CALCULATE WITH CONFIDENCE

Counting, Permutations & Combinations

Lattice Path & Grid Path Calculator

Count shortest monotone paths consisting only of right and up steps.

Counting & Combinatorics

Count shortest monotone grid paths

Right and up steps only

Exact shortest paths

—

Enter valid values to see the result.

Your entries are calculated in this browser and are not submitted to 365CALCS.COM.

Quick guide

How to use this calculator

  1. Enter the required right and up steps.
  2. The path may use only those two directions.
  3. Read the number of distinct shortest paths.

Calculation method

Choose which steps are right steps

Every shortest path contains r+u steps. Choosing the r positions occupied by right steps determines the path.

Worked example

Cross a 3 by 2 grid

Every shortest path uses three right steps and two up steps.

C(5,3) = 10

Supported inputs

Precision and limits

Discrete domain

Inputs are whole counts. Negative, fractional, grouped, and scientific-notation inputs are rejected.

Exact integers

Results use arbitrary-precision integers and are never rounded. Inputs and output size are bounded to keep the page responsive.

Obstacles

This calculator assumes an unobstructed rectangular grid and does not count diagonal or backward moves.