# Pascal's triangle generator

## World's simplest math tool

Free online Pascal's Triangle generator. Just specify how many rows of Pascal's Triangle you need and you'll automatically get that many binomial coefficients. There are no ads, popups or nonsense, just an awesome triangular array of the binomial coefficients calculator. Press button, get Pascal's Triangle. Created by mathematicians for mathematicians.

A link to this tool, including input, options and all chained tools.

Pascal's triangle generator tool
What is a pascal's triangle generator?

This tool calculates binomial coefficients that appear in Pascal's Triangle. Pascal's Triangle starts at the top with 1 and each next row is obtained by adding two adjacent numbers above it (to the left and right). You can choose which row to start generating the triangle at and how many rows you need. You can also center all rows of Pascal's Triangle, if you select prettify option, and you can display all rows upside down, starting from the last row first. This tool can generate arbitrary large Pascal's Triangles. Mathabulous!

Pascal's triangle generator examples
Click to use

Generate Ten Rows of Pascal's Triangle

This example calculates first 10 rows of Pascal's Triangle.

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1
1 9 36 84 126 126 84 36 9 1

**Required options**

Start generating Pascal's
Triangle from this row.

How many rows of Pascal's
Triangle to generate?

Calculate Five Rows of Pascal's Triangle

This example finds 5 rows of Pascal's Triangle starting from 7th row.

1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1
1 9 36 84 126 126 84 36 9 1
1 10 45 120 210 252 210 120 45 10 1

**Required options**

Start generating Pascal's
Triangle from this row.

How many rows of Pascal's
Triangle to generate?

Draw Pascal's Triangle in a Pretty Form

This example draws Pascal's Triangle in a pretty form with all rows centered.

**Required options**

Start generating Pascal's
Triangle from this row.

How many rows of Pascal's
Triangle to generate?

Center all Pascal's Triangle rows.

Flip Pascal's Triangle Upside Down

This example reverses the order of binomial coefficients and the last row comes first.

1 9 36 84 126 126 84 36 9 1
1 8 28 56 70 56 28 8 1
1 7 21 35 35 21 7 1
1 6 15 20 15 6 1
1 5 10 10 5 1
1 4 6 4 1
1 3 3 1
1 2 1
1 1
1

**Required options**

Start generating Pascal's
Triangle from this row.

How many rows of Pascal's
Triangle to generate?

Center all Pascal's Triangle rows.

Flip Pascal's Triangle upside down.

Pro tips
Master online math tools

You can pass options to this tool using their codes as query arguments and it will automatically compute output. To get the code of an option, just hover over its icon. Here's how to type it in your browser's address bar. Click to try!

https://onlinemathtools.com/generate-pascals-triangle?&start=1&count=10

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