Calculation of an arc length without its central angle is a tough problem since the arc length is based on the angle. The arc length is the measured distance along a circle's circumference. Its calculation depends on the radius and the angle under the arc length with the following equation; arc length = radius * angle in radian measurement — radians are angular measurement units based on the constant pi. When not given the angle, you can calculate its measurement with the radius and the chord associated with the arc length, or the straight line that travels from one end of the arc length, through the circle, and to the other end, by angle = 2 * arcsin (chord / 2*radius), where arcsin is the inverse of the trigonometric sine function. Knowing the arc length can then help in a variety of other circular calculations.
Double the length of the radius, then divide it into the length of the chord. For this example, the radius is 5 and the chord is 2. Multiplying the radius 5 by 2 results in 10, and dividing the chord 2 by 10 equals 0.2.
Calculate the arcsin of the quotient from the previous step by using your calculator, then double the product. The arcsin function should be represented as "arcsin" or "sin^-1." If you cannot find the function, then use an online arcsin calculator like the one found at RapidTable.com (see Resources). For this example, the arcsin of 0.2 is 0.20135 radians, which when doubled is 0.4027 radians.
Multiply the angle by the radius to calculate the arc length. For this example, 5 multiplied by 0.4027 radians equals 2.0136 radians.
TL;DR (Too Long; Didn't Read)
Some calculators require setting an option to display radians before the calculation.