Volume Calculator

Volume calculator at a glance#

What is volume?#

Volume refers to the amount of space that a solid object occupies. It's measured in cubic units like cubic inches, cubic feet, or cubic centimeters. Think of a cubic inch as the space inside a cube with each edge being 1 inch long. If an object has a volume of 216 cubic inches, that means it could be filled with that many small cubes.

How do you calculate volume?#

To calculate volume, select the formula corresponding to the shape and substitute its measurements, ensuring all are in the same unit. For a box, use length × width × height. For a cylinder, use π × r² × h. For a sphere, use 4/3 × π × r³. In the calculator above, you select the shape and unit, input the dimensions, and it calculates the volume in cubic units based on your selected unit.

What is the volume of a box measuring 2 cm by 7 cm by 3 cm?#

The volume of this box is 42 cubic centimeters. You find this by multiplying the length, width, and height together: 2 × 7 × 3 = 42. This box can hold 42 milliliters since one cubic centimeter is equal to one milliliter.

What volume measures#

Imagine a cube-shaped box that is 6 inches on each side. Its bottom layer contains 6 rows of 6 one-inch cubes, totaling 36 cubes. By stacking 6 of those layers, the box becomes full, so it holds 216 cubes and its volume is 216 cubic inches. Every volume formula acts as a shortcut to this count, even for shapes with curved sides where real cubes wouldn't fit neatly.

OpenStax Prealgebra 2e explains volume in the same way, as the space inside a solid, counted in cubic units. Since it's a cubic measure, the unit is multiplied three times. Switching from inches to feet divides the number by 12 × 12 × 12 = 1,728, not by 12, making 216 cubic inches only 0.125 cubic feet.

Volume formulas for every shape in the calculator#

The calculator includes 11 different shapes. Each shape has a specific formula, but you always input lengths in one unit. The table lists all of these formulas, and the sections below break down the common ones using the same 6 inch example.

Cube and rectangular box#

A cube has equal edges, so V = a³. For a 6 inch cube, that calculates to 216 cubic inches. A rectangular box, referred to in the calculator as a rectangular tank, features three different edge lengths, so V = length × width × height. A shoebox that measures 13 inches in length, 8 inches in width, and 5 inches in height contains 520 cubic inches, which is approximately 8.5 liters.

Cylinder, cone and sphere#

Imagine fitting a can inside a 6 inch box so it touches all four sides and the lid. The can's radius would be 3 inches, and its height would be 6 inches, leading to a volume of π × 3² × 6 = 54π, or about 169.6 cubic inches. A cone with the same base and height would hold exactly a third of the can's volume, which is 18π, or about 56.5 cubic inches. A sphere measuring 6 inches in diameter has a radius of 3 inches and holds 4/3 × π × 3³ = 36π, approximately 113.1 cubic inches.

When a cone, sphere, and cylinder share the same width and height, they maintain a consistent volume ratio of 1 to 2 to 3. This ratio, dating back to Archimedes, serves as a quick verification: a sphere always contains two-thirds the volume of the cylinder it fits inside.

To find a missing radius or height from a known volume or side area, use the cylinder volume calculator.

Units and conversions#

The calculator uses a single unit for every input, providing the result in that unit cubed. If feet are chosen, the output is in cubic feet. Selecting centimeters gives cubic centimeters. Mixing units, such as using feet for length and inches for height, gives incorrect answers. So, ensure that everything is converted to one unit first. To switch between units, use the conversion factors provided below, sourced from NIST Handbook 44.

A cubic foot contains approximately 7.48 US gallons, with a US gallon precisely defined as 231 cubic inches. In metric terms, a liter is 1,000 cubic centimeters, making one cubic centimeter equal to one milliliter. For landscaping and concrete work, where materials are sold by the cubic yard, the cubic yards calculator takes every dimension in inches or centimeters and returns cubic yards directly.

Pool and tank volume in gallons#

When dealing with pool chemicals and estimating fills, you'll often work in gallons. The process typically involves calculating the volume in cubic feet and then converting it. Always measure the inside dimensions of the pool and use the water depth, not the wall height.

For a rectangular pool, select the rectangular tank shape and input measurements in feet. If the pool bottom slopes, take the average of the shallow and deep ends. Suppose a pool is 32 feet long and 16 feet wide, with a depth ranging from 3.5 feet at one end to 6.5 feet at the other end. The average depth is 5 feet, so you'd calculate:

• 32 × 16 × 5 = 2,560 cubic feet
• 2,560 × 7.4805 gives about 19,150 US gallons, which is approximately 72,500 liters

Sources#

• OpenStax, Prealgebra 2e, section 9.6: Solve Geometry Applications: Volume and Surface Area
• NIST Handbook 44 (2024), Appendix C: General Tables of Units of Measurement

Frequently asked questions#

How do you find the volume of a cube?#

To find the volume of a cube, cube the edge length, V = a³. For example, a cube with a side of 5 inches contains 5 × 5 × 5 = 125 cubic inches of space. Similarly, a cube measuring 10 centimeters on each side holds 1,000 cubic centimeters, which is exactly 1 liter.

How do you find the volume of a capsule?#

A capsule is shaped like a cylinder with a half ball on each end. The formula for its volume is V = 4/3 × π × r³ + π × r² × h, where h represents the length of the straight middle section only. If you have a capsule with a radius of 3 inches and a middle section of 6 inches, the volume calculates to 36π + 54π = 90π, which is about 282.7 cubic inches.

How do you find the volume of a spherical cap?#

A spherical cap is the segment cut off a ball by a flat plane. Its volume is found using V = π × h² × (3R − h) ÷ 3, where R is the radius of the ball and h is the height of the cap. Input any two of the base radius, ball radius, and height, and the calculator fills in what it needs before calculating the volume.

How do you find the volume of an irregular object?#

To find the volume of an irregular object, use the displacement method. Start by filling a measuring jug with water, noting the initial water level marked in milliliters. When you submerge the object, record the new water level. The increase in milliliters directly corresponds to the object's volume in cubic centimeters. If the object can be broken down into simple shapes, like a box topped with a half cylinder, calculate each part's volume and sum them.

What units does the volume calculator use?#

The volume calculator supports a wide range of units: inches, feet, yards, miles, millimeters, centimeters, meters, kilometers, micrometers, nanometers, and angstroms. You select the unit for your input, and the calculator will provide the result in the same unit cubed.