This is the simplified formula of arc length. Now, the circumference of a circle can be written as 2πr as well, right? So the proportion becomes: Where L is the arc length and theta is the central angle. This means the proportion between these two values is constant. As you may already know, for a 360 (2π) degrees angle, arc length is equal to the circumference.
Let’s derive the formula to find the length of an arc of any circle. Visit our other circle-related tool e.g Circumference and Circle area calculator.
It is different from the chord of a circle because a chord is a straight line between two points while an arc is curved. It depends on the central angle and the radius of the circle. The length along the curve of a circle between two points of its circumference. This tool also allows choosing the units of the input quantities because they are of significant importance when computing some value. Then you can follow the same method as the given examples.Arc length in radians calculator computes the arc length and other related quantities of a circle. Similarly, if you are given the sector area and the central angle, you can use the sector area formula to find the radius. Use the sector of an area formula and rearrange it in a way that will give you the value of the central angle. Step 2: Find the central angle through the sector area. If you have a circle of 6m radius which has a sector of area 40m 2 then find its arc length? Find the arc length of this sector.Įxample 2 (using radius and sector area): A sector of the circle makes an angle of 40 degrees. Some solved examples are given below to remove any further confusion.Įxample 1 (Using radius and central angle):Īssume a circle of radius 10 m. Put both values in the arc length formula and solve.Find the radius using the formula: r = diameter/2.Measure or calculate the central angle.To compute arc length, follow these instructions. Because it provides you with other circle-related measurements without much effort.
#Arc length calculator calculus how to
L = r * θ How to find the arc length of a circle?Īrc length can be calculated using a number of methods depending on the given data but the most suitable one is using the tool above. We can replace C with 2πr i.e value of the circumference in radians.
#Arc length calculator calculus full
Where C is the circumference (length of an arc) and 2 π is the central angle of the full circle. Keeping in mind a full circle, we can write: This formula is derived from the fact that the proportion between angle and arc length remains the same. If you have the central angle in the degrees, then: Where theta θ is the central angle in radians and r is the radius. The arc length is calculated using this formula: But in order to calculate its length, you have to know the radius of the circle that would be drawn by continuing the arc. An arc is not specified to a circle only. The image above is of a sector of a circle. An arc is always curved and this is what separates it from a chord which is the straight line joining the endpoints of an arc. This calculator can find four geometrical measurements in two different units.Īrc length is the measurement of the distance between the endpoints of an arc along the circumference. You can find the arc length in both radians and degrees with this calculator. The length of an arc calculator finds the total distance of an arc for any circle.
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