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Volume Calculator – Compute Volume of 3D Shapes Online

Calculate the volume of any 3D shape with our free online volume calculator. Supports cube, sphere, cylinder, cone, pyramid, and more with formula references and instant results.

Volume Calculator
Select a 3D shape and enter dimensions to calculate volume.
Formula
V = s³
Examples:

Understanding Volume

Volume measures how much space a 3D object occupies. Think of it as the amount of water a container can hold, or the capacity of a box. Volume is measured in cubic units – cubic inches, cubic feet, cubic meters, and so on.

Whether you're sizing a water tank, calculating concrete for a cylindrical pillar, or figuring out how much ice cream fits in a cone, this volume calculator covers the essential 3D shapes. Each formula is shown clearly, with step-by-step working so you understand exactly how the result is derived.

Volume Formulas for 3D Shapes

Cube

V = s³
V = side³

Cuboid (Rectangular Prism)

V = l × w × h
V = length × width × height

Sphere

V = (4/3)πr³
V = (4/3) × π × radius³

Cylinder

V = πr²h
V = π × radius² × height

Cone

V = (1/3)πr²h
V = (1/3) × π × radius² × height

Rectangular Pyramid

V = (1/3)lwh
V = (1/3) × base area × height

Triangular Prism

V = (1/2)bhl
V = (1/2) × base × triangle height × length

Hemisphere

V = (2/3)πr³
V = (2/3) × π × radius³

How Volume Works for Each Shape

Cube

All six faces are equal squares. Volume is simply the side length cubed. A cube with 5-inch sides holds 125 cubic inches – whether that's water, sand, or air.

Cuboid (Rectangular Prism)

Think of a shoebox or a brick. Multiply length, width, and height. This is the 3D equivalent of a rectangle's area. A 10×6×4 box has volume 240 cubic units.

Sphere

Perfectly round like a basketball. The formula (4/3)πr³ might look intimidating, but it's just scaling the radius cubed by a constant. A sphere with radius 4 has volume about 268 cubic units.

Cylinder

A circular prism – like a can or pipe. Base area (πr²) times height. A cylinder with radius 4 and height 10 holds about 503 cubic units.

Cone

Like an ice cream cone or traffic cone. Volume is exactly one-third of a cylinder with the same base and height. That 1/3 factor appears because the cone tapers to a point.

Rectangular Pyramid

Think of the Egyptian pyramids. Square or rectangular base, triangular faces meeting at the apex. Same 1/3 rule as the cone: one-third of base area times height.

Triangular Prism

A triangular tube – like a Toblerone box. Find the triangle's area (½ × base × height), then multiply by the prism length. The cross-section stays constant throughout.

Hemisphere

Half a sphere – like a dome or a bowl. Volume is exactly half of a full sphere: (2/3)πr³. A hemisphere with radius 5 holds about 262 cubic units.

Real-World Volume Calculations

Fish tank capacity
Rectangular tank: 24" × 12" × 16" = 4,608 cubic inches. Divide by 231 to get gallons: about 20 gallons of water.
Concrete for a column
Cylindrical column, radius 0.3m, height 3m. Volume = π × 0.09 × 3 ≈ 0.85 cubic meters of concrete per column.
Storage tank volume
Spherical tank, radius 2 meters. Volume = (4/3)π × 8 ≈ 33.5 cubic meters. At 1000 L per m³, that's 33,500 liters.
Ice cream cone
Cone with radius 3 cm, height 12 cm. Volume = (1/3)π × 9 × 12 ≈ 113 cubic centimeters (about 113 ml of ice cream).
Moving box capacity
Cube box, 18-inch sides. Volume = 18³ = 5,832 cubic inches. Divide by 1,728 for cubic feet: about 3.4 cubic feet.

Frequently Asked Questions

What units should I use for volume?

Use consistent linear units for all dimensions. If you enter centimeters, volume will be in cubic centimeters (cm³). Convert to liters (1000 cm³ = 1 L) or other units as needed.

Why does the cone formula have 1/3?

A cone occupies exactly one-third the volume of a cylinder with the same base and height. This was proven by Archimedes. You can verify it experimentally by filling a cone with water and pouring it into a matching cylinder – it takes exactly three cones to fill the cylinder.

How do I convert volume to capacity?

For liquids: 1 cubic centimeter = 1 milliliter, 1000 cm³ = 1 liter. For gallons: 1 cubic inch ≈ 0.00433 gallons, or 231 cubic inches = 1 US gallon. For cubic feet: 1 ft³ ≈ 7.48 gallons.

Can I find volume from surface area?

For a cube, yes – take the square root of (surface area ÷ 6) to get the side, then cube it. For other shapes, you need more information. Different shapes can have the same surface area but different volumes.

What's the difference between volume and capacity?

Volume measures the space an object occupies. Capacity measures how much a container can hold. A thick-walled box has a certain volume (including the walls) but a smaller capacity (the empty space inside).

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