Volume of a sphere, formula and calculator.

The volume of a sphere is V = 4/3 × π × r³. Take a radius of 5 cm. Cube it: 5 × 5 × 5 = 125. Multiply by π (3.14159265): 125 × 3.14159265 = 392.70. Multiply by 4/3: 523.5988 cm³. That is 0.5236 liters. The tool does these steps for any size and writes them out.

How to use the converter

1. Choose Find: volume from the radius or diameter, a hemisphere, a spherical cap (a slice off the top), or the radius from a volume.
2. Pick Radius or Diameter under I know the, type the number, and choose a Unit of length.
3. Read the big result, then The working, which shows each step with your numbers.
4. The cards give the surface area, diameter, circumference, liters and US gallons. Use Copy result or Copy link to keep the answer.

Where the formula comes from

A sphere fits inside a cylinder with the same radius and a height of 2r. That cylinder has a volume of π × r² × 2r = 2πr³. The sphere takes up exactly two thirds of it: 2/3 × 2πr³ = 4/3 × πr³. This is a way to remember the formula, and it explains why r is cubed: volume grows with length three times over. With a diameter d, r = d ÷ 2 and the formula becomes V = π × d³ ÷ 6. For d = 10 cm that is 523.5988 cm³, the same as r = 5.

Doubling the radius

Because of r³, a sphere with twice the radius has eight times the volume. Radius 5 cm gives 523.5988 cm³ and radius 10 cm gives 4,188.7902 cm³, and 8 × 523.5988 is the same number. A ball 10 percent wider holds 1.1³ = 1.331 times as much, about a third more.

Volume for radius 1 to 10 cm

Worked examples

• A ball 24 cm across. The radius is 24 ÷ 2 = 12 cm. 12³ = 1,728 and 4/3 × π × 1,728 = 7,238.23 cm³, or 7.238 liters.
• A round tank of radius 1.5 m. 1.5³ = 3.375, so V = 4/3 × π × 3.375 = 14.1372 m³. One cubic meter is 1,000 liters, so that is 14,137.17 liters. In US gallons, with 3.785411784 liters to a gallon, it is 3,734.6.
• A radius for exactly 1 liter. 1 liter is 1,000 cm³. r³ = 3 × 1,000 ÷ (4π) = 238.732, so r = 6.2035 cm. Use the "Radius from a volume" mode for this.
• A marble of diameter 16 mm. The radius is 8 mm. V = 4/3 × π × 512 = 2,144.66 mm³, which is 2.145 cm³.

The liter and gallon figures

A liter is 1,000 cm³, which is 0.001 m³ (NIST Special Publication 811, Appendix B.8 gives 1 L = 1.0 E-03 m³ as exact, checked 24 Oct 2026). A US gallon is 231 cubic inches exactly (NIST Handbook 44 (2026), Appendix C, checked 24 Oct 2026), and an inch is 2.54 cm exactly, so a gallon is 231 × 16.387064 cm³ = 3,785.411784 cm³. The tool uses those two facts, so the liters and gallons are as exact as your input.

Hemisphere and spherical cap

A hemisphere is half a sphere, cut through the middle. Its volume is 2/3 × π × r³. For r = 5 cm that is 261.7994 cm³, exactly half of 523.5988. Its outside is a curved part of 2 × π × r² = 157.0796 cm² and a flat face of π × r² = 78.5398 cm², so the total surface is 3 × π × r² = 235.6194 cm². The converter has a Hemisphere choice under Find for this.

A spherical cap is a slice cut off the top by a flat plane. With the sphere radius r and the cap height h, the volume is π × h² × (3r − h) ÷ 3. Take r = 5 cm and h = 2 cm: π × 4 × 13 ÷ 3 = 54.4543 cm³, which is 10.40 percent of the whole ball. The flat cut is a circle of radius √(h × (2r − h)) = √16 = 4 cm. Two checks show the formula is sound. With h = r it gives the hemisphere, and with h = 2r it gives the whole sphere. A round-bottomed flask filled to a depth h holds a cap of that volume. Use Spherical cap under Find.

When you only know the circumference

Wrap a tape round the widest part of a ball and you have the circumference C. The radius is r = C ÷ (2 × π), and the volume is C³ ÷ (6 × π²). For C = 40 cm, r = 40 ÷ 6.28318531 = 6.3662 cm and V = 1,080.76 cm³. Type the radius into the tool, or the diameter, which is C ÷ π = 12.7324 cm.

Sphere, cylinder and cone

A cylinder with radius r and height 2r holds 2 × π × r³. A cone of the same radius and height holds 2/3 × π × r³. The sphere holds 4/3 × π × r³. So cone : sphere : cylinder is 1 : 2 : 3. Put another way, a ball that just fits inside a can takes up two thirds of the can. In a cube of side 2r the ball takes up π ÷ 6 = 52.36 percent.

Ball sizes by diameter in inches

The formula with a diameter d is V = π × d³ ÷ 6. One cubic inch is 16.387064 cm³ exactly (2.54³), so liters follow, and a US gallon is 231 cubic inches.

Mistakes to avoid

• Using the diameter as the radius. The volume comes out 8 times too big. A 10 cm ball is r = 5, not r = 10.
• Squaring instead of cubing. 5² = 25 gives a number with the wrong unit. Volume needs r³ and the answer is in cubic units.
• Mixing units. A radius of 5 cm is 0.05 m. In meters the volume is 0.0005236 m³, the same as 523.5988 cm³. Pick one unit before you start.
• Rounding π to 3.14 early. For r = 5, 3.14 gives 523.33 against 523.60, a gap of 0.27 cm³.

For a flat shape or a box, the area and volume calculator covers more shapes, and the volume of a cylinder page does the can and the pipe.