is how the Height of Circular Segment calculation can be explained with given input values -> 5 = 5-sqrt(5^2-(10/2)^2).

FAQ

What is Height of Circular Segment?

The Height of Circular Segment formula is defined as the maximum vertical distance of the Circular Segment when the chord of Circular Segment is the base and is represented as h = r-sqrt(r^2-(l_c/2)^2) or Height of Circular Segment = Radius of Circular Segment-sqrt(Radius of Circular Segment^2-(Chord Length of Circular Segment/2)^2). Radius of Circular Segment is the radius of the circle from which the Circular Segment is cut & Chord Length of Circular Segment is the length of the linear boundary edge of a Circular Segment.

How to calculate Height of Circular Segment?

The Height of Circular Segment formula is defined as the maximum vertical distance of the Circular Segment when the chord of Circular Segment is the base is calculated using Height of Circular Segment = Radius of Circular Segment-sqrt(Radius of Circular Segment^2-(Chord Length of Circular Segment/2)^2). To calculate Height of Circular Segment, you need Radius of Circular Segment (r) & Chord Length of Circular Segment (l_c). With our tool, you need to enter the respective value for Radius of Circular Segment & Chord Length of Circular Segment 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 Height of Circular Segment?

In this formula, Height of Circular Segment uses Radius of Circular Segment & Chord Length of Circular Segment. We can use 2 other way(s) to calculate the same, which is/are as follows -

Height of Circular Segment = Chord Length of Circular Segment/2*cot(-3/4*Central Angle of Circular Segment)
Height of Circular Segment = Radius of Circular Segment*(1-cos(Central Angle of Circular Segment/2))

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