Arc Length Calculator
An Arc Length Calculator helps you find the length of a curved section of a circle. It is useful for geometry, trigonometry, engineering, construction, and other situations where you need to measure part of a circular curve.
What Is Arc Length?
Arc length is the distance along the curved edge of a circle between two points. Unlike the straight-line distance between the points, arc length follows the circumference of the circle.
Arc Length Formula
When the angle is measured in radians, the arc length can be calculated using:
s = rθ
Where:
- s = arc length
- r = radius of the circle
- θ = central angle in radians
If the angle is given in degrees, use:
s = (θ / 360) × 2πr
Here, θ is the central angle in degrees and r is the radius.
How to Use the Arc Length Calculator
- Enter the radius of the circle.
- Enter the central angle.
- Select degrees or radians, depending on the values you have.
- Click the calculate button.
- The calculator will display the arc length.
Arc Length Example
Suppose a circle has a radius of 10 cm and a central angle of 90°.
Using the formula:
s = (90 / 360) × 2π(10)
s = 5π
So the arc length is approximately 15.71 cm.
Arc Length and Circumference
An arc is only part of a circle's circumference. The full circumference is calculated using:
C = 2πr
If the central angle is 360°, the arc represents the entire circle, so its length is equal to the circumference.
Minor Arc and Major Arc
A minor arc is the shorter curved path between two points on a circle, while a major arc is the longer path. The central angle can be used to determine which part of the circle is being measured.
Common Uses of Arc Length
Arc length calculations are commonly used in:
- Geometry and mathematics
- Engineering and design
- Construction and architecture
- Mechanical and circular systems
- Physics and motion problems
- Measuring curved structures
Frequently Asked Questions
What is the formula for arc length?
The formula is s = rθ when the angle is measured in radians. For degrees, use s = (θ / 360) × 2πr.
Can I calculate arc length using degrees?
Yes. If the central angle is given in degrees, use the degree-based arc length formula.
What is the difference between arc length and chord length?
Arc length measures the curved distance along the circle, while chord length measures the straight-line distance between the two endpoints of the arc.
Related Calculators
For more geometry calculations, try our Circumference Calculator and Math Calculators.
Conclusion
The Arc Length Calculator provides a quick way to determine the distance along a circular arc. By entering the circle's radius and central angle, you can calculate the curved distance accurately without having to perform the formula manually.