Sphere Calc: find V, A, d

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.

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. 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).

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. We can find the diameter of a sphere using the following equations:

1. With given radius: d = 2 × r;
2. With given diameter: d = √(A / π); and
3. With given volume: d = ³√(6 × V / π).

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 the radius is half of the diameter r = d / 2, then

A / V = 6 / d

You can estimate this quantity with our sphere calc too!

A sphere is widely used in physics to model different objects, like spherical capacitors or atoms of a gas. We have dedicated calculators for both topics: visit spherical capacitor calculator and van der Waals equation calculator to learn more!