Pyramid volume calculator

From ancient times, people needed to measure the amount of various substances. Bulk substances and liquids could be measured by filling them with vessels of a certain capacity, determining their quantity by volume. The concept of volume in solid geometry is introduced similarly to the concept of area in plane geometry. In plane geometry, we determined the area like this: the area of ​​a polygon is the value of the part of the plane that the polygon occupies. To formulate the concept of volume similarly to this concept. The magnitude of the part of the space occupied by the geometric body is called the volume of this body. Volume is measured in "cubic" units.

Pyramid — is a polyhedron, one of whose faces (called the base) is an arbitrary polygon, and the remaining faces (called side faces) are triangles that have a common vertex. According to the number of base angles, triangular (tetrahedron), quadrangular pyramids are distinguished, etc. A pyramid is a specific case of a cone.

Calculating the volume of a pyramid can be a challenging task, but with our pyramid volume calculator, you can easily find the volume of different types of pyramids. Whether you need to calculate the volume of a regular triangular, quadrangular, right or any other pyramid, our calculator can do the job for you.

Pyramid Volume Formula

The formula for finding the volume of a pyramid depends on the type of pyramid you are dealing with. Here are some of the most common formulas:

Regular Triangular Pyramid

The volume of a regular triangular pyramid is equal to one third of the product of the height of the pyramid and the area of an equilateral triangle. The formula for finding its volume is:

V = \dfrac{ha^2}{4\sqrt{3}}

where V is the volume, a is the side of the base, and h is the height of the pyramid.

Regular Quadrangular Pyramid

The volume of a regular quadrangular pyramid is calculated by the same method as any other pyramid, namely, the area of the base and the height, and since the base is a square, the volume is equal to one third of the product of the height of the pyramid and the side of the base squared. The formula for finding its volume is:

V = \dfrac{1}{3}ha^2

where V is the volume, a is the side of the base, and h is the height of the pyramid.

Right Pyramid

If you have a right pyramid, the formula for finding its volume is:

V = \dfrac{hna^2}{12*tg\left( \dfrac{180^o}{n} \right)}

where V is the volume, a is the side of the base, n is qty of the sides, and h is the height of the pyramid.

Since the base of the regular pyramid is a regular polygon (that is, all sides are equal), then knowing the height of the pyramid, the length of the side of the base and the n number of their sides, you can find the volume of the pyramid.

General Formula for Volume of Pyramid

In general volume of the pyramid can be found by the area of the base and the height of the pyramid, which is equal to one third of their product:

V = \dfrac{1}{3}Sh

where V is the volume, S is the area of the base, and h is the height of the pyramid.

How to Use the Pyramid Volume Calculator

Using our pyramid volume calculator is easy. Simply enter the required parameters and our calculator will automatically give you the volume of your pyramid.

1. Select the type of pyramid you want to calculate the volume for.
2. Enter the required values in the input boxes provided.
3. The calculator will automatically calculate the volume of the pyramid and display it on the screen.