Calculate Circular Arc
Calculator for the length of arc and chord, of radius and angle, in a circle. A circular arc is that part of the circular line, which is enclosed by an angle starting at the origin of the circle. Please enter two values, but not c and l together. The other two values will be calculated. The chord can have a maximum length of twice the radius (diameter).
The formulas for the length of the chord and the length of the circular arc are:
c = 2 * sin(α/2) * r
l = α/360° * 2 * π * r
The angle must be entered in degrees. Here you can convert radian into degrees. The length of the chord s is calculated using the sine of half the angle and twice the radius (or diameter). 2 * sin(α/2) is something different than sin(α), so the formula cannot be simplified in this way. The sine of half the angle in the unit circle gives the length of half the chord, but the sine of the whole angle does not give the length of the whole chord.
The length of the arc l is calculated from the circumference of the circle multiplied by the fraction that the angle has of the entire circle, i.e. of 360 degrees.
If you calculate with concrete shapes of a certain size, then all three lengths have the same unit. This could be centimeters, for example.
A chord in geometry is the linear connection between two points on a curve. In music, a chord is made of musical pitches that sound simultaneously. So both can be seen as multiple points at once, to make a connection here.
The extension of the chord to a straight line is called a secant. In general, secants are straight lines that intersect a circle. If the angle and thus the length of the chord and the length of the arc are zero, then the corresponding straight line is called a tangent.