Arc Length Calculator

If you need to calculate the length of an arc within a circular sector, this ARC calculator can help you to calculate your values. Simply you need to enter the degrees of rotation or central angle along with the radius, and you’ll quickly discover the length you’re looking for.

Arc Length Calculator

Enter any 2 values to calculate the missing variable





































arc length calculation tool

What is Arc Length?

The arc length is the distance along the curved line making up the arc. It is a portion of the circumference of a circle.

How to Use the Calculator

  1. Enter the Radius: Input the radius of the circle.
  2. Enter the Central Angle: Input the angle in degrees or radians.
  3. Click Calculate: The calculator will find the arc length.

Example Input Values

  • Radius: 5 units
  • Central Angle: 45 degrees

How to Calculate Arc Length

Formula

L=r×θL = r \times \theta

Variables

Variable Meaning
LL Arc Length
rr Radius
θ\theta Central Angle (in radians)

Basic calculator Calculation Example

Let’s calculate the arc length step-by-step using the basic example values.

1 .Convert the angle to radians if necessary.

45 degrees = 45×π18045 \times \frac{\pi}{180}

2. Multiply the radius by the angle in radians.

L=5×0.7854L = 5 \times 0.7854

3. The result is the arc length.

L=3.927L = 3.927

Advanced Calculator Calculation Example

Let’s calculate the arc length step-by-step using the advanced example values.

1 . Convert the angle to radians if necessary.

90 degrees = 90×π18090 \times \frac{\pi}{180}

2. Multiply the radius by the angle in radians.

L=10×1.5708L = 10 \times 1.5708

3. The result is the arc length.

L=15.708L = 15.708

Calculator Input Examples

1. Basic Example

Radius Central Angle Arc Length
5 units 45 degrees 3.93 units

2. Advanced Example

Radius Central Angle Arc Length
10 units 90 degrees 15.71 units

FAQs

What units should I use?

You may use any units for radius and angle, but it is essential to be consistent.

Can I put in the angles in degrees?

Yes, the calculator is able to convert degrees to radians.

What if the angle amounts to more than 360 degrees?

The calculator will process any angle, although angles greater than 360 degrees will cycle around the circle.

Final Thought

How do you think about our arc length calculator? Please, share your experiences and feedback with us. Your insights help us improve the tool.

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