# How to find the arc length of a circle?

Do you want to know “**How to find the arc length of a circle?**“Draw a line segment from the center of the circle to one of the points on the circle. This line segment will be the radius of the circle.

Use a protractor to measure the angle between the line segment and the other point on the circle. This angle is the angle between the two points on the circle.

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## How to find the arc length of a circle?

The arc length of a circle is the length of the portion of the circle’s circumference between any two points on the circle.

The arc length of a circle can be found using the following formula:

**Arc Length = (r^2 * θ) / 2r**

where the radius is the circle’s radius and the angle is the angle between the two points on the circle.

For example, if the radius of a circle is 5 and the angle between two points on the circle is 30 degrees, then the arc length of the circle between those two points is:

arc length = (5 * 30) / 2

= 75 / 2

= 37.5

Thus, the arc length of the circle between those two points is 37.5 units.

### Arc Length – Formula

The formula for arc length of a circle is:

Arc Length = (r^2 * θ) / 2r

Where r is the radius and θ is the angle in radians.

Arc Length – Formula Explained

**The formula for arc length is derived from the formula for the circumference of a circle.**

**Circumference = 2 π r**

This formula is derived from the equation for a circle. This is a derivation of the equation for a circle:

x^2 + y^2 = r^2

The equation for a circle is derived from the equation for a line, which is derived from the equation for a point:

x = r cosθ

y = r sinθ

**If we substitute this into the equation for a circle:**

x^2 + y^2 = r^2

r^2 cos^2θ + r^2 sin^2θ = r^2

Next **r^2 (cos^2θ + sin^2θ) = r^2**

r^2 = r^2

This proves that the equation for a circle is valid.

**Now we can substitute the equation for a line into the equation for circumference:**

Circumference = 2 π r

Circumference = 2 π r cosθ

Now we can solve for arc length:

Arc Length = (r^2 * θ) / 2r

Arc Length = (r^2 * θ) / (2r * 1)

## What is the easiest way to find arc length?

The easiest way to find arc length is to use the formula:

arc length = (radius * angle) / 2

where the radius is the circle’s radius and angle is the angle of the arc in degrees.

For example, if the radius of the circle is 5 and the angle of the arc is 30, then the arc length would be:

arc length = (5 * 30) / 2

= 15

### Another way

If you want to find the arc length of a circle without using a formula or measuring with a ruler or tape measure, you can use the following method:

- Use a ruler or tape measure to measure the length of the line segment. This length is the radius of the circle.
- Use the formula: arc length = (radius * angle) / 2 to calculate the arc length of the circle between the two points.