Calculate volume for common 3D shapes.
The Volume Calculator is a comprehensive geometric tool designed to calculate the volume of various three-dimensional shapes. Volume represents the amount of three-dimensional space enclosed by a closed surface, measured in cubic units (such as cubic meters, cubic feet, or liters). The shapes supported include cubes, rectangular prisms, cylinders, spheres, cones, and pyramids.
Each shape has a specific mathematical formula for volume: - **Cube:** V = s³ (side length cubed) - **Rectangular Prism:** V = l × w × h (length × width × height) - **Cylinder:** V = πr²h (base area × height) - **Sphere:** V = (4/3)πr³ (four-thirds pi × radius cubed) - **Cone:** V = (1/3)πr²h (one-third cylinder volume) - **Pyramid:** V = (1/3) × base_area × height
Volume calculations are critical in shipping and logistics (determining cargo space), civil engineering (estimating concrete or soil requirements), packaging design, and manufacturing. In chemistry, volume determines container capacity and dilution ratios. The volume calculator automates these different formulas, providing instant conversions between cubic measurements and liquid capacities, ensuring accuracy in academic homework and professional project planning.
Understanding Volume
Volume measures the three-dimensional space occupied by a solid object.
How it Works & Formula
Unified volume calculations for cubes, spheres, cylinders, and cones.
Practical Examples
Cylinder tank with r=2m, h=5m has volume = π × 2² × 5 ≈ 62.83 m³ (62,830 liters).
Frequently Asked Questions
Volume is expressed in cubic units, such as cubic meters (m³), cubic centimeters (cm³), liters, or gallons.
1 cubic meter (m³) = 1,000 liters. To convert liters to m³, divide by 1,000. To convert m³ to liters, multiply by 1,000.
Volume is the total 3D space occupied by an object. Capacity refers to how much a container can hold (its interior volume). For a solid object, they are the same.
One practical method is water displacement: submerge the object in water and measure how much the water level rises. The displaced volume equals the object's volume.
Volume = Length × Width × Height. For example, a box measuring 4m × 3m × 2m has a volume of 24 cubic meters.