Calculate the radius

Do you need calculate the radius of a circle? Use our calculator and you can get its value from the diameter or from its length.

We also show you how to calculate the radius for different geometric figures from their formula. 

Calculate the radius of a circle

Calculate the radius

There are different ways to obtain the radius of a circle or a circumference. Let's see some of them.

From diameter

In this case, the radius is removed dividing the diameter by twoi.e:

r = diameter /2

From the perimeter

Yes you know the length of the circleyou can calculate the radius with the following formula:

r = perimeter / 2π

From your area

In the event that you have to calculate the radius of a circle knowing its area, the formula to be used is this:

r = √(A/π)

That is, you have to make the square root of the area by pi.

Calculate the radius squared

If what you need is to square the radius, you can use our exponents calculator.. Thanks to it you will be able to calculate how much the radius is worth if you raise it to the square, to the cube or to any other exponent.

Calculate the radius of a rope

Radius of a rope

For calculate the radius from the length of a string and its angle αwe have to use the following formula:

r = chord length / (2sen(α/2))

Where does this formula come from? It is the one that we obtain after clearing the value of the radius in the formula that allows us to calculate the length (c) of an arc and that we show you below:

c = 2r sin(α/2)

If you are still not very clear about what is a chord on a circleIn the figure above these lines you have one represented by the C segment.

Calculate the radius of a curve

If we want to to get the radius of a curvewe can get it from the angle α and its length. We just have to apply the following formula and that's it:

r = curve length / α

In the figure you have in the previous point you can see a curve within a circle represented by the letter L.

Calculating the radius of a regular pentagon

Here we are going to show you how to calculate the radius of the circumscribed circle of any regular polygon. To do this we apply the following formula:

r = L / 2sen(α/2)

In the formula we can see two unknowns. L will be the length of one of the sides of the regular polygon and α is the central angle to be calculated with this other formula:

α = 360º / N

In this case, N will be the number of sides the polygon has.

Circumcircumscribed circle in a pentagon

For the sake of clarity, let's see how to calculate the radius of the circumscribed circle of a pentagon whose sides measure 7 centimeters. As you know, it has five sides so its central angle will be:

α = 360º / 5 = 72º.

Now we will calculate the radius of the pentagon:

r = 7 cm / 2sin(72º/2) = 7 cm / 2sin(36º) = 7 cm / (2 x 0.588) = 5.95 centimeters

This procedure you can apply it to any n-sided polygon..

Obtain the radius of a cylinder

The radius of a cylinder can be obtained by different methods. The simplest are from its volume or from its lateral area. Let's see how to proceed in each case:

From its lateral area

The formula for the lateral area of a cylinder es:

AL = 2πrh

We remove the value of the radius and we have that its value is obtained by applying:

r = lateral area / 2πh

From its volume

If we know the volume of a cylinderwe can also remove the radius easily with the following mathematical expression:

r = √(volume/πh)

From the surface of its base

The base of a cylinder is a circle and we have already seen above how to calculate the radius of a circle. Take a look at it.

Finding the radius of a sphere

Finally, let's take a look at how to calculate the radius of a sphere from its area and volume:

If we are given the area of a sphere

With the area of the sphere it is feasible to calculate the radius with this formula:

r = √(area/4π)

If we have the volume of the sphere

In the case that the mathematical exercise provides us with the volume of the spherewe can calculate its radius with the following expression:

r = ∛(3V/4π)

Note well that in this formula we will have that calculating the cube root.

If you have any doubts about how to calculate the radius in different geometric figures, you can write us a comment and we will help you to solve the problems you have.

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