Sphere Volume Calculator
The volume of a sphere is V = (4/3) π r³, and this sphere volume calculator works it out the moment you enter a radius (or diameter). You'll get the answer at once in cubic inches or feet, liters, and gallons, plus the result in terms of pi and the surface area. It handles a full sphere, a ball, or a hemisphere, and it shows the formula and the steps with every result.
- Sphere or ball
- Hemisphere too
- Radius or diameter
- In terms of pi
- Surface area shown
Last updated June 15, 2026 Method: V = (4/3)πr³ Reviewed by the Calcowa math team
Enter a positive radius to see the volume.
Show all units
V = (4/3)π × 5³ = 523.6 in³
What is the volume of a sphere?
The volume of a sphere is the space it fills, found with V = (4/3) × π × r³, where r is the radius. For a radius of 5 in, the sphere volume is about 523.6 cubic inches.
Spherical volume only depends on the radius, since a sphere is perfectly round in every direction. A ball is just a solid sphere, so the volume of a ball uses the same formula. If you've got the diameter instead, halve it first to get the radius. One measurement does it.
How do you calculate the volume of a sphere?
To find the volume of a sphere, cube the radius, then multiply by pi and by four-thirds. Here's the full sequence:
- 1
Measure the radiusMeasure the radius. If you only have the diameter, divide it by 2.
- 2
Cube the radiusMultiply the radius by itself twice to get r cubed.
- 3
Multiply by piMultiply r cubed by pi (about 3.14159).
- 4
Multiply by four-thirdsMultiply that by 4/3 to get the volume.
- 5
Convert the unitsConvert to liters, gallons, or cubic feet if that's what you need.
Volume of a sphere from the diameter
If you measured across the widest part, you've got the diameter, not the radius. Halve it (r = d ÷ 2) and then use V = (4/3)πr³. You can also work straight from the diameter with V = (π/6) × d³, which gives the same answer. Switch the calculator to Diameter and it'll do the halving for you, so you'll get the volume of a sphere from the diameter in one entry.
Volume of a sphere in terms of pi
For a math class you'll often need the volume in terms of pi, which means leaving π as a symbol. Work out (4/3)r³ and keep the pi: for r = 3 that's (4/3) × 27 = 36, so the volume is 36π cubic units. The result panel shows this in-terms-of-pi value next to the decimal, so you can write whichever form your teacher asks for.
Volume of a hemisphere
A hemisphere is half of a sphere, like a dome or a bowl, so it's exactly half the full sphere: V = (2/3) × π × r³. Set the calculator to Hemisphere and it switches to this formula, which is handy for domes, bowls, and rounded tank ends. The volume formula for half of a sphere is just the four-thirds replaced by two-thirds.
Surface area and volume of a sphere
A sphere has two key measures, and they're easy to mix up. The volume, V = (4/3)πr³, is the space inside. The surface area, A = 4πr², is the curved skin on the outside. This calculator shows both from the same radius, so you'll read the area and volume of a sphere together. For the full surface-area breakdown, see the sphere surface area calculator.
A sphere volume example, step by step
Say you've got a sphere with a radius of 7 cm. Cube the radius to get 343, multiply by pi for about 1,077.57, then multiply by four-thirds.
V = (4/3)π × 7³ ≈ 1,436.76 cm³
about 1.44 liters
Type a radius of 7 and pick centimeters above, and you'll get the matching liters and gallons without converting by hand.
Units and accuracy
Calcowa shows the sphere volume in liters, US and UK gallons, milliliters, fluid ounces, and cubic mm, cm, m, inches, feet, and yards at once, plus the answer in terms of pi. The results use the full value of pi, not a rounded 3.14, so they're accurate for engineering, school, and everyday work.
| Unit | Best for | Good to know |
|---|---|---|
| Cubic inches (in³) | Small balls, bearings, marbles | Default when you enter inches |
| Cubic feet (ft³) | Large balls, domes, tanks | 1 ft³ = 1,728 in³ |
| Liters (L) | Everyday capacity of a ball | 1 L = 1,000 mL |
| US gallons (gal) | Spherical tanks and floats | 1 US gallon = 3.785 L |
| In terms of pi (π) | Exact math answers | Leaves the result as a multiple of pi |
Frequently asked questions
Is the volume of a ball the same as the volume of a sphere?
Yes. A ball is a solid sphere, so its volume uses the same formula, V = (4/3)πr³. The word sphere often means just the surface in math, while a ball is the filled shape, but for volume they give the same number.
The volume of a sphere is V = (4/3) × π × r³, where r is the radius. For a radius of 5 in, that's about 523.6 cubic inches. A ball is a solid sphere, so the same formula gives the volume of a ball.
Divide the diameter by 2 to get the radius, then use V = (4/3)πr³. You don't have to do that by hand: switch the measurement to Diameter and the calculator halves it for you before working out the volume.
A hemisphere is half a sphere, so its volume is V = (2/3) × π × r³, which is exactly half of the full sphere formula. Switch on the Hemisphere option and the calculator uses this version.
Rearrange the formula to r = cube root of (3V ÷ 4π). Multiply the volume by 3, divide by 4 times pi, then take the cube root. That'll give you the radius of a sphere in the same length unit.
Volume comes first. To get the weight, multiply the sphere's volume by the material's density (weight = volume × density). To get the density of a sphere, divide its mass by the volume shown here. For water, 1 litre weighs about 1 kilogram.
It comes from calculus, by adding up thin circular slices through the sphere, and Archimedes showed the same result geometrically: a sphere fills exactly two-thirds of the cylinder that just contains it. The derivation is why the four-thirds factor appears.
The surface area of a sphere is A = 4 × π × r², which is the curved area of its whole outer skin. This calculator shows it next to the volume, and our sphere surface area tool covers it in full.
Related calculators
Working with round shapes? These geometry tools pair well with sphere volume.
The 4πr² skin of the same sphere.
Cylinder volumeVolume of a solid or hollow cylinder.
Cone volumeVolume of a cone or pointed solid.
Need a sphere volume fast?
Try the calculator above, or browse every shape in the geometry hub.