Quick answer: the volume of a sphere is V = (4/3) π r³. From a diameter, use V = (π/6) d³; from a circumference, first divide by 2π to get the radius. Because the radius is cubed, doubling it multiplies the volume by eight.
The sphere volume formula, step by step
where π ≈ 3.14159 · r = radius (center to surface)
Worked example — a sphere with a 3-inch radius:
- Cube the radius: 3³ = 27
- Multiply by π: 27 × 3.14159 = 84.82
- Multiply by 4/3: 84.82 × 1.3333 = 113.10 in³
If you're starting from a different measurement, convert to radius first:
| You measured… | Get the radius by… | Direct formula |
|---|---|---|
| Diameter (d) | r = d ÷ 2 | V = (π/6) d³ |
| Circumference (C) | r = C ÷ 2π | V = C³ / 6π² |
| Surface area (S) | r = √(S ÷ 4π) | V = (S/3) × √(S ÷ 4π) |
The calculator's mode menu handles the first two automatically — no hand conversion needed.
Volumes of real balls — quick reference
Handy for checking your own measurement, or for settling exactly how much air is in a basketball:
| Ball | Diameter | Volume | Liters |
|---|---|---|---|
| Golf ball | 1.68 in | 2.48 in³ | 0.04 |
| Billiard ball | 2.25 in | 5.96 in³ | 0.10 |
| Tennis ball | 2.70 in | 10.31 in³ | 0.17 |
| Softball | 3.82 in | 29.2 in³ | 0.48 |
| Soccer ball (size 5) | 8.65 in | 339 in³ | 5.55 |
| Basketball (size 7) | 9.51 in | 450 in³ | 7.38 |
| Beach ball (20 in) | 20 in | 4,189 in³ | 68.6 |
Notice the jump from soccer ball to basketball: the diameter grows only 10%, but the volume grows 33% — the cube in the formula at work.
Where sphere volume shows up in real life
Balloons, bubbles and party planning
A 12-inch balloon inflated to a rough sphere holds (π/6) × 12³ ≈ 905 in³ ≈ 14.8 liters of air or helium. A standard helium tank rated "fills 50 balloons" is making exactly this calculation for you.
Spherical tanks and floats
Industry stores gas in spheres because the shape has the least surface area per unit of volume — less steel, even stress. A 3-ft-diameter float ball: V = (π/6) × 27 = 14.14 ft³, displacing about 882 lb of water — which is exactly why mooring buoys hold up so much chain. Half-spheres like domes and bowl-shaped tanks get their own hemisphere calculator.
Planets, for perspective
Earth's mean radius is 6,371 km, so V = (4/3)π × 6,371³ ≈ 1.083 × 10¹² km³ — about 1.3 million Earths would fit inside the Sun. The same one-line formula scales from a marble to a star.
Common mistakes & pro tips
- Diameter used as radius. The result comes out 8× too large — worse than the cylinder's 4× error, because the sphere formula cubes it. If the number spans the whole ball, halve it or use Diameter mode.
- Forgetting the 4/3. πr³ alone is not a volume formula. If your hand calculation is 25% under the calculator's, this is why.
- Pro tip — measure with a wrap. Rulers slip off curved surfaces. Wrap a tape or string around the widest point and use Circumference mode; it's the most repeatable measurement you can take on a ball.
- Pro tip — squash test. Real "spheres" (fruit, balloons) are often slightly oblate. If the height and width differ by more than a few percent, the ellipsoid calculator with three semi-axes gives a noticeably better answer.
How to use this calculator
- Choose your measurement. Pick Radius, Diameter or Circumference from the menu — whichever you can actually measure. A tape wrapped around a ball gives circumference; a caliper gives diameter.
- Enter the value and unit. Type the measurement and select its unit (mm, cm, m, in, ft or yd).
- Let it apply V = (4/3)πr³. The calculator converts your input to a radius, cubes it, and multiplies by 4/3 π — showing the substitution as it goes.
- Switch the output unit. Read the same result in cubic units, liters or gallons from the result menu.
Frequently asked questions
How do you find the volume of a sphere with the diameter?
Halve the diameter to get the radius, then use V = (4/3)πr³ — or use the direct form V = (π/6)d³. A sphere 10 cm across: V = (π/6) × 1,000 = 523.6 cm³. This calculator has a Diameter mode that handles it automatically.
How do I find sphere volume from the circumference?
Divide the circumference by 2π (6.2832) to get the radius, then apply V = (4/3)πr³. A basketball measuring 29.5 inches around has r = 4.70 in, so V ≈ 434 in³. Wrapping a tape around the widest point is usually the easiest accurate way to measure a ball.
How do I find the radius if I know the volume?
Rearrange the formula: r = ∛(3V / 4π). For a 1-liter sphere (1,000 cm³): r = ∛(3,000 ÷ 12.566) = ∛238.7 ≈ 6.20 cm. So a 1-liter round flask is about 12.4 cm across.
What is the volume of a sphere with radius 2?
V = (4/3) × π × 2³ = (4/3) × π × 8 = 33.51 cubic units. In centimeters that's 33.51 cm³; in inches, 33.51 in³ (about 0.55 liters).
Why is the sphere formula (4/3)πr³?
Archimedes proved a sphere occupies exactly two-thirds of the cylinder that encloses it. That cylinder has volume πr² × 2r = 2πr³, and two-thirds of that is (4/3)πr³. He considered it his finest result — the sphere-in-cylinder figure was carved on his tomb.
What happens to volume when you double the radius?
It multiplies by eight, because the radius is cubed: 2³ = 8. That's why a beach ball twice the width of a soccer ball holds eight times the air, and why small increases in tank diameter buy large increases in capacity.