Sphere Volume Calculator
Find the volume and surface area of a sphere.
Results update as you type.
How it works
A sphere is a perfectly round three-dimensional object where every point on its surface lies the same distance, the radius, from its centre. Balls, planets, bubbles, and droplets are all approximately spherical, so finding a sphere's volume and surface area comes up in physics, engineering, manufacturing, and everyday estimation. This sphere volume calculator takes a single input, the radius, and returns both the volume, the amount of space the sphere encloses, and the surface area, the total area of its curved outer skin. The volume follows the formula four-thirds times pi times the radius cubed, which grows very quickly as the radius increases because the radius is raised to the third power. The surface area is four times pi times the radius squared, equal to the combined area of four flat circles the size of the sphere's widest cross-section. For a sphere with a radius of 3 units, the volume is about 113.1 cubic units and, in this particular case, the surface area is also about 113.1 square units. Engineers sizing tanks, scientists modelling cells or planets, and students studying solid geometry all rely on a sphere volume calculator to apply these two formulas accurately from just the radius.
volume = 4⁄3 × π × r³; surface area = 4 × π × r²
The volume of a sphere is four-thirds of pi times the radius cubed, a result derived through integral calculus by summing infinitely many thin circular slices stacked from pole to pole. The surface area is four times pi times the radius squared, which is exactly the area of four great circles of the sphere. Both formulas depend only on the radius, so cubing it drives the volume and squaring it drives the surface area as the ball grows.
Source:Euclidean geometry
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter radius.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Volume updates instantly as you type — no button to press.
Frequently asked questions
What is the formula for the volume of a sphere?
The volume of a sphere equals four-thirds multiplied by pi multiplied by the radius cubed. In symbols that is four over three times pi times r to the third power. Because the radius is cubed, the volume increases dramatically as the sphere grows: doubling the radius makes the volume eight times larger. The calculator applies this formula directly using the precise value of pi built into the computation.
How do I find a sphere's surface area?
The surface area of a sphere is four times pi times the radius squared. This equals the area of four great circles, the largest circles you can draw on the sphere. Because the radius is squared rather than cubed, surface area grows more slowly than volume as the sphere enlarges. Enter the radius and the calculator returns the surface area alongside the volume in a single step.
What if I only know the diameter?
The diameter is twice the radius, so simply halve the diameter to get the radius before entering it. If a ball measures 6 units across, its radius is 3 units, which is the value to type into the calculator. Both the volume and surface area formulas are written in terms of the radius, so converting the diameter first ensures the results come out correctly.
Why does volume grow so much faster than surface area?
Volume depends on the radius cubed while surface area depends on the radius squared, so as the radius increases the volume rises with the third power and the surface area only with the second. This is why large spheres enclose far more space relative to their skin than small ones, a fact that matters in biology for cell size and in engineering for storage tanks and pressure vessels.
What units does the answer use?
The volume is expressed in cubic units of whatever unit you used for the radius, such as cubic centimetres or cubic metres, while the surface area is in square units of the same measure. If you enter the radius in centimetres, the volume is in cubic centimetres and the surface area in square centimetres. Keeping the radius in a single consistent unit ensures both results are meaningful.