Sphere Volume Calculator
A sphere with a radius of 6 has a volume of about 904.78 and a surface area of 452.39. This sphere volume calculator uses V = (4/3) pi r cubed and reports the surface area and diameter alongside. Because the radius is cubed, small measurement errors grow fast, doubling the radius multiplies the volume by 8.
Quick answer
Volume = (4/3) x pi x radius cubed.
Volume
904.7787
Surface area
452.3893
Diameter
12
What this tells you
- •Volume = (4/3) x pi x radius cubed.
- •Surface area = 4 x pi x radius squared, exactly 4 circles' worth.
- •The radius is half the diameter, the distance straight through the center.
- •Volume scales with the cube of size, so a ball twice as wide holds 8 times as much.
How to Use
- 1Enter the radius of the sphere.
- 2Read the volume as the main result, with surface area and diameter below.
- 3If you measured the diameter, halve it before entering.
- 4For a real ball, measure the circumference with a tape and divide by 2 pi to get the radius.
How It Works
Formula
V = (4/3) pi r^3Cube the radius, multiply by pi, then by four thirds. For radius 6, the cube is 216, times pi gives 678.58, and four thirds of that is 904.78. Archimedes proved the sphere fills exactly two thirds of its surrounding cylinder, which is where the 4/3 ultimately comes from.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
Radius 6 sphere
Four thirds of pi times 216. The surface area is 452.39.
Basketball (radius 12.1 cm)
A regulation basketball holds about 7.4 liters of air.
Marble with a 1 cm radius
The smallest clean case: four thirds of pi itself.
Sphere Volumes by Radius
Volume and surface area for common radii.
| Radius | Volume | Surface area |
|---|---|---|
| 1 | 4.19 | 12.57 |
| 2 | 33.51 | 50.27 |
| 3 | 113.10 | 113.10 |
| 5 | 523.60 | 314.16 |
| 6 | 904.78 | 452.39 |
| 10 | 4188.79 | 1256.64 |
Common mistakes
- Using the diameter as the radius. Since the radius gets cubed, this inflates the volume 8 times.
- Squaring instead of cubing. Radius squared belongs to surface area, radius cubed to volume.
- Rounding pi to 3. That understates the volume by almost 5 percent, which matters for tanks and containers.