Number of Rectangles in Grid Calculator

Calculate Number of Rectangles





Formula

The formula to calculate the Number of Rectangles is:

\[ \text{NRectangles} = C(\text{NHorizontal Lines}+1, 2) \times C(\text{NVertical Lines}+1, 2) \]

Definition

The Number of Rectangles is the total count of rectangles that can be formed by using a given set of horizontal and vertical lines from a plane. Number of Horizontal Lines is the total count of given straight lines which are horizontally oriented on a plane. Number of Vertical Lines is the total count of given straight lines which are vertically oriented on a plane.

Example Calculation

Let's assume the following values:

Using the formula:

\[ \text{NRectangles} = C(10+1, 2) \times C(9+1, 2) = \frac{11 \cdot 10}{2} \times \frac{10 \cdot 9}{2} = 2475 \]

The Number of Rectangles is 2475.

Conversion Chart

Number of Horizontal Lines Number of Vertical Lines Number of Rectangles
1 1 1
1 2 3
1 3 6
1 4 10
1 5 15
1 6 21
1 7 28
1 8 36
1 9 45
1 10 55
2 1 3
2 2 9
2 3 18
2 4 30
2 5 45
2 6 63
2 7 84
2 8 108
2 9 135
2 10 165
3 1 6
3 2 18
3 3 36
3 4 60
3 5 90
3 6 126
3 7 168
3 8 216
3 9 270
3 10 330
4 1 10
4 2 30
4 3 60
4 4 100
4 5 150
4 6 210
4 7 280
4 8 360
4 9 450
4 10 550
5 1 15
5 2 45
5 3 90
5 4 150
5 5 225
5 6 315
5 7 420
5 8 540
5 9 675
5 10 825
6 1 21
6 2 63
6 3 126
6 4 210
6 5 315
6 6 441
6 7 588
6 8 756
6 9 945
6 10 1,155
7 1 28
7 2 84
7 3 168
7 4 280
7 5 420
7 6 588
7 7 784
7 8 1,008
7 9 1,260
7 10 1,540
8 1 36
8 2 108
8 3 216
8 4 360
8 5 540
8 6 756
8 7 1,008
8 8 1,296
8 9 1,620
8 10 1,980
9 1 45
9 2 135
9 3 270
9 4 450
9 5 675
9 6 945
9 7 1,260
9 8 1,620
9 9 2,025
9 10 2,475
10 1 55
10 2 165
10 3 330
10 4 550
10 5 825
10 6 1,155
10 7 1,540
10 8 1,980
10 9 2,475
10 10 3,025