Sphere Radius from Volume
A sphere's volume is 4π times the radius cubed, divided by three. Going the other way therefore takes a cube root.
Your numbers
Radius
10cm
Diameter
20cm
Surface area
1,256.68cm²
Formula
Radius = ∛(3 × Volume ÷ (4π))
The volume has to grow eightfold for the radius to double. Doubling the volume widens the radius by only 1.26 times.
What to enter
| Input | Default | Accepted range |
|---|---|---|
| Volume (cm³)The space a solid holds — length cubed. | 4,189 | 0 and up |
Step by step
Quick reference table
Results when only Volume (cm³) changes and everything else stays put.
| Volume (cm³) | Radius (cm) | Diameter (cm) | Surface area (cm²) |
|---|---|---|---|
| 2,095 | 7.938 | 15.876 | 791.78 |
| 3,142 | 9.086 | 18.172 | 1,037.42 |
| 4,189 | 10 | 20 | 1,256.68 |
| 6,284 | 11.448 | 22.895 | 1,646.8 |
| 8,378 | 12.599 | 25.199 | 1,994.85 |
What each result means
| Result | At default values |
|---|---|
| Radius (cm)Centre to edge — half the diameter. | 10 |
| Diameter (cm)The longest line across a circle — twice the radius. | 20 |
| Surface area (cm²)The total area of a solid’s outer skin. | 1,256.68 |
Common mistakes
The volume has to grow eightfold for the radius to double. Doubling the volume widens the radius by only 1.26 times.
Glossary
- Volume
- The space a solid holds — length cubed.
- Radius
- Centre to edge — half the diameter.
- Diameter
- The longest line across a circle — twice the radius.
- Surface area
- The total area of a solid’s outer skin.
Frequently asked questions
Q. How is Sphere Radius from Volume calculated?
Radius = ∛(3 × Volume ÷ (4π)) — A sphere's volume is 4π times the radius cubed, divided by three. Going the other way therefore takes a cube root.
Q. Can you walk through an example?
With Volume 4,189cm³, the answer is Radius 10cm.
Q. What do I need to enter?
Enter Volume. The result recalculates as you type, and an empty box counts as zero.
Q. How much does the answer move if I change a number?
Changing only Volume (cm³) moves the answer to Volume (cm³) 2,095 → Radius (cm) 7.938 and Volume (cm³) 8,378 → Radius (cm) 12.599. The table below lays out five steps.
Q. How are the numbers rounded?
Money is shown to the nearest whole unit, percentages to one decimal place and everything else to two. What you see is rounded; the calculation itself carries the unrounded value forward.
Q. Anything to watch out for?
The volume has to grow eightfold for the radius to double. Doubling the volume widens the radius by only 1.26 times.
Related calculators
Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.