# Sphere Calc: find V, A, d

Created by Dominik Czernia, PhD candidate
Reviewed by Bogna Szyk
Last updated: Mar 25, 2022

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)).

Try our equation of a sphere calculator to learn how to calculate the volume of a sphere from its equation.

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