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Calculate the volume of common three-dimensional shapes like cubes, cylinders, and spheres.
125.0000
cubic units
Everything you need to know
Volume measures the three-dimensional space occupied by an object or enclosed within a container. From determining how much water your swimming pool holds to calculating the capacity of a shipping box, volume calculations are essential in construction, manufacturing, logistics, cooking, science, and everyday life.
Our volume calculator computes the capacity of the most common geometric shapes: cubes, rectangular prisms, cylinders, spheres, cones, and pyramids. Each calculation includes the formula, a detailed example, and practical applications to help you understand both the math and its real-world relevance.
Concrete pours, water tanks, swimming pools, and excavation projects all require precise volume calculations to determine material quantities and costs.
Freight companies calculate the volume of packages and containers to determine shipping costs, load capacity, and storage requirements. Dimensional weight pricing means volume directly impacts shipping rates.
Product designers calculate volumes to determine material needs, weight estimates, and fluid capacities for everything from water bottles to fuel tanks.
Recipe scaling requires volume conversions between cups, tablespoons, milliliters, and liters to ensure consistent results.
Chemists measure reactant volumes, pharmacists calculate medication dosages by volume, and biologists measure cell cultures in volumetric units.
A cube has six equal square faces. All sides are the same length.
Formula: Volume = Side³ = s × s × s
Example: A cubic storage container measures 4 feet on each side. Volume = 4 × 4 × 4 = 64 cubic feet
A rectangular prism has six rectangular faces. This is the most common shape for boxes, rooms, and tanks.
Formula: Volume = Length × Width × Height
Example: An aquarium measures 48 inches long, 18 inches wide, and 20 inches tall. Volume = 48 × 18 × 20 = 17,280 cubic inches Convert to gallons: 17,280 ÷ 231 = 74.8 gallons
A cylinder has two parallel circular bases connected by a curved surface.
Formula: Volume = π × Radius² × Height
Example: A water tank has a diameter of 6 feet (radius = 3 feet) and stands 8 feet tall. Volume = 3.14159 × 3² × 8 = 3.14159 × 9 × 8 = 226.2 cubic feet Convert to gallons: 226.2 × 7.48 = 1,692 gallons
A sphere is a perfectly round three-dimensional object where every point on the surface is equidistant from the center.
Formula: Volume = (4/3) × π × Radius³
Example: A spherical gas storage tank has a diameter of 30 feet (radius = 15 feet). Volume = (4/3) × 3.14159 × 15³ = 1.333 × 3.14159 × 3,375 = 14,137 cubic feet
A cone has a circular base and tapers to a single point called the apex.
Formula: Volume = (1/3) × π × Radius² × Height
Example: A conical pile of gravel has a base diameter of 10 feet (radius = 5 feet) and a height of 6 feet. Volume = (1/3) × 3.14159 × 5² × 6 = 0.333 × 3.14159 × 25 × 6 = 157.1 cubic feet
A pyramid has a polygonal base and triangular faces that meet at an apex.
Formula: Volume = (1/3) × Base Area × Height
Example: A square pyramid-shaped roof has a base of 20 feet × 20 feet and a height of 12 feet. Volume = (1/3) × (20 × 20) × 12 = 0.333 × 400 × 12 = 1,600 cubic feet
| Unit | Used For | Equivalent |
|---|---|---|
| Cubic inch (in³) | Small containers, engine displacement | 1/1,728 cu ft |
| Cubic foot (ft³) | Construction, large containers | 1,728 cu in |
| Cubic yard (yd³) | Concrete, excavation, landscaping | 27 cu ft |
| Cubic meter (m³) | International standard | 35.315 cu ft |
| Liter (L) | Beverages, automotive fluids | 1,000 mL |
| Milliliter (mL) | Medicine, cooking | 1 cm³ |
| Gallon (US) | Fuel, water, paint | 3.785 L |
| Quart (US) | Cooking, motor oil | 0.946 L |
| Pint (US) | Beverages, dairy | 0.473 L |
| Cup (US) | Cooking | 236.6 mL |
| Fluid ounce (US) | Cooking, cosmetics | 29.57 mL |
| Tablespoon | Cooking | 14.79 mL |
| Teaspoon | Cooking | 4.93 mL |
Pool dimensions: 30 feet long × 15 feet wide × 5 feet average depth Volume: 30 × 15 × 5 = 2,250 cubic feet Gallons: 2,250 × 7.48 = 16,830 gallons Chemical dosing: Knowing your exact gallonage ensures proper chlorine and pH balance
Slab dimensions: 20 feet × 15 feet × 0.5 feet (6 inches) thick Volume: 20 × 15 × 0.5 = 150 cubic feet Cubic yards: 150 ÷ 27 = 5.56 cubic yards With 10% waste: 5.56 × 1.10 = 6.1 cubic yards
Box dimensions: 24 inches × 18 inches × 18 inches Volume: 24 × 18 × 18 = 7,776 cubic inches Cubic feet: 7,776 ÷ 1,728 = 4.5 cubic feet
Standard barrel: 42 US gallons Cubic feet: 42 ÷ 7.48 = 5.61 cubic feet Liters: 42 × 3.785 = 158.99 liters
Internal dimensions: 19'4" × 7'8" × 7'10" Volume: ~19.33 × 7.67 × 7.83 = 1,161 cubic feet Cubic meters: ~32.9 m³
For objects that do not match standard geometric shapes:
Submerge the object in water and measure the volume of water displaced. The displaced volume equals the object's volume. This is how Archimedes reportedly discovered his famous principle.
Break complex shapes into simpler geometric components, calculate each volume, and add them together.
Example: An L-shaped tank can be divided into two rectangular prisms.
For highly irregular shapes, approximate using the closest standard shape and adjust based on visual estimation.
When calculating cylinders, spheres, and cones, the formula uses radius (half the diameter), not diameter. Using diameter instead of radius will overestimate volume by a factor of four.
Never multiply feet by inches. Convert all measurements to the same unit before calculating volume.
For spheres, remember to cube the radius (multiply it by itself three times), not just triple it. r³ is very different from 3r.
Volume measures the space inside a shape in cubic units. Surface area measures the total exterior area in square units. These are fundamentally different calculations.
When calculating the usable volume of a tank with internal structures (pipes, baffles, shelves), subtract the volume occupied by those structures.
Volume measures the total space an object occupies. Capacity measures how much fluid a container can hold. For hollow containers, the terms are often used interchangeably.
Measure length, width, and height, then multiply: Volume = Length × Width × Height. This gives you the cubic footage of the room.
No. Volume always represents a physical amount of space and must be a positive value.
Calculate the volume of the cylinder using the inner radius: Volume = π × (inner radius)² × length. Do not use the outer diameter unless you want the volume of the pipe material itself.
The Earth is approximately a sphere with a radius of 3,959 miles. Its volume is about 259 trillion cubic miles or 1.08 × 10²¹ cubic meters.
Calculate area of various 2D shapes.
Surface area of sphere, cube, cylinder, cone.
Calculate circle area, circumference, radius.
Solve for missing sides and angles of a triangle.