Sphere Calculator

Calculate the volume and surface area of any sphere from its radius.

What is a Sphere?

A sphere is a perfectly round three-dimensional geometric object. It is defined as the set of all points in three-dimensional space that are equidistant from a fixed central point. That distance from the center to any point on the surface is the radius (r). The diameter is twice the radius - the maximum straight-line distance across the sphere through its center.

Spheres are the three-dimensional counterpart of circles, and they share the same defining property: constant distance from a center point. Just as a circle is the most efficient two-dimensional shape (encloses maximum area for a given perimeter), a sphere is the most efficient three-dimensional shape - it encloses the maximum volume for a given surface area. This is the geometric reason why soap bubbles, liquid droplets in microgravity, and planetary bodies all tend toward spherical forms.

The two principal measurements of a sphere are its volume and surface area. Volume tells you how much three-dimensional space the sphere occupies - how much liquid it could hold, for instance. Surface area tells you how much material would be needed to cover the sphere’s outer surface - relevant in painting, coating, or heat transfer calculations.

The volume formula, (4/3)πr³, grows with the cube of the radius, meaning small increases in radius lead to large increases in volume. The surface area formula, 4πr², grows with the square of the radius. This difference in scaling rates has important practical implications: a sphere twice as large has 4 times the surface area but 8 times the volume, meaning large spheres are proportionally more efficient at containing volume per unit of surface area.

Spheres appear throughout science and engineering: ball bearings for mechanical efficiency, spherical tanks for storing pressurised gases (optimal shape for uniform stress distribution), spherical lenses in optics, and of course the roughly spherical shapes of planets and stars formed by gravitational self-compression.

Formula

Volume of a Sphere:

V = (4/3) × π × r³

V = Volume (cubic units)

π = Pi ≈ 3.14159265

r = Radius

Surface Area of a Sphere:

SA = 4 × π × r²

SA = Surface Area (square units)

Diameter:

d = 2r

How to Use This Calculator

Enter the radius of your sphere in the input field. Use any unit (cm, m, inches, feet).
Click Calculate to instantly compute the volume, surface area, and diameter.
Read the results - volume is in cubic units, surface area is in square units, and diameter is in the same linear unit as the radius.
Real-world application - for example, if you know the diameter of a ball (say, a basketball with diameter 24 cm), enter radius = 12 to find its volume and surface area.

Example Calculations

Example 1 - Football (Soccer Ball)

A standard football has a radius of approximately 11 cm. Calculate its volume and surface area.

r = 11 cm

Volume = (4/3) × π × 11³ = (4/3) × π × 1331 = 5,575.28 cm³

Surface Area = 4 × π × 11² = 4 × π × 121 = 1,520.53 cm²

Diameter = 2 × 11 = 22 cm

Volume = 5,575.28 cm³ | Surface Area = 1,520.53 cm² | Diameter = 22 cm

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Example 2 - Large Storage Tank

A spherical water tank has a radius of 3 m. How much water can it hold?

r = 3 m

Volume = (4/3) × π × 27 = 113.10 m³

Since 1 m³ = 1,000 litres, capacity = 113,097 litres ≈ 113,100 litres

Surface Area = 4 × π × 9 = 113.10 m² (material needed to construct/coat the tank)

Volume = 113.0973 m³ | Surface Area = 113.0973 m² | Diameter = 6 m

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Frequently Asked Questions

What is the formula for the volume of a sphere?+

Volume = (4/3) × π × r³, where r is the radius. For a sphere with radius 5 cm, Volume = (4/3) × π × 125 = 523.60 cm³. Volume is measured in cubic units.

What is the formula for the surface area of a sphere?+

Surface Area = 4 × π × r². For a sphere with radius 5 cm, Surface Area = 4 × π × 25 = 314.16 cm². Notice that the surface area of a sphere equals exactly four times the area of a circle with the same radius.

How do I find the radius of a sphere from its volume?+

Rearrange the volume formula: r = ∛(3V / (4π)). For example, if V = 523.6 cm³, then r = ∛(3 × 523.6 / (4π)) = ∛(125) = 5 cm.

What is the difference between a sphere and a circle?+

A circle is a two-dimensional shape - all points at a given distance from a center point in a plane. A sphere is the three-dimensional equivalent - all points at a given distance from a center point in three-dimensional space. A circle has area and circumference; a sphere has volume and surface area.

What are some real-world examples of spheres?+

Balls (football, basketball, tennis ball), planets, stars, soap bubbles, ball bearings, globes, and water droplets in zero gravity are all approximately spherical. Spheres are the shape that minimises surface area for a given volume, which is why bubbles and liquid drops naturally form this shape.

How do you calculate the volume of a sphere?+

Volume of a sphere = (4/3) x pi x r^3, where r is the radius. Example: a sphere with radius 6 cm has volume = (4/3) x 3.14159 x 6^3 = (4/3) x 3.14159 x 216 = 904.78 cm^3. If you know the diameter, divide by 2 to get radius first. Volume is in cubic units.

How do you find the surface area of a sphere?+

Surface area of a sphere = 4 x pi x r^2. Example: a sphere with radius 5 cm has surface area = 4 x 3.14159 x 25 = 314.16 cm^2. An interesting fact: the surface area of a sphere equals exactly 4 times the area of a circle with the same radius. This relationship was discovered by Archimedes.

What is the relationship between a sphere and a cylinder?+

A sphere inscribed in a cylinder (same radius, height = diameter of sphere) has volume equal to 2/3 of the cylinder. Also, the surface area of the sphere equals the lateral surface area of that same cylinder (2 x pi x r x 2r = 4 x pi x r^2). These elegant relationships show that a sphere fits perfectly inside a cylinder with the same proportions, a discovery Archimedes considered his greatest achievement.