Volume Calculator

Volume Formulas Reference

If you need to calculate volume by hand, here are the formulas for the most common 3D geometric shapes:

Specific Shape Calculators

If you need a dedicated calculator for a specific shape, check out our specialized tools:

What is Volume?

Volume is the quantity of three-dimensional space enclosed by a closed surface. It determines how much capacity an object has. For example, the volume of a cup tells you how much liquid it can hold, while the volume of a concrete block helps builders know how much space it will occupy in a wall.

In mathematics and physics, volume is a scalar quantity, usually denoted by V. It is derived from length (width, height, and depth) and is expressed in cubic units.

Common Units of Volume

The unit you use for volume depends on the system of measurement:

• SI (Metric) System: The standard unit is the cubic meter ($m^3$). For smaller quantities, cubic centimeters ($cm^3$) or liters (L) are commonly used (1 Liter = 1000 $cm^3$).
• Imperial / US Customary System: Common units include cubic feet ($ft^3$), cubic inches ($in^3$), gallons, and fluid ounces.

Real-World Applications

Understanding how to calculate volume is crucial in many industries and daily activities:

1. Construction & Engineering: Calculating the volume of concrete needed for a foundation, the amount of soil to assume for excavation, or the capacity of HVAC systems to heat a room properly.
2. Shipping & Logistics: Warehouses need to know the volume of packages to optimize storage space and shipping costs (often using “volumetric weight”).
3. Manufacturing: Designing containers (bottles, cans, boxes) requires precise volume calculations to ensure they hold the correct amount of product while minimizing material usage.
4. Science & Medicine: Measuring the volume of liquids in chemistry labs or calculating the volume of organs or tumors in medical imaging.
5. Swimming Pools: Pool owners need to calculate volume to know how much water is needed and correctly dose chemicals like chlorine.

How to Calculate Volume for Any Shape

While every shape has its own specific formula, there is a general rule for many common objects (like prisms and cylinders):

For example, a cylinder is just a circle extruded upwards. So, you calculate the area of the circular base ($\pi r^2$) and multiply it by the height ($h$). A cube is a square base ($s^2$) multiplied by height ($s$), giving $s^3$.

Shapes that taper to a point, like cones and pyramids, typically follow the rule of “one-third the volume of a prism with the same base and height”: $V = \frac{1}{3} \times Base \times Height$.