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Area of a Circle Calculator

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How to Calculate Circumference, Diameter, Area, and Radius

The circle calculator finds the area, radius, diameter and circumference of a circle labeled as a, r, d and c respectively.

For those having difficulty using formulas manually to find the area, circumference, radius and diameter of a circle, this circle calculator is just for you. The equations will be given below so you can see how the calculator obtains the values, but all you have to do is input the basic information.  The calculator does the rest.
Explaining how to find the circumference of a circle

Finding the Circumference:

The circumference is similar to the perimeter in that it is the total length needed to draw the circle.

We note the circumference as c.

c = 2πr


c = πd

This depends on whether or not you know the radius (r) or the diameter (d)

Let’s calculate one manually, for example.

If r = 6 cm, the the circumference is c = 2π(6) = 12π cm, if writing in terms of π. If you prefer a numerical value, the answer rounded to the nearest tenth is 37.7 cm.

Suppose you only know the diameter? If the diameter is 8 cm, then the circumference is c = π(8) = 8π or 25.1 cm, rounded to the nearest tenth.

A great thing about the formulas is that you can manipulate it to solve for an unknown if you know one of the other quantities. For example, if we know the circumference, but don’t know the radius, you can solve c = 2πr for r and get \(r = \frac{c}{2\pi}\).  Similiarly, if you want the diameter from the circumference, simply take c =πd and solve for d to get d = \(\frac{c}{\pi}\).


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Finding the Area:

Let a = area of the circle

a = πr²

If you know the diameter and not the radius, simply divide the diameter by 2 to get the radius and still use the formula above.

Again, the formula can be used to solve for the radius, if you know the area. Simply divide a by π to get r² and take the square root of
the result.

If you wish to know the diameter from the area, follow the procedure above but double the result you get for r. This is because the diameter is twice the length of the radius.

Try an example manually to get the area.

Suppose r = 5 inches

a = πr²

a = π(25) = 25π

If rounding to the nearest tenth the area is 78.5 square inches.

If you know the diameter, simply divide by 2 to get the radius and use the same formula as above.

Of course, you don’t have to go through all the manual calculations to use this calculator. Simply input the information you know and the rest will be computed for you nearly instantly.