How to Calculate Volume: Box, Cylinder, Cone, Sphere and Cube

 

To calculate volume, identify the three-dimensional solid and measure the dimensions required by its formula. A box, cylinder, cone and sphere do not use the same inputs. Use one consistent length unit throughout the calculation, and remember that volume is expressed in cubic units rather than square units.

The Volume Calculator supports rectangular prisms, cubes, cylinders, complete cones and spheres. It also converts the result to cubic feet, cubic yards, cubic meters and liters. The result describes an ideal geometric solid, not a guaranteed material order or a measured container capacity.

Calculate a box or rectangular prism

A rectangular prism, also called a cuboid or box, has volume = length x width x height. The dimensions are perpendicular to one another. A box measuring 12 ft long, 10 ft wide and 0.5 ft high has volume 12 x 10 x 0.5 = 60 cubic feet.

If the depth is given as 6 inches, convert it to 0.5 feet before multiplying by dimensions in feet. Multiplying 12 x 10 x 6 without converting mixes units and makes the result twelve times too large.

Use one edge length for a cube

A cube has equal length, width and height, so volume = side cubed. With an edge length of 3 ft, its volume is 3 x 3 x 3 = 27 cubic feet. That equals one cubic yard, because a yard is three feet along each of three dimensions.

A cube's volume is not its total surface area. Surface area measures the outside faces in square units; volume measures the three-dimensional region enclosed by those faces.

Calculate a cylinder from radius and height

Cylinder volume = pi x radius squared x perpendicular height. The circular base area is pi x radius squared; multiplying by height extends that area through the solid. A radius of 2 ft and height of 5 ft give 20 x pi, or approximately 62.831853 cubic feet.

The radius is half the diameter. If you measure a diameter of 4 ft, enter Radius 2. For an internal capacity estimate, use internal dimensions and usable height. External dimensions include wall thickness and may overstate the usable space.

Calculate the volume of a cone

A complete cone has one third the volume of a cylinder with the same base radius and perpendicular height. Its formula is volume = pi x radius squared x height / 3. With a radius of 3 ft and height of 4 ft, the result is 12 x pi, or approximately 37.699112 cubic feet.

Use perpendicular height from the base plane to the apex, not the slant length along the side. A truncated cone, or frustum, requires a different formula using two radii. This tool's cone mode does not calculate that shape or the volume of a hollow shell.

Calculate sphere volume

Sphere volume = 4 / 3 x pi x radius cubed. A sphere with radius 3 ft has volume 36 x pi, or approximately 113.097336 cubic feet. A diameter of 6 ft corresponds to that same radius.

Entering a diameter as a radius makes a sphere's calculated volume eight times too large. A hemisphere is half a sphere, but the sphere mode returns the complete sphere's volume.

Convert cubic units and liters

One foot equals exactly 0.3048 meters, so one cubic foot equals 0.3048 cubed, or 0.028316846592 cubic meters. The 60-cubic-foot box is therefore 1.69901079552 cubic meters, displayed as 1.699011.

One cubic yard contains 27 cubic feet, and one cubic foot contains 1728 cubic inches. One cubic meter equals 1000 liters. These are volume conversions; a surface measurement in square feet needs a depth before it can become cubic feet or cubic yards.

Separate geometry from purchasing decisions

Irregular containers, partial fills, hollow shapes and sloped excavations may need several calculations or another model. For flat shapes, use the Area Calculator. Material density, compaction, waste and bag yield are separate inputs, so use supplier information before ordering. This calculator runs locally without saving or transmitting your measurements.