Arc Length Calculator | Curve Calculator - Mathauditor

The article below suggests you have a look at the incorporation of arc length formula and calculator. Also, it tells you how to use the calculator by putting values. It tells you how to derive the method and use it methodically. Read the article below to know more.

Arc length calculator

Before moving straight to what’s and how’s of the Arc length calculator (calc), let us recall what an arc is? An arch is a curve formed in a crescent shape, which gets generally found in a circle. Arcs could get found anywhere around you as well like the moon. But the question arises how one could find the length of an arc? We’ll find out soon.

The Arch length calculator is a tool, which could help you find out the length of the crescent shape arc and also, the area of a circle sector. Now, let us move ahead with the details about the arc length formula and its calculations.

How to use the arc length formula calculator?

Firstly, the length of an arch revolves around the radius and the central angle, theta, of the circle. With the necessary knowledge, we know that the central intersection is equal to 360 degrees, which is further equivalent to 2π. So, now the length of the arch is similar to the circumference. Hence it is proved that the proportion is constant between the arch length and the central intersection.Now, the arc length formula is derived by:

S / Θ = C / 2π

Where the S= Arc length; Θ= central angle; C= circumference; 2π= 360 degrees.
As the circumference gets derived as C = 2πr,

Then, S / Θ = 2πr / 2π S / Θ = r

Now, calc* arc length formula by multiplying theta to the radius, which results as,

S = r * Θ

The result will get calculated in radians.

How to find the area of a sector of a circle

Similarly, as above operations, we could find out the area of a sector of a circle. So, as we all know that the area of a circle is equal to πr². Now, let us see what proportions could lead us to. Now,

  • A / Θ = πr² / 2π
  • A / Θ = r² / 2

The area of a sector of a circle’s formula is:   A = r² * Θ / 2

How to calculate the arc length and the area of a sector: An example?

The following points would tell you how to find the length of the arch by an example:

  • Let us think about the radius first. Let the radius be 15 cm, or you could choose the diameter as well for the area of a sector in the calculator itself.
  • Now, consider the angle between the ends of given curve as 45 degrees or π/4.
  • Then, obtain the result by putting values to the arc length formula in terms of Pi mentioned above L = r * Θ = 15 * π/4 = 11.78 cm.
  • After that, put the values to the area of sector formula, which further results into A = r² * Θ / 2 = 15² * π/4 / 2 = 88.36 cm².
  • Also, you can use the arc measure calculator to find the central angle and the radius of a circle. All you need is to put any two values in the formula and solve the equation.

Equation forming by the length of curve calculator without radius

The following points would suggest some of certain ways to find the arc length calc without radius:

With the central angle and sector area

  • First of all, you must start with multiplying the area by 2 and then divide the result with the angle at the centre formed, which is theta. The answer turns out to be radians.
  • Now, please take out the square root of the given outcome, which was obtained after dividing it.
  • In order to get the arch length, multiply the square root with the central intersection again.
  • Then the units will turn out to be the square root of a given area of the sector angle.

With the central angle and the chord length

  • Firstly, divide the angle at the centre by 2 in radians and then apply the sin function to the equation.
  • Secondly, you must divide the chord length by the double of the result obtained in the point above. The answer you get is the value of the radius.
  • Last but not least, you must multiply the central intersection with the radius in order to obtain the arch length.

The circle arc calc using radians:

The answer to this query is as simple as a multiplication. All you need to do is take the central intersection in radians and multiply it to the radius of the circle.

The central angle calculator

The following points would suggest you find the arch length without the angle at the centre:

With radius and sector area

  • First of all, you must multiply the area by 2.
  • Then all you have to do is divide the result obtained through the point above to the squared radius. Also, make sure they have the same units.
  • Following the steps above would help you get the central intersection.

With the radius and the chord length

  • Firstly, double the radius and then divide the chord length to it.
  • Then, you must find the inverse sin of the result obtained in the point above.
  • Now, double the result formed by the inverse sin. This operation will be your central edge in radians.
  • So, now you have your central edge and radius to find the arch length.
  • Also, note that the S=r theta calc becomes more comfortable when the central edge is in radians, albeit you can use any unit of angles. Radians make the calculations more straightforward and effective like multiplication. Also, as the arch length is a distance measurement and hence cannot be in radians.