Calculations at a circular arc. A circular arc is a part of the outer line of a circle. It is enclosed by two straight lines starting at the center of the circle in a certain angle α. At 360° or 2π, the circle is complete. Enter two of the three values radius, length and angle. Choose the number of decimal places, then click Calculate. The angle can be entered in degrees, as radian or as multiples of π, it also will be calculated in those units.
Formulas:
360° ≙ 6.283185307179586 ≙ 2π
l = 2 π r * α/360°
oder
l = 2 π r * α/(2π)
pi:
π = 3.141592653589793...
Radius and arc length have the same one-dimensional unit (e.g. meter).
The length of the circular arc is the circumference of the entire circle multiplied by the angle from the center of the circle, divided by 360 degrees or 2 pi. The shape that the circular arc forms together with the two straight lines from the center is a circular sector. The straight line between the two end points of the circular arc is called the chord, the shape that the circular arc and the chord form is the circular segment. At an angle of 180 degrees or pi, the circular sector and the circular segment are identical and a semicircle is created.
The circular arc is one-dimensional, even if it extends in two dimensions, a plane. However, the circular arc has no area. If you connect two non-adjacent points of an arc in a straight line, then this chord and the arc together form a plane. To the length of the circular arc then comes the height of the resulting circular segment perpendicular to this and the chord; for the calculation of this and the area of the circular segment, see there.
Curved lines are generally difficult to calculate. For a circle, this problem is solved by using the number π, which was difficult to determine but is now known and is the same for every circle. If the bend does not come from a circle, then no such number is available.