Pyramid Volume Calculator

Pyramids have fascinated humans since always: learn how to calculate the volume of a pyramid with our tool.

Here you will learn:

• What is a pyramid, and their elements;
• How to calculate the volume of a pyramid;
• The general formula for the volume of a pyramid.

And much more. Insert the data; we'll give you the result in a second!

A pyramid is a 3D solid composed by:

• A polygonal base, with
  • $n$ sides; and
  • $n$ angles.
• $n$ lateral faces.

The sides of the lateral oblique faces connect at the apex of the pyramid.

We can identify different types of pyramids:#

• Regular pyramids: the base is a regular polygon;
• Irregular pyramids: the base is any polygon;
• Oblique pyramids: the apex doesn't lie above the centroid of the base;
• Right pyramid: the apex is exactly above the centroid of the base.

A pyramid with an infinite number of sides is a cone. You can learn how to calculate the volume of a cone, and see the difference between these calculations and the one for a pyramid.

To find the volume of a pyramid. one formula fits all:

Where:

• $V$ is the volume;
• $B$ is the area of the base; and
• $h$ is the height of the pyramid.

This formula for the pyramid volume is valid for every right and oblique pyramid. This is how to calculate the volume of a pyramid.

Only for regular pyramids you can find the volume without knowing the surface area: it's enough to know the value of the base's side.

Where:

• $n$ is the number of the sides of the bases; and
• $a$ is the side's length.

Let's look in detail at the case of a pyramid with a square base.

The formula for the volume of the pyramid is:

$a$ is the side of the base; thus, $a^2$ is the area of the base.

This formula for the volume of a pyramid with a square base is equivalent to the more complex expression:

Since $\cot{\left(\tfrac{\pi}{4}\right)}=1$, you can see how this expression simplifies to the first one.

For example. define the lengths of sides and height:

• $a=4\ \text{cm}$; and
• $h=12\ \text{cm}$.

Calculate the area of the base:

Now calculate the volume of this pyramid with a square base:

Use our tool to calculate the volume of a regular pyramid, and not only!

Choose the base type. It can be either:

• Regular-base area;
• Irregular-base area; and
• Known base area.

This choice will change the calculator's behavior: insert the values you know: we will calculate everything else!

If you click on advanced mode, you'll see more parameters of the pyramids you are interested in:

• Slanted height (we calculate it with the Pythagorean theorem);
• Lateral edge length; and
• Surface area.