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How to use
One measurement such as radius or diameter determines all core properties of a sphere. The calculator first normalizes the input to radius, then derives volume, surface area, great-circle circumference and great-circle area using full floating-point π.
- Choose whether the known value is radius or diameter.
- Enter a positive value and choose a length unit.
- Calculate; the input is normalized to radius.
- Read volume, surface area and great-circle measurements with the correct units.
How it is calculated
Example
For radius 3 cm, diameter is 6 cm, surface area is 36π ≈ 113.097 cm², volume is also 36π ≈ 113.097 cm³, and great-circle circumference is 6π ≈ 18.850 cm.
Important notes
Volume uses the cubic length unit and surface area the squared unit. This models an ideal geometric sphere; a real object that is not perfectly spherical, or a tank with wall thickness, needs additional modeling.
Worked examples and interpreting results
For a sphere with radius 2, its surface area is 16π, and its volume is 32π divided by 3.
| Case | Calculation | Result |
|---|---|---|
| Surface area | 4 × π × 2² | 50.265482 |
| Volume | 4 × π × 2³ ÷ 3 | 33.510322 |
How to check the result
Surface area is squared; volume is cubic. Enter radius or diameter correctly: diameter equals twice the radius.
Frequently asked questions
What is the difference between a circle and a sphere?
A circle is 2D; a sphere is a 3D solid with volume and surface area.
Why does volume grow so quickly with radius?
Because volume scales with r³, while surface area scales with r².
Can I enter diameter directly?
Yes. Choose diameter and the calculator divides it by two to get radius.