Sphere Calc: find V, A, d
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:
- With given radius:
V = 4/3 * π * r³, - With given diameter:
V = 1/6 * π * d³, - 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:
- With given radius:
A = 4 * π * r², - With given diameter:
A = π * d², - 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:
- With given radius:
d = 2 * r, - With given diameter:
d = √(A / π), - 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!