Area of Circular Segment given Chord Length Calculator

✖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%
✖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%

✖Area of Circular Segment is the total quantity of plane enclosed by the boundary of a Circular Segment.ⓘ Area of Circular Segment given Chord Length [A]

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Area of Circular Segment given Chord Length Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of Circular Segment = ((2*Central Angle of Circular Segment)-sin(Central Angle of Circular Segment))/4*(Chord Length of Circular Segment^2)/(2-(2*cos(Central Angle of Circular Segment)))
A = ((2*∠_Central)-sin(∠_Central))/4*(l_c^2)/(2-(2*cos(∠_Central)))
This formula uses 2 Functions, 3 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
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

Area of Circular Segment - (Measured in Square Meter) - Area of Circular Segment is the total quantity of plane enclosed by the boundary of a Circular Segment.
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.
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

Central Angle of Circular Segment: 180 Degree --> 3.1415926535892 Radian (Check conversion here)
Chord Length of Circular Segment: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = ((2*∠_Central)-sin(∠_Central))/4*(l_c^2)/(2-(2*cos(∠_Central))) --> ((2*3.1415926535892)-sin(3.1415926535892))/4*(10^2)/(2-(2*cos(3.1415926535892)))

Evaluating ... ...

A = 39.2699081698613

STEP 3: Convert Result to Output's Unit

39.2699081698613 Square Meter --> No Conversion Required

FINAL ANSWER

39.2699081698613 ≈ 39.26991 Square Meter <-- Area of Circular Segment

(Calculation completed in 00.020 seconds)

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< Area of Circular Segment Calculators

Area of Circular Segment given Chord Length

LaTeX Go Area of Circular Segment = ((2*Central Angle of Circular Segment)-sin(Central Angle of Circular Segment))/4*(Chord Length of Circular Segment^2)/(2-(2*cos(Central Angle of Circular Segment)))

Area of Circular Segment

LaTeX Go Area of Circular Segment = ((2*Central Angle of Circular Segment)-sin(Central Angle of Circular Segment))/4*Radius of Circular Segment^2

Area of Circular Segment given Chord Length Formula

LaTeX Go

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 Area of Circular Segment given Chord Length?

Area of Circular Segment given Chord Length calculator uses Area of Circular Segment = ((2*Central Angle of Circular Segment)-sin(Central Angle of Circular Segment))/4*(Chord Length of Circular Segment^2)/(2-(2*cos(Central Angle of Circular Segment))) to calculate the Area of Circular Segment, Area of Circular Segment given Chord Length formula is defined as the amount of 2D space bounded by a chord and a corresponding arc and calculated using the chord length of the Circular Segment. Area of Circular Segment is denoted by A symbol.

How to calculate Area of Circular Segment given Chord Length using this online calculator? To use this online calculator for Area of Circular Segment given Chord Length, enter Central Angle of Circular Segment (∠_Central) & Chord Length of Circular Segment (l_c) and hit the calculate button. Here is how the Area of Circular Segment given Chord Length calculation can be explained with given input values -> 39.26991 = ((2*3.1415926535892)-sin(3.1415926535892))/4*(10^2)/(2-(2*cos(3.1415926535892))).

FAQ

What is Area of Circular Segment given Chord Length?

Area of Circular Segment given Chord Length formula is defined as the amount of 2D space bounded by a chord and a corresponding arc and calculated using the chord length of the Circular Segment and is represented as A = ((2*∠_Central)-sin(∠_Central))/4*(l_c^2)/(2-(2*cos(∠_Central))) or Area of Circular Segment = ((2*Central Angle of Circular Segment)-sin(Central Angle of Circular Segment))/4*(Chord Length of Circular Segment^2)/(2-(2*cos(Central Angle of Circular Segment))). 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 & Chord Length of Circular Segment is the length of the linear boundary edge of a Circular Segment.

How to calculate Area of Circular Segment given Chord Length?

Area of Circular Segment given Chord Length formula is defined as the amount of 2D space bounded by a chord and a corresponding arc and calculated using the chord length of the Circular Segment is calculated using Area of Circular Segment = ((2*Central Angle of Circular Segment)-sin(Central Angle of Circular Segment))/4*(Chord Length of Circular Segment^2)/(2-(2*cos(Central Angle of Circular Segment))). To calculate Area of Circular Segment given Chord Length, you need Central Angle of Circular Segment (∠_Central) & Chord Length of Circular Segment (l_c). With our tool, you need to enter the respective value for Central Angle 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 Area of Circular Segment?

In this formula, Area of Circular Segment uses Central Angle of Circular Segment & Chord Length of Circular Segment. We can use 1 other way(s) to calculate the same, which is/are as follows -

Area of Circular Segment = ((2*Central Angle of Circular Segment)-sin(Central Angle of Circular Segment))/4*Radius of Circular Segment^2

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