Arc Length Calculator – Guide & Formulas
Calculate the length of a circular arc using radius and central angle (in degrees or radians). Complete step-by-step math solver.
Find the curve distance of an arc along a circle. Perfect for roadway curved designs, mechanical gears, and circular tracks.
Key Takeaway
Use the free Arc Length Calculator to calculate the length of a circular arc using radius and central angle (in degrees or radians). complete step-by-step math solver. Get instant results with step-by-step explanations.
How to Use the Arc Length Calculator
- Enter the radius of the circle.
- Enter the central angle in degrees or radians.
- View the computed arc length, chord length, and full circle circumference.
The Formula
Variable Definitions
- s: The calculated length of the arc curve
- r: Radius of the circular base
- θ: The central angle subtending the arc
Curve of a Running Track Turn
A running track turn sweeps out a 120-degree curve with a radius of 100 feet. Find the distance along the curve.
- Step 1: Set radius r = 100 feet and angle θ = 120 degrees.
- Step 2: Use the degrees formula: s = 2 * π * 100 * (120 / 360).
- Step 3: Simplify: s = 200π * (1/3) ≈ 209.44 feet.
- Step 4: The curve distance is approximately 209.44 feet.
Frequently Asked Questions
What is the difference between arc length and chord length?
Arc length is the actual curved distance along the outer circle edge. Chord length is the straight-line distance cutting through the circle between the two endpoints of the arc.
How do you convert degrees to radians?
Multiply the angle in degrees by π and divide by 180 (Radians = Degrees * π / 180).
Can an arc length be larger than the circumference?
No. The maximum possible arc length is the full circumference of the circle, corresponding to a central angle of 360 degrees (2π radians).