# Find number of squares inside a given square grid in C++

In this tutorial, we will check out how to find the number of squares inside a given square grid in C++ with the corresponding code.
If the square grid contains a side of N*N, then we are going to find the total number of squares present in it.

## calculate the number of squares inside a square grid in C++

If we observe the number of squares that exist in smaller square grids then we can draw a pattern that will guide us to construct a simple formula to find the number of squares in a square grid of any length.

• The total number of squares in a square grid of side 1 =1.
• Total number of squares in a square grid of side 2 =5.  ⇒ 4 small squares, and 1  2×2 square.
• The total number of squares in a square grid of side 3 =14.  ⇒ 9 small squares, 4  2×2 squares and 1  3×3 square.
• The total number of squares in a square grid of side 4 =30. ⇒ 16 small squares, 9  3×3 squares,  4  2×2 squares and 1  4×4 square.
By observing above sentences we can draw a pattern
• 1×1 :-1^2 = 1.
• 2×2 :- 2^2 + 1^2 = 5.
• 3×3 :- 3^2 + 2^2 + 1^2 = 14.
• 4×4 :- 4^2 + 3^2 + 2^2 + 1^2 = 30.
• Likewise, for nxn is n^2 + (n-1)^2 + (n-2)^2…………….(n-n+1)^2.
`Then N(s)n = n^2 + (n-1)^2 + (n-2)^2................(n-n+1)^2 = n(n + 1)(2n + 1)/6`

1.By using the formula N(s)n = n^2 + (n-1)^2 + (n-2)^2…………….(n-n+1)^2:

```#include <bits/stdc++.h>
using namespace std;
int main()
{
int n,squares=0;
cout<<"enter the length of a square:";
cin>>n;
while(n>0)
{
squares += pow(n, 2);
n--;
}
cout<<"no of squares in a square grid:"<<squares;
return 0;
}```

Output:

```enter the length of a square:5
no of squares in a square grid:55```

2.By using the formula N(s)n =n(n + 1)(2n + 1)/6:

```#include <iostream>
using namespace std;

int squares(int n)
{

return n * (n + 1) * (2 * n + 1) / 6;
}
int main()
{
int m;
cout<<"enter length of a square:";
cin>>m;
cout <<"no of squares in a square grid:"<< squares(m);

return 0;
}```

Output:

```enter length of a square:10
no of squares in a square grid:385```

Similarly, you can find the number of squares inside a given square grid of any length by using these programs.