# Pyramid Volume Calculator

Created by Hanna Pamuła, PhD and Steven Wooding
Reviewed by Bogna Szyk, Jack Bowater and Adena Benn
Last updated: Jan 10, 2023

Determine the volume of any pyramid-like solid with our pyramid volume calculator. Choose between two options: calculate the volume of a pyramid with a regular base, so you need to have only the side, shape, and height given, or directly enter the base area and the pyramid height. The calculator doesn't have any problems with determining the tetrahedron volume or the volume of a square pyramid. If you are still not sure how to use the tool or how to calculate the pyramid volume – keep reading!

## Pyramid volume formula

A pyramid is a polyhedron formed by connecting a polygonal base and an apex. The basic formula for pyramid volume is the same as for a cone:

• volume = (1/3) × base_area × height, where height is the height from the base to the apex.

That formula works for any type of base polygon and oblique and right pyramids. All you need to know are those two values – base area and height.
However, there are other useful formulas in case you don't know the base area. For any pyramid with a regular base, you can use the equation:

• volume = (n/12) × height × side_length² × cot(π/n), where n is the number of sides of the base for a regular polygon

## How to calculate the pyramid volume? Volume of a square pyramid calculation example

We know the formula, and what's next? How to use this pyramid volume calculator? The best way to demonstrate how it works is the world's best-known pyramid – the Cheops pyramid:

1. Select the base shape. The Cheops pyramid, also called the pyramid of Khufu, is a square. Of course, it's not an ideal square, but we can assume it is – the difference between the length of the edges is smaller than 1‰.

2. Enter the height of a pyramid. Khufu pyramid height is equal to 146 m (you can change the units to meters with a simple click on the unit. Also, you can check out our volume converter).

3. Determine the side length. The Cheops pyramid edge length is, on average, 230.36 m.

4. The approximate volume of a square pyramid is equal to 2,582,532 m³.

## Pyramid volume names

A pyramid with an n-sided base has:

• n+1 faces (n-triangles + 1 n-gon);
• 2n edges; and
• n+1 vertices.

The name of the pyramid comes from the shape of its base:

Faces

Edges

Vertices

Shape of base

Pyramid name

4

6

4

Triangle

Tetrahedron / triangular pyramid

5

8

5

Square

Square pyramid

6

10

6

Pentagon

Pentagonal pyramid

7

12

7

Hexagon

Hexagonal pyramid

8

14

8

Heptagon

Heptagonal pyramid

9

16

9

Octagon

Octagonal pyramid

## Tetrahedron volume calculation

As an example, let's take the example of a loose-leaf tea pyramid:

1. Choose the shape of the base. In our case, it's a regular triangle.
2. Type the pyramid's height. Assume that for a tea pyramid, it's equal to 1.2 in.
3. Enter the side length. For example, 1.5 in.
4. Tetrahedron volume appears below. For our tea pyramid, it is equal to 0.39 cu in.

If you want to calculate the regular tetrahedron volume – the one in which all four faces are equilateral triangles, not only the base – you can use the formula:

volume = a³ / 6√2, where a is the edge of the solid

The height, in this case, can be calculated as:
height = a√3 / 6 ~ 0.2887 × a, so if you want to calculate, e.g., the volume of a regular polyhedron with the edge = 3, type 3 * 0.2887 into the pyramid volume calculator's "Height" box.

## What next?

Now you are an expert and know exactly how to calculate the pyramid volume! Why not check out our other volume calculators? These include our cone volume calculator and the cylinder volume calculator.

## FAQ

### How do I find the volume of a pyramid?

To estimate the volume of any pyramid:

1. Evaluate the pyramid's base area.
2. Multiply the base area by its height.
3. Divide everything by 3.
4. The good thing is this algorithm works perfectly for all types of pyramids, both regular and oblique.

### How do I find the volume of a hexagonal pyramid?

To get the volume of a regular hexagonal pyramid of the side length a and the height h:

1. Square the side length to get a².
2. Multiply a² by its height, h.
3. Multiply this product by the square root of three, √3.
4. Divide everything by 2.
5. The result is your desired volume! Alternatively, you can write it in the single formula form: V = √3 / 2 × a² × h.

### What is the volume of the Great Pyramid of Giza?

The Great Pyramid of Giza's volume is roughly 92 million ft³ or 2.6 million m³. We can obtain this value by assuming the Pyramid of Khufu is a right square pyramid – see the right square pyramid calculator. It has a length of 756.4 ft (230.6 m) and a height of 481.4 ft (146.7 m).

### How do I find the volume of a pentagonal pyramid?

To get the volume of a regular pentagonal pyramid with a side length of a and a height of h:

1. Square the side length to get a².

2. Multiply a² by its height, h.

3. Multiply this product by √(25 + 10√5).

4. Divide everything by 12.

5. You can also write the resulting formula as:

V = √(25 + 10√5) / 12 × a² × h.

### How do I find the volume of an octagonal pyramid?

To get the volume of a regular octagonal pyramid with a side length of a and a height of h:

1. Square the side length to get a².

2. Multiply a² by its height, h.

3. Multiply this product by 2 × (1 + √2).

4. Divide everything by 3.

5. That's all! The general formula for a regular octagonal pyramid reads:

V = 2 × (1 + √2) / 3 × a² × h.

Hanna Pamuła, PhD and Steven Wooding
Base type
Regular-shaped base The volume formula works for both right and oblique pyramids.
Shape of base
square (4-sides)
Height (h)
in
Side length (a)
in
Volume
cu in
Use Advanced mode to show slant height, lateral edge length and surface area, for right pyramids.
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