Arc Length of a Circle
Part of the circumference.
Key idea
Part of the circumference.
In depth
An arc is a fraction of the circumference. If the central angle is θ degrees, arc length = (θ/360) × 2πr. In radians, s = rθ.
Worked example
A 60° arc of a circle with radius 6: (60/360) × 12π = 2π ≈ 6.28.
Formula
Real-world uses
- Measuring the curved length of a bend in a road or a section of a rounded handrail
Common mistake
Using degrees in s = rθ, which requires radians.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Arc Length of a Circle?
Part of the circumference. It is a topic at the advanced level in Geometry.
What is the formula for Arc Length of a Circle?
The key formula is s = rθ.
Where is Arc Length of a Circle used in real life?
Real-world examples: Measuring the curved length of a bend in a road or a section of a rounded handrail.
What should I learn before Arc Length of a Circle?
Make sure you are comfortable with The Number Pi, the previous topic in Geometry.
What is a common mistake with Arc Length of a Circle?
Using degrees in s = rθ, which requires radians.
How can I practise Arc Length of a Circle?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Arc Length of a Circle?
Move on to Sector Area next.
Related advanced topics in Geometry
- Heron’s Formula – Triangle area from three sides.
- Regular Polygon Area – Use apothem and perimeter.
- Sector Area – Part of the circle’s area.
- Central and Inscribed Angles – An inscribed angle is half the central angle on the same arc.
- Chord and Tangent Properties – A tangent is perpendicular to the radius at the point of contact.
- Cones – Volume and surface area of a cone.