If you need to determine the length of an arc or the area of a circle sector, then this is the tool for you. This arc length calculator can help you to not only work out calculations in an instant, but educate you on how to do it by hand as well.
Below, find out what the arc length formula is, obtain instructions for its use, and get the equation for an arc’s sector.
What is the Arc Length Formula?
The central angle and the radius of a circle determine what the length of an arc can be. For the angle to be 2π (or 360 degrees), the arc’s length is going to be the same as the circumference. This proves that the arc length and angle are constant, as you can see below:
Θ = central angle
C = 2πr
L / Θ = C / 2π
L / Θ = rYou can then determine that when you multiply that equation by the central angle (Θ), you work out the arc length formula.L = r x ΘThe arc length is equal to the radius multiplied by the central angle.
What is the Area of Circle’s Sector?
Similarly, you can work out a circle’s sector, because you know the circle’s area in its entirety is the same as πr².
A / Θ = πr² / 2π
A / Θ = r² / 2The sector area formula, therefore, is: A = r² * Θ / 2
An Example of How to Find the Arc and Sector Area Length
1. Identity your circle’s radius. For this example, we can say it’s six inches
2. Identify the angle between the arc endings. In this case, it’s 45 degrees
3. Use the above formula to calculate the length of the arc
L = r x Θ = 6 x π/4 = 4.71 inches
4. Calculate the sector’s area
A = r² x Θ / 2 = 6² * π/4 / 2 = 14.14 inches-squared
If you want to find out the central angle or radius of a circle, you can also use an arc length calculator. Enter the values you have into the boxes, and the arc length calculator will take care of it for you.