Volume Calculator

Cone
  • Cone
  • Cube
  • Cuboid/Rect. Prism
  • Cylinder
  • Sphere
Radius & Height
  • Radius & Height
  • Radius & Slant Height
  • Height & Slant Height
  • Base Area & Height

Radius =

Height =

volume illustration

Hello there!

Please provide your input and click the calculate button
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About the Volume Calculator

This volume calculator lets you calculate the volume for several different solid shapes. The shapes currently supported are cones, cubes, cuboids (rectangular prisms), cylinders, and spheres.

For most shapes, you have the option to choose what combination of inputs you want to provide. And to top it all, the calculator will give you not just the answer, but also the step by step solution.

Usage Guide

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i. Valid Inputs

Each of the inputs provided must be a non-negative real number. In other words, the input must be 0 or greater. Here are a few examples.

  • Whole numbers or decimals → 2\hspace{0.2em} 2 \hspace{0.2em}, 4.25\hspace{0.2em} 4.25 \hspace{0.2em}, 0\hspace{0.2em} 0 \hspace{0.2em}, 0.33\hspace{0.2em} 0.33 \hspace{0.2em}
  • Fractions → 2/3\hspace{0.2em} 2/3 \hspace{0.2em}, 1/5\hspace{0.2em} 1/5 \hspace{0.2em}
  • Mixed numbers → 51/4\hspace{0.2em} 5 \hspace{0.4em} 1/4 \hspace{0.2em}

ii. Example

If you would like to see an example of the calculator's working, just click the "example" button.

iii. Solutions

As mentioned earlier, the calculator won't just tell you the answer but also the steps you can follow to do the calculation yourself. The "show/hide solution" button would be available to you after the calculator has processed your input.

iv. Share

We would love to see you share our calculators with your family, friends, or anyone else who might find it useful.

By checking the "include calculation" checkbox, you can share your calculation as well.

Here's a quick overview of the concept of volume and its formula for a few important shapes.

Volume — Concept and Formulas

The volume of any three-dimensional or solid figure is a the amount of space it occupies.

Let's look at the formulas for the volumes of the some of the most common solid shapes.

Volume of a Cone

A labeled right circular cone
A right circular cone

The volume of a cone with a radius r\hspace{0.2em} r \hspace{0.2em} and height h\hspace{0.2em} h \hspace{0.2em} is given by,

V=13πr2hV \hspace {0.25em} = \hspace {0.25em} \frac{1}{3} \pi r^2 h

Volume of a Cube

A cube with an edge length of a
A cube

For a cube with an edge-length of a\hspace{0.2em} a \hspace{0.2em}, the volume would be,

V=a3V \hspace{0.25em} = \hspace{0.25em} a^3

Volume of a Cuboid (Rectangular Prism)

A cuboid with an length of l, breadth b, and height h
A cuboid/rectangular prism

The formula for the volume of a cuboid (or rectangular prism) with a length l\hspace{0.2em} l \hspace{0.2em}, width w\hspace{0.2em} w \hspace{0.2em}, height h\hspace{0.2em} h \hspace{0.2em} is

V=l⋅w⋅hV \hspace{0.25em} = \hspace{0.25em} l \cdot w \cdot h

Volume of a Cylinder

A labeled right circular cylinder
A right circular cylinder

The volume of a cylinder with a radius r\hspace{0.2em} r \hspace{0.2em} and height h\hspace{0.2em} h \hspace{0.2em} is

V=πr2hV \hspace{0.25em} = \hspace{0.25em} \pi r^2 h

Volume of a Sphere

A labeled sphere
A sphere

The sphere of radius r\hspace{0.2em} r \hspace{0.2em} has a volume equal to

V=43πr3V \hspace{0.25em} = \hspace{0.25em} \frac{4}{3} \pi r^3

Volume Calculations — Examples

Example

A rectangular prism has dimensions of length 10\hspace{0.2em} 10 \hspace{0.2em} meters, width 4\hspace{0.2em} 4 \hspace{0.2em} meters, and height 6\hspace{0.2em} 6 \hspace{0.2em} meters. Calculate its volume.

Solution

The formula for the volume of a rectangular prism is

V=l⋅w⋅hV \hspace{0.25em} = \hspace{0.25em} l \cdot w \cdot h

Substituting the values, we get —

V=10⋅4⋅6=240\begin{align*} V \hspace{0.25em} &= \hspace{0.25em} 10 \cdot 4 \cdot 6 \\[1em] &= \hspace{0.25em} 240 \end{align*}

So, the volume of the rectangular prism is 240 m3\hspace{0.2em} 240 \text{ m}^3 \hspace{0.2em}.

Example

Calculate the volume of a cone with a radius of 5 in\hspace{0.2em} 5 \text{ in} \hspace{0.2em} and a height of 8 in\hspace{0.2em} 8 \text{ in} \hspace{0.2em}.

Solution

Using the formula for a cone's volume,

V=13πr2h=13π⋅62⋅8=301.59\begin{align*} V \hspace {0.25em} &= \hspace {0.25em} \frac{1}{3} \pi r^2 h \\[1.75em] &= \hspace {0.25em} \frac{1}{3} \pi \cdot 6^2 \cdot 8 \\[1.75em] &= \hspace {0.25em} 301.59 \end{align*}

The volume of the cone is 301.59 cu. in\hspace{0.2em} 301.59 \text{ cu. in} \hspace{0.2em}.

Example

If a cube has a volume of 125 cubic inches, what is the length of each edge?

Solution

We know the volume of a cube is given by the formula,

V=a3V \hspace{0.25em} = \hspace{0.25em} a^3

We can rearrange it to make a\hspace{0.2em} a \hspace{0.2em} the subject of the formula. That would give us,

a=V3a \hspace{0.25em} = \hspace{0.25em} \sqrt[3]{V}

And now, substituting the value of V\hspace{0.2em} V \hspace{0.2em}, we get

a=1253=5\begin{align*} a \hspace{0.25em} &= \hspace{0.25em} \sqrt[3]{125} \\[1em] &= \hspace{0.25em} 5 \end{align*}

Each of the cube's edges has a length of 5 in\hspace{0.2em} 5 \text{ in} \hspace{0.2em}.

Example

Find the volume of a sphere with a radius of 3.25\hspace{0.2em} 3.25 \hspace{0.2em} centimeters.

Solution

We saw earlier that a sphere's volume is given by the formula —

V=43πr3V \hspace{0.25em} = \hspace{0.25em} \frac{4}{3} \pi r^3

Substituting the value of r\hspace{0.2em} r \hspace{0.2em}, we have

V=43π⋅3.253=34.33\begin{align*} V \hspace{0.25em} &= \hspace{0.25em} \frac{4}{3} \pi \cdot 3.25^3 \\[1.75em] &= \hspace{0.25em} 34.33 \end{align*}

So, the volume of the sphere is 143.79 cm3\hspace{0.2em} 143.79 \text{ cm}^3 \hspace{0.2em}.

Example

A 10\hspace{0.2em} 10 \hspace{0.2em} centimetres high cylindrical tank has a volume of 40π cm3\hspace{0.2em} 40 \pi \text{ cm}^3 \hspace{0.2em}. Calculate the volume of the tank.

Solution

The formula for a cylinder's volume is

V=πr2hV \hspace{0.25em} = \hspace{0.25em} \pi r^2 h

Rarranging the formula to make r\hspace{0.2em} r \hspace{0.2em} its subject, we have

r=Vπh=40ππ10=2\begin{align*} r \hspace{0.25em} &= \hspace{0.25em} \sqrt{\frac{V}{\pi h}} \\[1.75em] &= \hspace{0.25em} \sqrt{\frac{40 \pi}{\pi 10}} \\[1.75em] &= \hspace{0.25em} 2 \end{align*}

The cylinder's radius is 2 cm\hspace{0.2em} 2 \text{ cm} \hspace{0.2em}

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