Arc length and sector area
An arc is a slice of a circles edge, and a sector is the pie-shaped wedge it bounds. From a radius and a central angle this calculator finds the arc length, the sector area, and the straight chord across the arc — the three measures you need to lay out or cut a curved piece.
The formulas
With the angle in radians: arc length = radius times angle, and sector area = one half times radius squared times angle. That clean form is exactly why radians exist. The chord, the straight line between the arcs endpoints, is 2 times radius times the sine of half the angle.
Why radians make it simple
In radians the arc length is just radius times angle, with no extra constant. In degrees you first multiply by pi over 180, which is what the tool does for you before applying the formula.
Related tools
To switch your angle between degrees and radians, use the angle converter calculator; for the whole circle, the circle calculator.
Worked example
A radius of 10 with a 60-degree central angle gives an arc length of about 10.47, a sector area of about 52.36, and a chord of exactly 10.
FAQ
What is the difference between arc length and chord?
Arc length follows the curve; the chord is the straight shortcut between its ends. The chord is always shorter, and the gap grows with the angle.
Can the angle exceed 360 degrees?
It can, and the arc length keeps growing, but past a full turn the arc wraps over itself — usually you want an angle between 0 and 360.