Arc Length Calculator
An arc is a curved segment of a circle's circumference. This calculator computes the arc length and the area of the circular sector from the radius and the central angle. The central angle can be entered in either degrees or radians. The arc length formula is straightforward when using radians: Arc length = radius times the angle in radians. The sector area is calculated as half the radius squared times the angle in radians. Both measurements depend only on the radius and the central angle.
Arc length formulas
Arc length = r * theta (theta in radians)
Arc length = (r * theta * pi) / 180 (theta in degrees)
Sector area = (1/2) * r^2 * theta (theta in radians)
Sector area = (r^2 * theta * pi) / 360 (theta in degrees)
Example calculation
For an arc with radius 10 and central angle of 60 degrees:
- Arc length = (10 * 60 * pi) / 180 = 10.47 units
- Sector area = (10^2 * 60 * pi) / 360 = 52.36 square units
Arc length calculator: frequently asked questions
What is an arc?
An arc is a portion of the circumference of a circle. It is defined by two endpoints and the radius of the circle.
What is the formula for arc length?
The arc length is calculated as: Arc length = r * theta, where r is the radius and theta is the central angle in radians. In degrees: Arc length = (r * theta * pi) / 180.
How do I convert between degrees and radians?
To convert degrees to radians: radians = degrees * pi / 180. To convert radians to degrees: degrees = radians * 180 / pi.
What is a central angle?
A central angle is an angle formed by two radii of a circle. The vertex of the angle is at the center of the circle. The arc length depends on the size of this central angle.
How are arc length and sector area related?
Both use the central angle and radius. Arc length measures the curved distance, while sector area measures the space enclosed by two radii and the arc between them.
Official sources
- Wolfram MathWorld: Arc Length.
- ISO 80000-2: Mathematical signs and symbols.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.