Height of Circular Segment given Radius and Central Angle 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%
✖Central Angle of Circular Segment is the angle subtended by the arc of a Circular Segment with the center of the circle from which the Circular Segment is cut.ⓘ Central Angle of Circular Segment [∠_Central]			+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 given Radius and Central Angle [h]

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Height of Circular Segment given Radius and Central Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Height of Circular Segment = Radius of Circular Segment*(1-cos(Central Angle of Circular Segment/2))
h = r*(1-cos(∠_Central/2))
This formula uses 1 Functions, 3 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

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.
Central Angle of Circular Segment - (Measured in Radian) - Central Angle of Circular Segment is the angle subtended by the arc of a Circular Segment with the center of the circle from which the Circular Segment is cut.

STEP 1: Convert Input(s) to Base Unit

Radius of Circular Segment: 5 Meter --> 5 Meter No Conversion Required
Central Angle of Circular Segment: 180 Degree --> 3.1415926535892 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h = r*(1-cos(∠_Central/2)) --> 5*(1-cos(3.1415926535892/2))

Evaluating ... ...

h = 4.99999999999852

STEP 3: Convert Result to Output's Unit

4.99999999999852 Meter --> No Conversion Required

FINAL ANSWER

4.99999999999852 ≈ 5 Meter <-- Height of Circular Segment

(Calculation completed in 00.004 seconds)

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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 given Radius and Central Angle Formula

LaTeX Go

Height of Circular Segment = Radius of Circular Segment*(1-cos(Central Angle of Circular Segment/2))
h = r*(1-cos(∠_Central/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 given Radius and Central Angle?

Height of Circular Segment given Radius and Central Angle calculator uses Height of Circular Segment = Radius of Circular Segment*(1-cos(Central Angle of Circular Segment/2)) to calculate the Height of Circular Segment, Height of Circular Segment given Radius and Central Angle formula is defined as the maximum vertical distance of the Circular Segment when the chord of the Circular Segment is the base and calculated using the radius and central angle of the Circular Segment. Height of Circular Segment is denoted by h symbol.

How to calculate Height of Circular Segment given Radius and Central Angle using this online calculator? To use this online calculator for Height of Circular Segment given Radius and Central Angle, enter Radius of Circular Segment (r) & Central Angle of Circular Segment (∠_Central) and hit the calculate button. Here is how the Height of Circular Segment given Radius and Central Angle calculation can be explained with given input values -> 5 = 5*(1-cos(3.1415926535892/2)).

FAQ

What is Height of Circular Segment given Radius and Central Angle?

Height of Circular Segment given Radius and Central Angle formula is defined as the maximum vertical distance of the Circular Segment when the chord of the Circular Segment is the base and calculated using the radius and central angle of the Circular Segment and is represented as h = r*(1-cos(∠_Central/2)) or Height of Circular Segment = Radius of Circular Segment*(1-cos(Central Angle of Circular Segment/2)). Radius of Circular Segment is the radius of the circle from which the Circular Segment is cut & Central Angle of Circular Segment is the angle subtended by the arc of a Circular Segment with the center of the circle from which the Circular Segment is cut.

How to calculate Height of Circular Segment given Radius and Central Angle?

Height of Circular Segment given Radius and Central Angle formula is defined as the maximum vertical distance of the Circular Segment when the chord of the Circular Segment is the base and calculated using the radius and central angle of the Circular Segment is calculated using Height of Circular Segment = Radius of Circular Segment*(1-cos(Central Angle of Circular Segment/2)). To calculate Height of Circular Segment given Radius and Central Angle, you need Radius of Circular Segment (r) & Central Angle of Circular Segment (∠_Central). With our tool, you need to enter the respective value for Radius of Circular Segment & Central Angle 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 & Central Angle of Circular Segment. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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