Central Angle Calculator
Compute the central angle of a circle arc from arc length and radius.
Input Data
Arc Length
units
Radius
units
Results
Central angle in degrees.
89.95°
Central Angle Radians
1.57rad
Fraction Of Circle
24.99%
At a glance:θ = s/r (rad); in degrees θ = 360·s/(2πr); fraction = s/(2πr). Complements arc-length and circle.
Formula
θ = s / r (rad).
θ(deg) = 360·s/(2πr).
$$\theta = \frac{L}{r}$$$$\theta^\circ = \frac{L}{r} \cdot \frac{180^\circ}{\pi}$$How to Use
- Enter arc length and radius.
- The tool returns the angle and fraction.
Case Studies
s=5, r=5
θ = 1 rad = 57.3°; fraction = 5/(2π·5) ≈ 0.159.
FAQ
Radians or degrees?
Both are shown; radians are natural for calculus.
Related Tools
References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.