Radius of a Sphere Calculator

The Radius of a Sphere Calculator is a tool that provides a precise result not only for the radius of a sphere but also for circumference, area and volume, only by knowing one of the listed parameters. Therefore, these values will be fully described in the following text.

Also, suppose that this topic draws your attention. In that case, we recommend checking out other related calculators such as the Area Calculator to calculate the area of various geometry figures, Volume Calculator to find the volume of geometry figures, Spherical Coordinates Calculator, Golden ratio, Circle Calculator and others that our site offers.

This article contains information about the geometry of a sphere and all formulas necessary for the basic calculations of a sphere, including radius, area, volume, etc. The topic will be processed first by explaining the sphere’s radius, then calculating it, enclosed by the example and tutorial on using our calculator. Altogether, this will sink in by going through the text. Feel free to leave feedback and contact us if there are certain topics you wish us to write about.

What is the Radius of a Sphere?

A sphere is a three-dimensional object analogue to a two-dimensional circle. It is a set of points whose distance from the centre is always the same. The distance from the centre to any point on the circumference is the radius, marked with the letter r. With that in mind, the diameter is created by extending the radius to the opposite side of the sphere (d).

However, the diameter must go through the centre, and points connected by diameter are antipodal points of each other. Contrary, a line that connects two points that lay on the circumference of a sphere that misses the centre is a chord.

Other values important for calculating the radius of a sphere:

• Volume of a sphere (V) is a space enclosed with all edge points of a sphere. Archimedes derived the formula for a sphere’s volume by pointing out that the volume inside a sphere is twice the volume between the sphere and the circumscribed cylinder.
• Surface area of a sphere (A) is an area occupied by the surface of the three-dimensional sphere.
• Circumference of a sphere (C) –The same formula gives the circumference of a sphere as one for the circle.

An important fact is that a sphere has the lowest surface to volume ratio. Analogue to that, a circle encloses the largest area with a given perimeter.

The radius of a Sphere – Formulas

This section will discuss the various ways to calculate the sphere’s radius, depending on the available data. Formulas for the radius of a sphere are:

Data available	Formula
Volume	r=\sqrt[3]{3 \cdot \frac{V}{4 \cdot \pi}}
Surface area	r=\sqrt{\frac{A}{4 \cdot \pi}}
Diameter	r=\frac{d}{2}
The surface to volume ratio	r=\frac{3}{\frac{A}{V}}
Circumference	r=\frac {C}{2 \cdot \pi}

How to Find the Radius of a Sphere?

It is easy to find the radius of a sphere if any of the parameters listed above are known. For example, if we know the diameter of a sphere, the radius is half of that value, as the formula shows. But, if we don’t know where the centre of our sphere is, it can be a little bit harder to find its radius. Still, it is not unsolvable and here are two ways to find the centre point:

• Place two parallel planes, one on the top of the sphere and the other on the bottom, the distance between them is the diameter. Now, divide that length by two, and that is where the centre is.

• The other way is to find a volume of a sphere. We consider this solution more experimental than mathematical. Firstly, find a cylindrical object and pour water into it. Then, put a sphere in that cylinder and measure the amount of water pushed out of the cylinder, which is the volume of a sphere. Afterwards, apply the formula to find the radius so that you can find other parameters too.

The Radius of a Sphere Calculator – How to Use?

While developing this tool, the CalCon calculator team put a lot of effort into keeping it easy to use and functional for any case that can come up while calculating the radius of a sphere. This calculator will give you a result by entering only one of the listed parameters.

By clicking on the unit next to the measure of the specified parameter, a drop-down menu will appear, allowing you to choose a unit. Also, this function allows you to convert units as you wish.

SI unit for the length of the radius is meter; you can choose prefixes if you want to manipulate the result, such as mili, centi and kilo. Also, other units that are available on this calculator are inches, feet, yards, miles and nautical miles.

The radius of a Sphere Calculator – Example

If you know that the surface area of a sphere is 40 m^{2} , calculate the radius of a sphere. r=\sqrt{\frac{A}{4 \cdot \pi}}

r=\sqrt{\frac{40}{4 \cdot \pi}}

r=3.18 m

The radius of a sphere calculator does the previous calculation for you and all other variants depending on the given parameters. Try to check the results using our tool.

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