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How to Find the Arc Length of a Function?

Finding the arc length of a function is not a die-hard task. You can use integration to find the length of the curve. The arc length is a total calculation of the curve. There are formulas and methods used to find this arc length. You can also use the arc length calculator that calculates the arc length, central angle, radius, diameter, sector area, segment height, and chord length of the circle. It may seem difficult at the start but after you get the clear ground root understanding of how to find it, it will become easier to find accurate information.

Finding the Arc Length:

For finding the exact length of a curve, we can suppose a situation in which we can get our value easily. Let us suppose a cricket ground and you are following the pitch: (2/3)x^(3/2). You are moving from (x=0, y=0) to (x=2, y=4). How you will find the value of how much you have walked. Let’s consider the little part of the path. After that, you have moved from delta x within the x-direction and delta y within the y-direction. This is a sort of a curve.

If you move from delta x north and delta x east, you are supposed to use this equation within the mathematical Pythagoras theorem. Due to this situation, you may find space between starting and finishing points. By taking the square root of (delta x^2 + delta y^2) we get a^2 + b^2 = c^2. There is no doubt that this process is complex to understand but you don’t have to worry about it. for ease, you have the option to use the arc length calculator through which you can find the length of an arc. 

If you need to understand the whole distance that you have covered by walking in my trek across cricket ground, You are about to realize this distance, this root of (delta x^2 + delta y^2), for every of those very little regions, and you can calculate it. This (delta x^2 + delta y^2), Now you can change the value of a delta x^2 from these 2 terms. You get (delta x^2)(1 + ((delta y)/(delta x))^2). As a result of it, you will get this delta x^2 as a product inside.  Your entire path becomes the total overall of those very little regions that you have walked of delta x times the root of (1 + ((delta y)/(delta x))^2).  This might be the calculation of the total distance covered by you.

This overall calculation can help in finding the arc length of the function but you may need to look for some further steps to sum it. But using the Arc Length Calculator will help you in finding out the total length of the curve without indulging in calculating the large set of a sum. You can calculate the whole arc length formula by using Arc length formula calculators.


Many students in the field of mathematics, engineering, and architecture find it difficult to find the arc length of functionality. But by following the productive methods can make your path much easier to find. You can use different formulas and methods. Pythagoras theorem may be a kind of theorem to find these values but these methods may seem too long and time taking. By using a length of arc calculator you can get accurate results without spending a lot of time finding every value.


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