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Central Angle Calculator.

Find a circle's central angle from arc length and radius.

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Central angle: 1.25 rad

Central angle

0.000000rad
Central angle: 71.619724 °

Central angle

0.000000°

Results update automatically as you type.

Use Cases

Geometry and Trigonometry Problems

Solve math problems involving circles, sectors, and arcs. Quickly find the central angle when you know the arc length and radius, saving time on homework or exam prep.

Example: Find the central angle of a sector with arc length 10 cm and radius 5 cm.

Engineering and Design Applications

Determine angles for circular components in mechanical design, architecture, or manufacturing, such as calculating the bend angle for a curved pipe or the angle of a circular segment.

Example: Calculate the angle of a curved railing with a radius of 3 m and arc length of 4 m.

Frequently Asked Questions

What is a central angle?
A central angle is an angle whose vertex is the center of a circle and whose sides (rays) extend to the circumference, intercepting an arc. Its measure is proportional to the arc length it subtends.
How do I find the central angle from arc length and radius?
Use the formula: angle (in radians) = arc length / radius. To convert to degrees, multiply by 180/π. For example, if arc length is 5 units and radius is 2 units, the angle is 2.5 radians or about 143.24 degrees.
What units should I use for arc length and radius?
Both arc length and radius must be in the same unit (e.g., meters, inches). The calculator accepts any unit as long as they match, and the resulting angle is unitless (radians) or degrees.

Tips & Common Mistakes

Tips

  • Ensure that the arc length and radius are in the same units before entering them into the calculator.
  • If you need the angle in degrees, the calculator will provide it; if you need radians, you can convert by multiplying degrees by π/180.
  • For a full circle, the arc length equals the circumference (2πr), so the central angle is 360° or 2π radians.
  • Double-check your inputs: a common error is mixing up arc length with chord length, which are different.

Common Mistakes to Avoid

  • Using different units for arc length and radius (e.g., meters for arc length and centimeters for radius) without converting, leading to incorrect results.
  • Confusing arc length with chord length. The chord is the straight line between two points on the circle, not the curved arc.
  • Forgetting to convert radians to degrees if the problem requires degrees, or vice versa.

Last updated: August 13, 2026