To calculate result you have to disable your ad blocker first.

# Square Pyramidal Number Calculator

To use square pyramidal Number Calculator, enter the number, and click calculate button

## Square Pyramidal Number Calculator

Square Pyramidal Number Calculator is an online tool that finds the number of squares that are used to construct a pyramidal with a square base.

## What is the Square Pyramidal Number?

It is a positive number which shows how many squares are required to construct the square pyramidal with a square base. It is obtained by arranging square numbers in the shape of a pyramid.

Each layer of the pyramid contains a square number of objects, and the total number of objects in the pyramid can be calculated by summing up these square numbers. It is graphically shown as a regular polygonal by squares or dots.

The formula of the Square number in the **n ^{th}-term** is written in mathematical form as.

`P`

_{n} = {n * (n + 1) * (2n + 1)} / 6

**Where, **

- “
**P**” is the Square number for the given_{n}**n**.^{th}-term

By continuing this process for different values of “**n**” we can calculate the square pyramidal numbers for higher heights of pyramids.

**For example:**

The first five terms in the square pyramidal Number sequence are given below.

P_{1} = 1

P_{2} = 5

P_{3} = 14

P_{4} = 30

P_{5} = 55

## How to evaluate the square pyramidal number?

Here are a few examples in which we find the square pyramidal numbers step-by-step.

**Example 1:**

Evaluate the Square number for the number “**5**”.

**Solution:**

**Step 1: **Write the data from the given condition.

n = 5, P_{n} =?

**Step 2: **Write the formula of the Square number.

`P`

_{n} = {n * (n + 1) * (2n + 1)} / 6

**Step 3: **Put the values of “**n**” and evaluate for the required results.

`n = 5,`

P_{5} = {5* (5 + 1) * (5*2 + 1)} / 6

P_{5} = {5* (6) * (11)} / 6

P_{5} = {5* (11)}

`P`

_{5} = 55

**Example 2:**

Evaluate the Square number for the number “**7**”.

**Solution:**

**Step 1: **Write the data from the given condition.

n = 7, P_{n} =?

**Step 2: **Write the formula of the Square number.

`P`

_{n} = {n * (n + 1) * (2n + 1)} / 6

**Step 3: **Put the values of “**n**” and evaluate for the required results.

`n = 7,`

P_{n} = {n * (n + 1) * (2n + 1)} / 6

P_{7} = {7 * (7 + 1) * (2*7 + 1)} / 6

P_{7} = {7*8* (15)}/ 6

P_{7} = 840/6

`P`

_{7} = 140