Arc of a Circle Calculator

Use this online math calculator to calculate the properties of the arc of a circle.

Arc of a Circle Calculator
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Arc of a circle calculator. This image shows an arc of a circle with associated calculations used by the Arc of a circle calculator

How to Calculate the Arc of a Circle

  1. Enter Diameter to calculate the Radius or enter the Radius to calculate the Diameter
  2. Either enter the Angle of the Arc or enter the length

You can also use the Arc of a Circle Calculator to:

  • Calculate the radius of a circle based of it's diameter
  • Calculate the diameter of a circle based of its radius
  • Calculate the length of an arc based of length and arc angle
  • Calculate the arc angle based on arc length and radius

About the Arc of a Circle Calculator

As the name suggests, the arc of a circle calculator lets you measure the length of an arc. We'll discuss more about this in this article. Before we do that, let's understand the arc of a circle in detail, shall we?

What is the Arc of a Circle?

In its truest form of definition, an arc of a circle is portion of the circumference of a circle. Arc length is thus the distance between two points on the arc of the circle. The arc of a circle can be calculated by using the following formula:

Arc: Length = Θ x r

Where r is the length of the radius and Θ (theta) is the angle between the two radii drawn from the center. Do remember this formula is applicable when the angle is in radians.

On the other hand, when the angle is in degrees, the formula above changes to:

Arc Length = (Θ x r x π)/180

How Arc of a Circle Calculator Works?

The arc of a circle calculator developed by icalculator requires you to enter the radius or the diameter (whichever is available) and the angle in degrees. The calculator will automatically give you the chord length as well as the arc length.

If you have an angle in radians, you'll need to first convert it into degrees to get the arc length. The formula for converting radians into degrees is:

(Angle in radians x 180)/π = Angle in degree

Why is Arc of a Circle Important in Real Life?

The most common usage of the arc of a circle calculator is in calculating really long distances across a curved path. The best example of such a case will be calculating the distance between two cities across two nations. Navigators and pilots worldwide call the distance covered across the globe a great circle.

Let's understand this example is detail now, shall we? On a global scale, we mark geographical landmarks and positions in terms of latitude and longitude. Now, consider this:

  • The latitude and longitude for the San Francisco airport are 37.6°N and 122°W.
  • The latitude and longitude for the London Heathrow airport are 51.5°N and 0.5°W.

Now, drawing a radius to each of these points from the center of the earth, the angle formed is 77.5°. Now, given the fact that earth's radius is 6371 km, you can easily calculate the arc length between the two airports, which turns out to be just about 8611km.

The above-mentioned data allows aviation companies and air traffic controllers to determine how to manage the aerial traffic across the world. From flight routes to how much an airplane can travel before needing to refuel, everything revolving around safe and hassle-free flights revolves around the arc length. If you want to calculate the distance between two cities, you can use the Distance through the Earth Calculator which uses the latitude and longitude of two points on earth to calculate the distance as described in the paragraph above.

Funnily enough, it's also the arc length that lets you identify the largest pizza slice and go for it before somebody else does.

The sprinklers that you see installed in large lawns are also built keeping the arc of a circle in mind. Have you noticed one of the two nozzles throws water further than the other? How much water should be thrown in a given area is also calculated on the basis of the area to be covered. Notice how these sprinklers cover a giver area at a time before moving to the next arc. The brilliant math put behind this simple looking machine results in lush green lawns.

Conclusion

The arc of a circle calculator holds great importance in our daily life, even without us realizing so. The geniuses behind these inventions and facilities are working hard to make our lives easy. We aim to make calculating large numbers easier, faster and more accurate for those entrepreneurs and inventors, one calculator at a time.

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