# 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!

## What is a pyramid?

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.

## How to find the volume of 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.

🙋 Alternatively, you can find the area of the base with our area of regular polygon calculator.

## How to calculate the volume of a pyramid with a square base

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:

## How to use our pyramid volume calculator

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!

🙋 Our calculators work in **reverse**, too: you can find the height or the base area if you know the volume.

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.

The volume formula works for both right and oblique pyramids.

**Advanced mode**to show slant height, lateral edge length and surface area, for right pyramids.