Volume Calculator: Find the Volume of 3D Shapes

Volume measures the three-dimensional space occupied by an object. Whether you need the volume of a box for shipping, a cylinder for a water tank, or a sphere for a ball, our Volume Calculator handles all common 3D shapes. Enter the required dimensions and get the volume in your choice of cubic units, with visual representations and formulas displayed.

Volume Formulas for Common Shapes

Each 3D shape has a specific formula. A rectangular prism (box) is length × width × height. A cylinder is π × r² × h. A sphere is 4/3 × π × r³. A cone is 1/3 × π × r² × h. A pyramid is 1/3 × base area × height. The calculator supports all these and more: cube, rectangular prism, sphere, cylinder, cone, pyramid, torus, ellipsoid, and triangular prism.

For irregularly shaped objects, you can use the water displacement method in a graduated cylinder, but for regular shapes, these formulas provide exact volumes.

Using the Volume Calculator

Select the shape from the dropdown menu. Enter the required dimensions — for a box, enter length, width, and height; for a cylinder, enter radius and height; for a sphere, enter radius. Choose your unit of measurement (inches, feet, centimeters, meters, etc.). The calculator shows the volume in cubic units and provides a cross-sectional view of the shape.

You can convert between different cubic units (cubic inches to cubic feet, cubic meters to liters, etc.) and calculate the liquid capacity of containers in gallons or liters.

Practical Applications

Shipping and Logistics

Calculate the volume of packages to determine shipping class and costs. Dimensional weight pricing means larger-volume packages may be charged based on volume rather than actual weight.

Aquariums and Pools

A rectangular aquarium measuring 48 × 18 × 20 inches has a volume of 48 × 18 × 20 = 17,280 cubic inches. Convert to gallons: 17,280 / 231 = 74.8 gallons. This tells you how much water and what size filter and heater you need.

Construction

A concrete slab measuring 10 × 12 × 0.5 feet (6 inches thick) needs 10 × 12 × 0.5 = 60 cubic feet. Convert to cubic yards: 60 / 27 = 2.22 cubic yards. Concrete is typically ordered by the cubic yard.

Unit Conversion Reference

• Cubic inches to cubic feet: Divide by 1,728
• Cubic feet to cubic yards: Divide by 27
• Cubic inches to gallons: Divide by 231
• Cubic feet to gallons: Multiply by 7.481
• Liters to gallons: Divide by 3.785
• Cubic meters to liters: Multiply by 1,000
• Cubic centimeters to milliliters: 1 cm³ = 1 mL

Real-World Example

You need a cylindrical water tank with a 3-foot radius that holds at least 500 gallons of water:

• Target volume in cubic feet: 500 gallons / 7.481 = 66.83 cubic feet
• Volume formula: V = π × r² × h, so h = V / (π × r²)
• Required height: h = 66.83 / (π × 9) = 66.83 / 28.27 = 2.36 feet
• Check: π × 9 × 2.36 = 66.8 cubic feet = 499.6 gallons

A spherical ball with radius 6 inches has volume: 4/3 × π × 6³ = 4/3 × π × 216 = 904.78 cubic inches = 0.524 cubic feet.

Start Calculating

Use our Volume Calculator below to find the volume of any 3D shape for construction, shipping, or science projects. Also check our Area Calculator for 2D measurements and our Concrete Calculator for construction material estimates.