Sphere Area and Volume Calculator


Online Sphere Area and Volume Calculator: Calculate the volume and area of a Sphere based on its radius r. Enter one unknown in the form and press the CALCULATE button.

Table of contents:

What is a Sphere?

a sphere is a surface made up of all the points located at the same distance from a point called the center. The value of this distance to the center is called the radius of the sphere.

The characteristics of the Sphere

All radii are equal to R. All diameters are equal to 2R.

The shortest distance on the sphere between two points is the geodesic distance: the arc of the great circle between these two points. This distance is called the spherical distance. It is measured by the angle at the center that crosses the arc.

Any intersection of the sphere and the plane produces a circle or a point if the plane is tangent to the sphere. The circle is minimum at this point of tangency. It is maximum when the section plane passes through the center.

The tangent plane is in contact with a single point T of the sphere. The radius OT is perpendicular to the tangent plane.

Calculate the area of a Sphere

Although it is entirely composed of a single curved surface, it is possible to calculate the area of the sphere.

A = 4 . π . r² where r = measure of the radius

From its curved surface, we can see a certain resemblance between this formula and that allowing to calculate the area of a disc. Thus, only one measurement is essential to allow the use of this formula, namely the measurement of the radius.

Calculate the volume of the Sphere

The volume of a Sphere corresponds to the space inside the sphere which delimits it. To find its volume, just apply this formula:

V = 4 . π .r3 with r = measure of the radius

Once again, only the radius measurement is necessary to complete the process.