# 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.

sneak preview
sssshhhhh

We're working on a new site – Online Text Tools – utilities for text processing. Check it out!

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

All math tools

Quickly visualize rules of an Lindenmayer rewrite system.

Quickly generate a list of primes.

Quickly generate a list of Fibonacci numbers.

Quickly generate a list of extended, negative Fibonacci numbers.

Quickly generate a list of Fibonacci primes.

Quickly generate a list of Fibonacci words.

Quickly generate a list of Tribonacci words.

Quickly generate a list of Lucas numbers.

Quickly generate a list of extended, negative Lucas numbers.

Quickly generate a list of Lucas numbers that are also prime numbers.

Quickly create a list of excessive numbers.

Quickly create a list of deficient numbers.

Quickly generate a list of perfect numbers.

Quickly create a list of slightly defective numbers.

Quickly generate random numbers.

Quickly generate a list of look-and-say sequence numbers.

Quickly create a list of Prouhet-Thue-Morse sequence values.

Quickly create a list of dragon curve sequence values.

Quickly create a list of Oldenburger-Kolakoski sequence values.

Quickly create a list of Gijswijt sequence values.

Quickly create a list of Golay-Rudin-Shapiro sequence values.

Quickly create a list of Baum-Sweet sequence values.

Quickly create a list of Moser-de Bruijn sequence values.

Quickly generate a list of even numbers.

Quickly generate a list of odd numbers.

Quickly find all factors of the given integer.

Quickly decompose integers into their prime factors.

Quickly find out if the given integer is a prime number.

Quickly check if the given number is a Fibonacci number

Quickly generate π constant's digits to arbitrary precision.

Quickly calculate Euler constant's digits to arbitrary precision.

Quickly calculate φ constant's digits to arbitrary precision.

Quickly calculate factorials.

Quickly create a triangluar array of binomial coefficients.

Quickly create a matrix with random elements.

Quickly create a unit matrix with ones along the diagonal.

Quickly find the transpose of a matrix.

Quickly find the inverse of a matrix.

Quickly calculate the determinant of a matrix.

Quickly find the sum of two or more matrices.

Find the difference of two or more matrices.

Quickly find the product of matrices.

Quickly draw a Hilbert space-filling curve.

Quickly draw a Heighway triangle fractal.

Quickly draw a Harter-Heighway space-filling dragon fractal.

Quickly draw a Davis-Knuth dragon fractal.

Quickly draw a triple dragon fractal.

Quickly draw a quaddragon fractal.

Quickly draw a hexdragon curve.

Quickly draw a Peano space-filling fractal.

Quickly draw a Moore space-filling curve.

Quickly draw a Peano-Gosper space-filling curve.

Quickly draw a Sierpinski arrowhead fractal curve.

Quickly draw a Sierpinski sieve fractal.

Quickly draw a Sierpinski closed plane fractal curve.

Quickly draw a Sierpinski carpet fractal.

Quickly draw a Sierpinski maze fractal.

Quickly draw a Sierpinski square fractal.

Quickly draw a Sierpinski pentaflake fractal.

Quickly draw a Sierpinski hexaflake fractal.

Quickly draw a Sierpinski n-gon fractal.

Quickly draw a Koch island fractal curve.

Quickly draw a Koch antisnowflake fractal.

Quickly draw a Koch triangle fractal.

Quickly draw a Koch n-gon fractal.

Quickly draw a quadratic Koch flake fractal.

Quickly draw a Cesaro fractal.

Quickly draw a Cesaro n-gon fractal.

Quickly draw a triflake fractal.

Quickly draw a quadric cross fractal.

Quickly draw a self-similar Levy C fractal curve.

Quickly draw a Vicsek snowflake fractal.

Quickly draw a T-square fractal.

Quickly draw a Cantor set fractal.

Quickly draw an asymmetric Cantor set fractal.

Quickly draw a generalized Cantor set fractal.

Quickly draw an ε-Cantor set fractal.

Quickly draw a Cantor dust fractal.

Quickly draw a Pythagoras tree fractal.

Quickly draw a Fibonacci word fractal.

Quickly draw an H-tree fractal.

Quickly draw a V-tree fractal.

Quickly generate a Morton Z-order fractal curve.

Coming soon
These math tools are on the way

Find n-th e Digit

Calculate the n-th digit of Euler's number.

Find n-th Golden Ratio Digit

Calculate the n-th digit of Golden Ratio.

Find n-th Pi Digit

Calculate the n-th digit of pi constant.

Decode a Look-and-say Sequence

Perform the inverse operation on a look-and-say sequence.

Generate Bell Number Sequence

Create a list of Bell numbers.

Generate Carmichael Number Sequence

Create a list of Charmichel numbers.

Generate Catalan Number Sequence

Create a list of Catalan numbers.

Generate Composite Number Sequence

Create a list of composite numbers.

Generate Secant Number Sequence

Create a list of secant numbers.

Generate Golomb Number Sequence

Create a list of Golomb-Silverman numbers.

Generate Euler's Totient Number Sequence

Create a list of Euler's phi numbers.

Generate Juggler Number Sequence

Create a list of juggler numbers.

Generate Lucky Number Sequence

Create a list of lucky numbers.

Generate Motzkin Number Sequence

Create a list of motzkin numbers.

Generate Padovan Number Sequence

Create a list of Padovan numbers.

Generate Pseudoperfect Number Sequence

Create a list of semiperfect numbers.

Generate Ulam Number Sequence

Create a list of Ulam numbers.

Generate Weird Number Sequence

Create a list of weird numbers.

Generate Superperfect Number Sequence

Create a list of superperfect numbers.

Partition a Number

Find all partitions of the given integer.

Generate Partition Number Sequence

Create a list of Partition function numbers.

Generate Arithmetic Progression

Create an arithmetic sequence of numbers.

Generate Geometric Progression

Create a geometric sequence of numbers.

Generate Natural Number Sequence

Create a list of natural numbers.

Generate Powers of Two

Create a list of numbers of powers of two.

Generate Powers of Ten

Create a list of numbers of powers of ten.

Multiply a Matrix by a Scalar

Multiply all matrix elements by a number.

Check if a Matrix is Singular

Determine if a matrix is degenerate.

Find the Co-factor Matrix

Given a matrix, find its cofactor matrix.

Find the Adjugate Matrix

Given a matrix, find its adjunct.

LU Factor a Matrix

Decompose a matrix into LU factors.

Find Matrix Eigenvalues

Find eigenvalues of a matrix.

Prettify a Matrix

Beautify a matrix by neatly aligning all its columns.

Reformat a Matrix

Convert matrix in one format to another format.

Draw a Fibonacci Spiral

Generate a Fibonacci spiral curve.

Draw Fibonacci Rectangles

Generate a drawing of Fibonacci rectangles.

Draw a Fibonacci Seed Head

Generate a Fibonacci flower head.

Draw a Padovan Fractal

Generate a Padovan equiliteral triangles fractal.

Draw a Apollonian Gasket

Generate an Apollonian gasket fractal.

Draw a Mandelbrot Fractal

Generate a Mandelbrot fractal.

Draw a Julia Fractal

Generate a Julia fractal.

Draw a Rauzy Fractal

Generate a Rauzy fractal.

Draw Blancmange Fractal Curve

Generate a Blancmange fractal.

Draw Weierstrass Function

Generate a Weierstrass fractal.

Draw Minkowski Question-mark Curve

Generate a Minkowski Question-mark fractal.

Draw Thomae's Function

Generate a Thomae's function (also known as popcorn or raindrop function).

Draw Dirichlet's Function

Generate a Dirichlet's function.

Convert Words to Numbers

Convert numbers as English text to actual digits.

Convert Numbers to Words

Convert numbers to written English text.

Convert Decimal Notation to Scientific Notation

Convert numbers written in decimal form to scientific form.

Convert Scientific Notation to Decimal Notation

Convert numbers written in scientific form to decimal form.

Round Numbers Up

Apply ceil operation to numbers.

Round Numbers Down

Apply floor operation to numbers.

Subscribe!
Never miss an update

Cool!

Notifications
We'll let you know when we add this tool

Cool!