Sphere calculator
Volume and surface area of a sphere from its radius, diameter or volume.
Fill in the fields and the result will appear here automatically.
Solves a sphere from whichever value you have: radius, diameter or the volume itself. The reverse direction comes up more often than expected — a tank volume tells you the radius, which tells you whether it fits through a hatch. The volume is reported in the cube of the chosen unit and the surface in its square: different powers of the same length, and they cannot share a conversion factor.
How it works
Formula and logic
V = (4 ÷ 3) · π · r³ and S = 4 · π · r²; the radius from a volume is the cube root of 3V ÷ (4π).
Example
A sphere of radius 3 m has a volume of 113.097 m³ and a surface area of 113.097 m².
Fields and units
- Length unit — list option
- What is known — list option
- Radius — cm
- Diameter — cm
- Volume — cm³
How to use
- — Choose the length unit.
- — Say whether you know the radius, the diameter or the volume.
- — Enter it and read the rest.
- — In volume mode enter the cube of the selected unit, for example cm³, not litres. 1 L = 1000 cm³. Radius, diameter and volume are positive; changing the unit does not convert the entered number.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- OpenStax: solid volumes and surface areas
- Limitation
- An ideal ball; surface and volume do not include walls or openings. Radius recovered from volume gives a geometric size, not a tank’s outer size when the input is internal capacity. Outputs are rounded.
FAQ
Why do the volume and surface match at radius 3?
When the numerical radius is 3 in the selected unit, the numerical volume and surface area coincide. The physical quantities are not equal: volume uses cubic units and area uses square units. Changing the unit scale changes that numerical coincidence.
How do I find the radius from a volume?
Choose the volume mode: the radius is the cube root of 3V ÷ (4π), and the surface follows from it.
What is the difference between a sphere and a ball?
A sphere is the surface only; a ball is the solid together with its interior. Volume belongs to the ball, surface area to the sphere bounding it.
Is the wall thickness of a tank taken into account?
No. The calculation is ideal — a geometric solid, not a vessel with material walls.