which converges to the following integral as n. Thus, arc length would be given as Arc Length 6 0. More generally, we approximate the length of the arc by inscribing a polygonal arc (made up of. Note that our answer will always be an area so the units will always be squared. Arc Length Formula Arc Length radius central angle (here, the angle is taken in radians) Consider that you have a circle with a radius of 6 meters and a central angle of 0.4 radians. We make a fraction by placing the part over the whole and we get \(\frac\) (or its decimal equivalent 0.2) to find our sector area, which is 5.654867 meters squared. Let’s try an example where our central angle is 72° and our radius is 3 meters.įirst, let’s find the fraction of the circle’s circumference our arc length is. So we need to find the fraction of the circle made by the central angle we know, then find the circumference of the total circle made by the radius we know.
#Arc length calculus how to#
It’s good practice to make sure you know how to calculate these measurements on your own.Īn arc length is just a fraction of the circumference of the entire circle. Our calculators are very handy, but we can find the arc length and the sector area manually. How to Calculate the Area of a Sector and the Length of an Arc It will also calculate the area of the sector with that same central angle. The calculator will then determine the length of the arc. If we are only given the diameter and not the radius we can enter that instead, though the radius is always half the diameter so it’s not too difficult to calculate. To use the arc length calculator, simply enter the central angle and the radius into the top two boxes. And, since you know that diameter JL equals 24cm, that the radius (half the length of the diameter) equals 12 cm.
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