Lattice Path Calculator - Find the Number of Unique Paths in a Grid

Have you ever wondered how many different ways you can navigate through a grid from one point to another, moving only right or down? If so, you've come to the right place! Our Lattice Path Calculator is designed to help you find the number of unique paths between two points in a grid with a specified size.

What is a Lattice Path?

A lattice path is a sequence of steps on a grid where you can only move right or down at each step. The grid consists of evenly spaced points, and each step moves from one point to an adjacent point, either horizontally or vertically. Lattice path problems have applications in mathematics, computer science, and various fields that involve navigating through structured spaces.

How Does the Lattice Path Calculator Work?

The Lattice Path Calculator uses the power of combinatorics to determine the number of unique paths through a grid of a given size. For a grid of size M x N (M rows and N columns), you need to take M steps down and N steps right to reach the bottom-right corner from the top-left corner. In total, you need to take (M + N) steps.

The calculator employs the combination formula to calculate the number of unique paths:

\text{Number of paths} = \dfrac{(M + N)!}{M! \times N!}

Where ! denotes the factorial function, and (M + N)! represents the product of all positive integers from 1 to (M + N).

How to Use the Lattice Path Calculator

Using the Lattice Path Calculator is easy! Follow these simple steps:

• Input the grid width (number of columns) and grid height (number of rows) in the corresponding fields.
• The calculator will display the number of unique lattice paths between the top-left and bottom-right corners of the grid.

Explore the fascinating world of combinatorics and find out how many different ways you can navigate through any grid. Try our Lattice Path Calculator today!