What Does An Arc Length Formula Calculate?

The arc length formula is used to calculate the measurement of the distance which is along the curved line which makes up the arc of the circle. An arc is simply the segment of the circle making up the circle. This is to be noted that, that the arc length measures longer than the straight line.

What is the formula for Arc Length?

The formula which is used to measure the length of the arc will be:

• Arc Length Formula, when θ is in degrees – then s = 2 π r (θ/360°)
• Arc Length Formula when θ is in radius – then s = ϴ  X r
• Arc Length Formula which is in Integral Form = s= ∫ba√1+(dydx)2dx∫ab1+(dydx)2dx

What are the Denotations of the Arc Length Formula?

In the above formula, we saw that there are some identities that are yet to be explained. The denotations are as follows:

• ‘S’ in the formula that denotes the arc length.
• ‘R’ is the radius of the circle.
• Θ here is the central angle of the arc present here.

What Will Be the Formula of Arc Length in Radians?

The arc length of the circle can be estimated with the use of varied formulae. This will be based on the unit of the central angle which is the arc here. The arc length formula is in radians which are to be expressed as follows:

Arc Length = θ × r

In this case – L is the arc length, θ is the center of the angle which is in radius, and r here is the radius of the circle.

How Will You Find the Arc Length Of a Curve?

The arc length of the circle is to be calculated using different formulae which are based on the given data. Thus, some of the important cases are as follows:

• Finding arc length with the radius and the central angle given
• Finding arc length without the radius
• Finding the arc length without the central angle.

How Can You Find The Arc Length With The Radius And The Central Angle?

In this case, you can find out the arc length of the circle by calculating the radius and the central angle by using the arc length formula here.

Length of the Arc will be θ × r, here θ  is in radii.

Length of an Arc will be θ × (π/180) × r where θ  will be termed in degree.

Steps To Find Out the Arc Length Without the Radius

The arc length of the circle is to be calculated without the radius and by using the central angle and the sector area. The steps to find out the arc length is as follows:

• First, multiply the sector area with 2, then divide the result which came after division by the central angle in the radians.
• Then find out the square root of the result of the divided number.
• Then you can multiply the root which is thereby obtained to get the arc length.
• Then the units of the arc length are to be the square root of the sector in terms of area units here.

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