How to use
- Enter the circle radius.
- Choose degrees or radians.
- Enter the central angle.
Formula
Degrees are converted to radians with angle × π ÷ 180. Arc length is that radian angle times the radius. The page also shows the radian angle, the arc as a percent of the full circumference 2πr, and the straight chord 2 × radius × sin(angle ÷ 2). Results are rounded to four decimal places.
Worked example
The form opens at radius 10 and 90 degrees. The angle is π/2 radians, shown as 1.5708. Arc length is 1.5708 × 10 = 15.708. That is 25% of the circumference. The chord across the same 90° is 14.1421, shorter than the arc.
How to read the result
15.708 is the distance along the curve, in the same unit as the radius. 14.1421 is the straight cut between the two ends of that arc. A larger angle lengthens the arc. At 360° the arc is the whole circumference and the chord formula returns 0 because the ends meet.
When this does not apply
The path is part of a circle. An ellipse, a road curve with a changing radius, or a 3D arc is not this formula. Enter the radius, not the diameter. A degree value typed while the menu says radians is treated as radians.