Volume Calculator
Calculate the volume of any common 3D shape instantly. Select a shape, enter its dimensions, and get accurate results in cubic units for cubes, cylinders, spheres, cones, pyramids, and more.
Volume Calculator
Inputs
Select a shape and enter its dimensions to calculate the volume.
Understanding Volume of 3D Shapes
Volume is the measure of how much three-dimensional space an object occupies. While area deals with flat, two-dimensional surfaces measured in square units, volume extends into the third dimension and is expressed in cubic units such as cubic centimeters (cm³), cubic meters (m³), or liters. Understanding volume is essential in fields ranging from civil engineering and manufacturing to cooking and medicine, anywhere you need to know how much space something takes up or how much a container can hold.
Volume of a Cube
A cube is the simplest 3D shape to calculate. Since all six faces are identical squares with side length s, the volume is V = s³. For example, a cube with a 5 cm edge has a volume of 125 cm³. The cube is the standard unit of volumetric measurement, which is why we call our units "cubic."
Volume of a Rectangular Prism
A rectangular prism (also called a cuboid or box) has three different dimensions: length, width, and height. Its volume is simply V = l × w × h. This is the formula you use for shipping boxes, rooms, swimming pools, and aquariums. When all three dimensions are equal, the rectangular prism becomes a cube.
Volume of a Cylinder
A cylinder is essentially a stack of circles. Its volume equals the area of the circular base multiplied by the height: V = πr²h, where r is the radius and h is the height. Cylinders appear everywhere in daily life: canned goods, pipes, water tanks, and silos. When calculating volume for a pipe, you may need to find the volume of an outer cylinder minus an inner cylinder to get the volume of the material.
Volume of a Sphere
The sphere formula V = 4/3 × πr³ gives the volume of a perfectly round ball. Archimedes discovered that a sphere's volume is exactly two-thirds the volume of its circumscribing cylinder. This relationship explains why the formula has the 4/3 factor. Spheres are found in nature (planets, bubbles, oranges) and in engineering (ball bearings, pressure vessels, fuel tanks) because they enclose the maximum volume for a given surface area.
Volume of a Cone and Pyramid
Both cones and pyramids share the same structural principle: they taper from a base to a single point (apex). Their volume formula follows the same pattern: V = 1/3 × B × h, where B is the base area and h is the perpendicular height. For a cone with a circular base, B = πr², giving V = 1/3 × πr² × h. For a pyramid with a rectangular base, B = l × w. The 1/3 factor means that a cone holds exactly one-third the volume of a cylinder with the same base and height.
The Displacement Method
For irregular objects that do not conform to a standard geometric shape, the displacement method provides an accurate volume measurement. Submerge the object in a known volume of liquid and measure how much the liquid level rises. The volume of displaced liquid equals the volume of the object. This technique, attributed to Archimedes, remains widely used in laboratories and manufacturing quality control.
Volume Formula Reference Table
Quick-reference volume formulas for common 3D shapes used in geometry, physics, and engineering.
| Shape | Formula | Variables |
|---|---|---|
| Cube | V = s³ | s = side length |
| Rectangular Prism | V = l × w × h | l = length, w = width, h = height |
| Cylinder | V = πr²h | r = radius, h = height |
| Sphere | V = 4/3 × πr³ | r = radius |
| Cone | V = 1/3 × πr²h | r = base radius, h = height |
| Pyramid (rectangular) | V = 1/3 × l × w × h | l = base length, w = base width, h = height |
| Hemisphere | V = 2/3 × πr³ | r = radius |
| Ellipsoid | V = 4/3 × πabc | a, b, c = semi-axes |
Step-by-Step Volume Examples
Practice computing volumes with these three real-world examples covering a rectangular pool, a cylindrical tank, and a sphere.
Example 1: Rectangular Swimming Pool
A swimming pool is 25 m long, 10 m wide, and 2 m deep. How many liters of water does it hold?
- Step 1: Identify dimensions: l = 25 m, w = 10 m, h = 2 m
- Step 2: Apply the rectangular prism formula: V = l × w × h = 25 × 10 × 2 = 500 m³
- Step 3: Convert to liters: 1 m³ = 1,000 liters, so 500 × 1,000 = 500,000 liters
Volume = 500 m³ = 500,000 liters
Example 2: Cylindrical Water Tank
A cylindrical tank has a radius of 3 m and a height of 5 m. Find its volume.
- Step 1: Identify values: r = 3 m, h = 5 m
- Step 2: Apply the cylinder formula: V = πr²h = π × 3² × 5 = π × 9 × 5 = 45π
- Step 3: Calculate: 45 × 3.14159 ≈ 141.37 m³
- Step 4: Convert to liters: 141.37 × 1,000 ≈ 141,372 liters
Volume ≈ 141.37 m³ ≈ 141,372 liters
Example 3: Sphere (Basketball)
A regulation basketball has a diameter of 24 cm. What is its volume?
- Step 1: Find the radius: r = diameter / 2 = 24 / 2 = 12 cm
- Step 2: Apply the sphere formula: V = 4/3 × π × r³ = 4/3 × π × 12³
- Step 3: Calculate r³: 12³ = 1,728
- Step 4: Multiply: V = 4/3 × 3.14159 × 1,728 = 4.18879 × 1,728 ≈ 7,238.23 cm³
Volume ≈ 7,238.23 cm³ (about 7.24 liters)
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