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# Arc Length Calculator

To find the arc length, enter the value of radius and angle in radians in the input boxes and hit the * calculate* button using this arc length calculator.

## Arc Length Calculator

Arc length in radians calculator computes the arc length and other related quantities of a circle. These values include:

- Sector Area
- Chord
- Diameter

This tool also allows choosing the units of the input quantities because they are of significant importance when computing some value. The results are in the SI units.

## What is the arc length?

The length along the curve of a circle between two points of its circumference. It depends on the central angle and the radius of the circle.

It is different from the chord of a circle because a chord is a straight line between two points while an arc is curved.

Visit our other circle-related tools e.g. Circumference and Circle area calculator.

## Arc length formula:

Let’s derive the formula to find the length of an arc of any circle. As you may already know, for a **360 **(**2π**) degrees angle, the arc length is equal to the circumference.

This means the proportion between these two values is constant.

**L / θ = C / 2π **

Where L is the arc length and theta is the central angle. Now, the circumference of a circle can be written as **2πr **as well, right? So the proportion becomes:

L / θ = 2πr / 2π

L / θ = r

**L = r * θ**

This is the simplified formula of** arc length**. This formula is applicable when the central angle is given in radians. But if the angle is measured in degrees, then multiply the angle with **π/180**.

L = r * θ * π/180

L = r * π * θ/180

**L = θ/180 * rπ**

The arc length calculator can find the arc length in whichever unit you provide the angle e.g. arcminutes or pi radians.

## How to find the arc length?

It is important to convert the units of the angle and radius in the **SI **unit. After that, multiply both values.

**Example:**

For a circle of **8 **meters, find the arc length with the central angle of **70 **degrees.

**Solution:**

**Step 1:** Write the given data.

Radius (**r**) = 8m

Angle (**θ**) = 70^{o}

**Step 2:** Put the values in the formula.

Since the angle is in degrees, we will use the degree arc length formula.

`L = θ/180 * rπ `

L = 70 / 180 * (8)π

L = 0.3889 * (8)π

L = 3.111 * π

**L = 9.774 meters**

## How to find arc length using sector area and central angle?

When the available data does not include the **radius **then it is possible to find the **arc length** using the sector area of the circle. The formula used is:

**L = θ * √2A/θ**

where **A **is the sector area. Follow these steps to use this formula.

- Multiply the sector area by
**2**. - Divide this value by the angle.
- Now, take the square root of the value.
- Lastly, multiply with the angle again.

A solved example for this case is given below.

**Example:**

What will be the arc length if the sector area is **360000 cm ^{2}** and the angle is

**60**degrees?

**Solution:**

**Step 1:** Convert the centimeters into meters and degrees to radians.

`1 centimeter`

^{2} = 1/10000 meter square

360000 cm^{2} = 360000/10000 meter square

**= 36 meter square**

`1 degree = π/180 radians`

60 degrees = 60 * π/180 radians

**= 1.0472 rad**

**Step 2:** Write the available data.

Area (A) = 36 m^{2}

Angle = 1.0472 rad

**Step 3:** Use the formula.

`L = θ * √2A/θ`

L = (1.0472) * √2 (36) /1.0472

L = (1.0472) * √72 /1.0472

L = (1.0472) * √75.3984

L = (1.0472) * 8.6832

**L = 9.09 meters**