Angle of Circular Arc given Sector Area Calculator

✖Sector Area of Circular Arc is the area enclosed by the sector formed by using the Circular Arc and corresponding radii.ⓘ Sector Area of Circular Arc [A_Sector]			+10% -10%
✖Radius of Circular Arc is the radius of the circle from which the Circular Arc is formed.ⓘ Radius of Circular Arc [r_Arc]			+10% -10%

✖Angle of Circular Arc is the angle subtended by the end points of a Circular Arc with the center of the circle from which the arc is formed.ⓘ Angle of Circular Arc given Sector Area [∠_Arc]

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Formula

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Angle of Circular Arc given Sector Area

Formula

`"∠"_{"Arc"} = (2*"A"_{"Sector"})/("r"_{"Arc"}^2)`

Example

`"41.25296°"=(2*"9m²")/(("5m")^2)`

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Angle of Circular Arc given Sector Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angle of Circular Arc = (2*Sector Area of Circular Arc)/(Radius of Circular Arc^2)
∠_Arc = (2*A_Sector)/(r_Arc^2)
This formula uses 3 Variables

Variables Used

Angle of Circular Arc - (Measured in Radian) - Angle of Circular Arc is the angle subtended by the end points of a Circular Arc with the center of the circle from which the arc is formed.
Sector Area of Circular Arc - (Measured in Square Meter) - Sector Area of Circular Arc is the area enclosed by the sector formed by using the Circular Arc and corresponding radii.
Radius of Circular Arc - (Measured in Meter) - Radius of Circular Arc is the radius of the circle from which the Circular Arc is formed.

STEP 1: Convert Input(s) to Base Unit

Sector Area of Circular Arc: 9 Square Meter --> 9 Square Meter No Conversion Required
Radius of Circular Arc: 5 Meter --> 5 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

∠_Arc = (2*A_Sector)/(r_Arc^2) --> (2*9)/(5^2)

Evaluating ... ...

∠_Arc = 0.72

STEP 3: Convert Result to Output's Unit

0.72 Radian -->41.252961249427 Degree (Check conversion here)

FINAL ANSWER

41.252961249427 ≈ 41.25296 Degree <-- Angle of Circular Arc

(Calculation completed in 00.004 seconds)

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Created by Anamika Mittal

Vellore Institute of Technology (VIT), Bhopal

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< 4 Angle of Circular Arc Calculators

Angle of Circular Arc given Arc Length and Circumference

Go Angle of Circular Arc = (2*pi*Arc Length of Circular Arc)/Circumference of Circle of Circular Arc

Angle of Circular Arc given Sector Area

Go Angle of Circular Arc = (2*Sector Area of Circular Arc)/(Radius of Circular Arc^2)

Angle of Circular Arc given Arc Length

Go Angle of Circular Arc = Arc Length of Circular Arc/Radius of Circular Arc

Angle of Circular Arc given Inscribed Angle

Go Angle of Circular Arc = 2*Inscribed Angle of Circular Arc

Angle of Circular Arc given Sector Area Formula

Angle of Circular Arc = (2*Sector Area of Circular Arc)/(Radius of Circular Arc^2)
∠_Arc = (2*A_Sector)/(r_Arc^2)

What is a Circular Arc?

Circular Arc is basically a piece of the circumference of a circle. More specifically it is a curve cut from the boundary of a circle in a particular central angle, which is the angle subtended by the end points of the curve with respect to the center of the circle. Any two points on a circle will give a pair of supplementary arcs. Out of them, the larger arc is called major arc and the smaller arc is called minor arc.

What is 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 Angle of Circular Arc given Sector Area?

Angle of Circular Arc given Sector Area calculator uses Angle of Circular Arc = (2*Sector Area of Circular Arc)/(Radius of Circular Arc^2) to calculate the Angle of Circular Arc, Angle of Circular Arc given Sector Area formula is defined as the angle subtended by the arc with the center of the circle from which the Circular Arc is made, and calculated using the sector area formed from that Circular Arc. Angle of Circular Arc is denoted by ∠_Arc symbol.

How to calculate Angle of Circular Arc given Sector Area using this online calculator? To use this online calculator for Angle of Circular Arc given Sector Area, enter Sector Area of Circular Arc (A_Sector) & Radius of Circular Arc (r_Arc) and hit the calculate button. Here is how the Angle of Circular Arc given Sector Area calculation can be explained with given input values -> 2363.621 = (2*9)/(5^2).

FAQ

What is Angle of Circular Arc given Sector Area?

Angle of Circular Arc given Sector Area formula is defined as the angle subtended by the arc with the center of the circle from which the Circular Arc is made, and calculated using the sector area formed from that Circular Arc and is represented as ∠_Arc = (2*A_Sector)/(r_Arc^2) or Angle of Circular Arc = (2*Sector Area of Circular Arc)/(Radius of Circular Arc^2). Sector Area of Circular Arc is the area enclosed by the sector formed by using the Circular Arc and corresponding radii & Radius of Circular Arc is the radius of the circle from which the Circular Arc is formed.

How to calculate Angle of Circular Arc given Sector Area?

Angle of Circular Arc given Sector Area formula is defined as the angle subtended by the arc with the center of the circle from which the Circular Arc is made, and calculated using the sector area formed from that Circular Arc is calculated using Angle of Circular Arc = (2*Sector Area of Circular Arc)/(Radius of Circular Arc^2). To calculate Angle of Circular Arc given Sector Area, you need Sector Area of Circular Arc (A_Sector) & Radius of Circular Arc (r_Arc). With our tool, you need to enter the respective value for Sector Area of Circular Arc & Radius of Circular Arc 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 Angle of Circular Arc?

In this formula, Angle of Circular Arc uses Sector Area of Circular Arc & Radius of Circular Arc. We can use 3 other way(s) to calculate the same, which is/are as follows -

Angle of Circular Arc = (2*pi*Arc Length of Circular Arc)/Circumference of Circle of Circular Arc
Angle of Circular Arc = Arc Length of Circular Arc/Radius of Circular Arc
Angle of Circular Arc = 2*Inscribed Angle of Circular Arc

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