Sphere Calculator (Radius, Diameter, Volume, Surface Area)

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Key Features

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A sphere's radius, diameter, volume, and surface area are all related by simple, well-known formulas — knowing any single one of them lets you solve for all the others. This all-in-one solver comes in handy whenever a real-world problem hands you one measurement (a ball's known volume from a product spec, a tank's known surface area for a coating job, a planet's known diameter from astronomical data) and you need the rest.

How it works

Choose which value you know and enter it. The calculator first solves for the radius: directly if you entered the radius, by halving if you entered the diameter, by inverting V=(4/3)πr³ (taking a cube root) if you entered the volume, or by inverting A=4πr² (taking a square root) if you entered the surface area. Once the radius is known, the calculator derives diameter (2r), volume ((4/3)πr³), and surface area (4πr²) from it directly.

Enter what do you know?.
Enter value.
Click Calculate to see your results.

Examples

Volume = 113.097...

Solving (4/3)πr³=113.097 for r gives r≈3. Diameter = 6. Surface area = 4π(3)² ≈ 113.10.

Surface area = 314.16

Solving 4πr²=314.16 for r gives r²≈25, so r=5. Diameter = 10. Volume = (4/3)π(125) ≈ 523.60.

Common mistakes to avoid

Selecting the wrong "known field" from the dropdown, which changes which formula is applied first and produces an incorrect radius.
Forgetting to take a cube root (not just dividing) when recovering the radius from a known volume.
Mixing up radius and diameter, which throws every other formula off by a factor of 2 or more.

Frequently asked questions

Select "diameter" from the dropdown — the calculator divides by 2 to get the radius first, then proceeds exactly as it would from a known radius.

It rearranges V=(4/3)πr³ to solve for r, which requires isolating r³ and then taking a cube root: r=∛(3V/(4π)).

Surface area scales with the square of the radius while volume scales with the cube, so a sphere's volume grows much faster than its surface area as it gets bigger — one reason larger spherical objects have proportionally less surface relative to their volume.

Yes — once you have the radius, verify that 2×radius matches your diameter, and that plugging the radius back into both the volume and surface area formulas reproduces your other known values.

None of radius, diameter, volume, or surface area can physically be negative, so a negative input doesn't correspond to any real sphere and should be treated as invalid.

Volume — it scales with r³ while surface area scales with r², so for large spheres, volume dominates surface area by an ever-widening margin.

Free Sphere Calculator (Radius, Diameter, Volume, Surface Area)