Volume Calculator
Volume Calculator
About Volume Calculator
Understanding Volume
Volume measures the amount of three-dimensional space occupied by an object, expressed in cubic units. It answers the question: how much space does this object take up, or how much can it hold? Volume calculations are critical in construction (concrete needed), shipping (container capacity), cooking (recipe measurements), manufacturing (material requirements), and science (liquid volumes, gas expansion). Every 3D shape has a specific volume formula that relates its dimensions to the space it encloses.
Common Volume Formulas
Cube: V = side^3. Rectangular Prism: V = length x width x height. Cylinder: V = pi x r^2 x height. Sphere: V = (4/3) x pi x r^3. Cone: V = (1/3) x pi x r^2 x height. Pyramid: V = (1/3) x base area x height. Notice that cones and pyramids are exactly one-third the volume of their corresponding cylinder or prism with the same base and height.
How to Use This Calculator
Select the 3D shape from the dropdown menu. Enter the required dimensions for that shape. Click Calculate to see the volume in your chosen unit, plus conversions to other common volume units (liters, gallons, cubic feet). The calculator also shows the surface area as a bonus calculation.
Frequently Asked Questions
What is the difference between volume and capacity?
Volume measures the space an object occupies. Capacity measures how much a container can hold. They are related: 1 liter = 1000 cubic centimeters. Capacity typically uses liters/gallons while volume uses cubic units.
How do I convert between cubic units?
Cube the linear conversion factor. Since 1 foot = 12 inches, then 1 cubic foot = 12^3 = 1,728 cubic inches. Since 1 meter = 100 cm, 1 cubic meter = 1,000,000 cubic centimeters.
Why is a cone one-third of a cylinder?
This can be proven through calculus (integration) or demonstrated experimentally by filling a cone with water and pouring it into a cylinder of the same base and height. It takes exactly three cone-fulls to fill the cylinder.
