Central Angle Calculator
Find the central angle from arc length and radius for an arc up to one full circle.
Formula
θ=s/r radians; degrees=180s/(πr).
Arc length s: 10 cm · Radius r: 5 cm · Angle in radians ≈ (10 cm × 0.01 m/cm)÷(5 cm × 0.01 m/cm)+0×sqrt(2×pi-(10 cm × 0.01 m/cm)÷(5 cm × 0.01 m/cm)) · Angle in degrees ≈ (2)×180÷pi
How to use
- Enter the curved arc length s.
- Enter the positive radius r.
- Read the angle in radians and degrees.
Examples
- s=10 cm, r=5 cm give 2 rad≈114.591559°.
Frequently asked questions
Can I enter chord length?
No. A chord is straight; this formula requires curved arc length.
Can the arc exceed a full circle?
No. This tool accepts 0≤s≤2πr. A complete circle is exactly 360°.
Must units match?
The unit picker converts both lengths to the same base unit.
Sources
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