 in
Diameter (d)
in
Surface area (A)
in²
Volume (v)
cu in
Surface to volume ratio (A / V)
1/
in

# Sphere Calc: find V, A, d

By Dominik Czernia, PhD candidate

Sphere calc is an advanced tool that finds the volume, area and diameter of a sphere. Enter one of your selected quantities to calculate other parameters or read the article below to learn about all the equations we have used. The notation is as follows:

• r - radius of a sphere,
• V - volume of a sphere (sphere calc: find V),
• A - area of a sphere (sphere calc: find A),
• d - diameter of a sphere (sphere calc: find d),
• A / V - surface to volume ratio of a sphere.

A sphere is defined as a set of points in three-dimensional space, that are all at the same distance from a given point, which is called the center. Sphere is widely used in physics to model different objects, like spherical capacitors or atoms of a gas. You should also check out our spherical coordinates calculator and see how you can use a sphere to describe the position of any given point in a 3D space.

## Sphere calc: find V

The volume of a sphere V is the space enclosed by a sphere, for example, the space that a substance (solid, liquid or gas) can occupy. Its value is expressed in cubic units of length, e.g., cubic meters `m³` or cubic feet `cu ft`. Try our volume conversion to learn how to convert between different volume units. The volume of a sphere can be found with the following equations:

1. With given radius: `V = 4/3 * π * r³`,
2. With given diameter: `V = 1/6 * π * d³`,
3. With given area: `V = √(A³ / (36 * π))`.

## Sphere calc: find A

The surface area of a sphere A is a measure of the total area that the surface of a sphere occupies. Its value is expressed in squared units of length, e.g., square meters `m²` or square feet `ft²`. Check out area conversion calculator to learn how to convert between different area units! The surface area of a sphere can be found with the following equations:

1. With given radius: `A = 4 * π * r²`,
2. With given diameter: `A = π * d²`,
3. With given volume: `A = ³√(36 * π * V²)`.

## Sphere calc: find d

The diameter of a sphere d is the longest straight line through a sphere, connecting two points of a sphere and passing through its center. The diameter is twice the radius. Diameter, just like radius, is expressed in units of length, e.g., meters `m` or feet `ft`. With our length conversion calculator you can quickly convert between different units of length. The diameter of a sphere can be found with the following equations:

1. With given radius: `d = 2 * r`,
2. With given diameter: `d = √(A / π)`,
3. With given volume: `d = ³√(6 * V / π)`.

## Surface to volume ratio

The interesting fact is that the sphere encloses the largest volume among all other closed surfaces with a given surface area. In other words, the surface to volume ratio `A / V` of a sphere is relatively high compared to other figures. You can easily find an explicit formula for the surface to volume ratio, knowing that the area is `A = 4 * π * r²` and the volume is `V = 4/3 * π * r³`:

`A / V = (4 * π * r²)/(4/3 * π * r³) = 3 / r`

or, if we know that radius is half of diameter `r = d / 2`, then

`A / V = 6 / d`

You can estimate this quantity with our sphere calc too!

Dominik Czernia, PhD candidate