r = 8 cm, θ = 90°
s = 8 × π/2 = 4π ≈ 12.57 cm
Measure the curve, not the shortcut
Arc Length Formula Calculator
Solve for arc length, radius, or central angle. Compare the arc with its chord and calculate sector area in the same step.
Free to use. No account required. Your inputs stay in this browser.
The essential relationship
s = rθ (θ in radians)
Arc length is the distance along part of a circle. In radians it is radius times central angle; in degrees, multiply 2πr by θ/360. The calculator keeps full precision internally and rounds only the displayed result.
Worked examples
Follow the numbers, one step at a time
r = 5 m, θ = 1.2 rad
s = 6 m
s = 10 cm, r = 4 cm
θ = 2.5 rad ≈ 143.24°
Built for understanding
More than an answer box
Every result includes the rearranged formula, substituted values, and a reasonableness check. Use the visual to connect the symbols to the measurement.
- Instant, private, browser-based calculation
- Decimal-friendly input and validation
- Responsive layout for phones and classrooms
- Copy-ready answer with units
Method and references
Formula basis
The formula follows standard textbook definitions. Unit symbols follow SI guidance; results are educational estimates, not engineering certification.
- OpenStax Precalculus, Radian Measure
- NIST SP 811, SI units
Quick answers
Frequently asked questions
What is the arc length formula?
s = rθ when θ is in radians, or s = 2πr(θ/360) in degrees.
What is the difference between arc and chord?
An arc follows the circle; a chord is the straight line between the endpoints.
Can the angle exceed 360°?
For one circular arc it is normally 0° to 360°; larger angles describe multiple turns.
How do I find sector area?
Use A = ½r²θ with θ in radians.
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