Arc Length Calculator

Arc Length Calculator is an online tool that calculates the length of an arc when we know the radius of the circle and the central angle of the arc. An arc is defined as a part of the circumference of a circle that lies between any two points.

What Is Arc Length Calculator?

Arc Length Calculator computes the length of the arc by using different formulas depending upon the unit of the specified central angle. The central angle can be expressed in either degrees or radians. To use the arc length calculator, enter the values in the given input boxes.

Arc Length Calculator

How to Use the Arc Length Calculator?

Please follow the steps mentioned below to find the arc length by using the Arc Length calculator.

• Step 1: Go to Cuemath's online arc length calculator
• Step 2: Enter the values in the given input boxes.
• Step 3: Click on the "Calculate" button to find the arc length.
• Step 4: Click on the "Reset" button to clear the fields and enter new values.

How Does Arc Length Calculator Work?

To calculate the arc length, we need to know two parameters. These are as follows:

• Radius of the circle - The distance from the center of the circle to any point on the circumference is known as the radius of the circle
• Central angle - The angle subtended by the arc at the center of the circle is called the central angle.

To find the length of the arc we can use two different formulas depending upon the unit of the central angle.

1. Central Angle is given in Radians.

• To find the length of the arc we simply multiply the radius with the value of the angle.

The formula is given as:

L = θ × r.

2. Central Angle is given in degrees.

• We first convert the angle from degrees to radians. This can be done by multiplying the angle by a factor of (π/180).
• Next, we take the product of the angle value obtained in step 1 and the radius of the circle. This gives us the length of the arc.

The formula is as follows:

L = θ × (π/180) × r

Here, L is the length of the arc, r is the radius of the circle, θ is the central angle, and π (pi) is a constant with a value of either 3.14 or 22/7.

Solved Examples on Arc Length

Example 1: Find the length of the arc whose radius is 5 units and the central angle is 4 radians. Verify the result using the arc length calculator.

Solution:

As the central angle is given in radians we use the formula, L = θ × r

L = 4 × 5

L = 20 units.

Thus, the arc length is 20 units.

Example 2: Find the length of the arc whose radius is 3.5 units and the central angle is 6 degrees. Verify the result using the arc length calculator.

Solution:

As the central angle is given in radians we use the formula, L = θ × (π/180) × r

L = 6 × (3.14 / 180) × 3.5

L = 0.37 units.

Thus, the arc length is 0.37 units.

Now, use the arc length calculator to find the arc length with the given dimensions:

• Radius = 20 units, Angle = 2 radians
• Radius = 14.3 units, Angle = 17 degrees

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