Direct answer

Volume measures three-dimensional space. Box: length × width × height. Cylinder: π × radius² × height. Sphere: (4/3) × π × radius³. Cone: (1/3) × π × radius² × height. Square pyramid: (1/3) × base² × height. Triangular prism: (base × height ÷ 2) × length. Ellipsoid: (4/3) × π × axis 1 × axis 2 × axis 3. Convert with: 1 cubic yard = 27 cubic feet, 1 cubic foot = 28.3168 liters = 7.48052 gallons.

Volume formulas

Each shape in the calculator above uses one of these formulas. Enter every dimension in the same unit:

• Box: V = length × width × height
• Cylinder: V = π × r² × h
• Sphere: V = (4/3) × π × r³
• Cone: V = (1/3) × π × r² × h
• Square pyramid: V = (1/3) × base² × height
• Triangular prism: V = (base × height ÷ 2) × length
• Ellipsoid: V = (4/3) × π × a × b × c

Unit conversions: 1 cubic yard = 27 cubic feet; 1 cubic foot = 28.3168 liters = 7.48052 gallons; 1 liter = 1,000 cubic centimeters.

Worked examples

Example 1 (box): 10 ft × 8 ft × 6 ft = 480 cubic feet = 480 ÷ 27 = 17.78 cubic yards = 13,592.1 liters = 3,590.6 gallons.

Example 2 (cylinder): Radius 3 ft, height 10 ft. Volume = π × 3² × 10 = 282.74 cubic feet.

Example 3 (cone): Radius 3 ft, height 7 ft. Volume = (1/3) × π × 3² × 7 = 21π ≈ 65.97 cubic feet.

Try the new shapes above: choose cone, square pyramid, triangular prism or ellipsoid, and pick an input unit — feet, inches, yards, meters or centimeters — the result is converted for you.

What to watch out for

Pick the input unit once and enter every dimension in it. The calculator converts the result to cubic feet, cubic yards, liters and gallons automatically.

FAQs

How do you calculate the volume of a box?

Multiply length × width × height, making sure all three dimensions use the same unit. For example, a box 10 ft long, 8 ft wide and 6 ft high holds 10 × 8 × 6 = 480 cubic feet. If your dimensions use mixed units, convert them first.

How many cubic feet are in a cubic yard?

There are exactly 27 cubic feet in a cubic yard, because 1 yard = 3 feet and 3³ = 27. Divide cubic feet by 27 to get cubic yards. For example, 480 cubic feet ÷ 27 = 17.78 cubic yards.

What is the volume formula for a cylinder?

The volume of a cylinder is π × radius² × height. For example, a cylinder with radius 3 ft and height 10 ft holds π × 9 × 10 ≈ 282.74 cubic feet. Use the radius (half the diameter), not the diameter itself.

What is the difference between volume and capacity?

Volume is the space an object occupies; capacity is how much a container can hold. The formulas are the same. In everyday use the words are often interchangeable, but capacity usually refers to the inside of a container.

What is the volume formula for a cone?

A cone’s volume is (1/3) × π × radius² × height — exactly one-third of the cylinder with the same base and height. For example, a cone with radius 3 ft and height 7 ft holds (1/3) × π × 9 × 7 = 21π ≈ 65.97 cubic feet. Try it with the cone option in the calculator above.

How do you convert cubic feet to liters?

Multiply cubic feet by 28.3168 to get liters. For example, 480 cubic feet × 28.3168 ≈ 13,592.1 liters. The calculator above shows liters and gallons automatically for every result.

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Last updated: November 1, 2026.