Sphere Calc: find V, A, d

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Dominik Czernia, PhD

Dominik CzerniaPhD, Institute of Nuclear Physics PAN

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Dominik Czernia, PhD, is a physicist at the Institute of Nuclear Physics in Kraków, specializing in condensed matter physics with a focus on molecular magnetism. He has led several national research projects, pioneering innovative approaches to novel materials for high technology. Passionate about making science accessible, Dominik has created various calculators, mostly in physics and math categories. In his free time, he enjoys family walks, city explorations, mountain hiking, and traveling everywhere by bike. See full profile

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Adena Benn

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Adena Benn is a Guyanese teacher with a degree in computer science who is always reading and learning. She loves problem-solving, everything tech, and working with teenagers. She has a passion for education and is especially interested in how children learn and the teaching methods that best suit their learning styles. She grew up on a farm in Pomeroon, Guyana, where she worked alongside her parents and siblings. As such, she is just as comfortable growing plants as teaching in the classroom. In her early life, she also gained expertise as a seamstress, which she learned from her mother. By grade 9, she had already acquired her dressmaker's certificate. Today she uses her skills to design many items for her family. In her free time, Adena loves to read, take long walks, write children’s stories and poetry, travel, or spend time with her family. See full profile

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The sphere calc is an advanced tool that finds a sphere's volume, area, and diameter. 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:

Sphere calc - a picture with the radius and diameter of a sphere.

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 a set of points in three-dimensional space at the same distance from a given point, called the center. 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)).

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

With given radius: d = 2 × r;
With given diameter: d = √(A / π); and
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 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!