# Pascal's triangle generator

## World's simplest number tool

Quickly draw Pascal's triangle in your browser. To get your triangle, just specify how many rows of the triangle you need in the options below, and this utility will generate a triangle of binomial coefficients with that many rows. Created by developers for developers.

announcement
a new project!

Super exciting news! We just launched TECHURLS – simple and fun tech news reader. 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 is an online browser-based utility for calculating and visualizing Pascal's triangle. Pascal's triangle is an infinite numerical triangle of numbers. It's constructed iteratively – the top element is a single one. The next two elements are another two ones. Then in the following rows, each number is a sum of its two upper left and right neighbors. It turns out that a triangle constructed this way has binomial coefficients as its elements. These numbers are invaluable in combinatorics, probability theory, and other mathematical fields. In this tool, you can construct Pascal's triangles of any size and specify which row to start from. By default, the tool creates a left-aligned Pascal's triangle. You can also make it centered and even turn it upside down. That's numberwang!

Pascal's triangle generator examples
Click to use

Left-aligned Pascal's Triangle

In this example, we draw the first 8 rows of Pascal's triangle and align them to the left.

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

**Required options**

Draw Pascal's triangle from
this row number.

Calculate this many rows of
Pascal's triangle.

Align all binomial coefficients
to the center.

Draw Pascal's triangle from
top to bottom.

Centered Pascal's Triangle

In this example, we calculate 7 rows of Pascal's triangle and we center the results. The top of the triangle is truncated as we start from the 4th row, which already contains four binomial coefficients.

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**

Draw Pascal's triangle from
this row number.

Calculate this many rows of
Pascal's triangle.

Align all binomial coefficients
to the center.

Draw Pascal's triangle from
top to bottom.

Upside-down Pascal's Triangle

In this example, we compute the first 10 rows of an inverted Pascal's triangle. The first row contains ten coefficients and each next row has one less. At the bottom, we have a single one.

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**

Draw Pascal's triangle from
this row number.

Calculate this many rows of
Pascal's triangle.

Align all binomial coefficients
to the center.

Draw Pascal's triangle from
top to bottom.

Pro tips
Master online number 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://onlinenumbertools.com/draw-pascal-triangle?&start=1&count=8&prettify-triangle=false&upside-down=false

All number tools

Quickly create a list of numbers in arithmetic series.

Quickly create a list of numbers in geometric series.

Quickly calculate the coefficients of the binomial expansion.

Quickly create a downloadable image from numbers.

Quickly create a list of random numbers.

Quickly create a list of random primes from a specific interval.

Quickly create a matrix with random numbers as its elements.

Quickly create a random row or column vector.

Quickly exchange rows and columns of a matrix.

Quickly find the determinant of any square matrix.

Quickly calculate any number of digits of number π.

Quickly generate the specified number of Euler constant's digits.

Quickly generate any number of golden ratio digits.

Quickly generate numbers of say what you see sequence.

Quickly calculate numbers of Fibonacci sequence.

Quickly calculate numbers of Lucas series.

Quickly generate Fibonacci-like series with custom start values.

Quickly create a sequence of prime numbers.

Quickly check if the given number is a prime.

Quickly compute all prime factors of a number.

Quickly compute all divisors of a number.

Quickly create a list of increasing or decreasing integers.

Quickly create a sequence of even numbers.

Quickly create a sequence of odd numbers.

Quickly generate a series of numbers in the form 2^n.

Quickly generate a series of numbers in the form 10^n.

Quickly choose one or more numbers from a list of numbers.

Quickly round one or more numbers to the given accuracy.

Quickly sort numbers in ascending or descending order.

Quickly sort number's digits in ascending or descending order.

Quickly randomize the order of digits in a number.

Quickly filter numbers according to certain criteria.

Quickly add up all the numbers in the given list and find their sum.

Quickly multiply all the given numbers together and find their product.

Quickly add up all the digits of the given numbers.

Quickly multiply all the digits of the given numbers.

Quickly create a diagonal matrix with ones on the main diagonal.

Quickly convert a number to the form 2^x.

Quickly express a number in the form 10^x.

Coming soon
These number tools are on the way

Generate Numberwang Numbers

Create a list of numberwang numbers.

Rewrite Numbers

Given numbers and a grammar, recursively rewrite them.

Generate Powers of 10

Create a list of numbers that are powers of ten.

Create a Floating Point Number

Create a number from the mantissa, base and exponent.

Convert a Number to the Scientific Notation

Convert a number to the a*10^b form.

Convert Scientific Notation to a Number

Convert a number in scientific notation to a regular number.

Generate Random Binary Numbers

Create a list of random binary numbers.

Generate Random Octal Numbers

Create a list of random octal numbers.

Generate Random Decimal Numbers

Create a list of random decimal numbers.

Generate Random Hex Numbers

Create a list of random hexadecimal numbers.

Calculate a Running Sum

Calculate a cumulative sum of a list of numbers.

Calculate a Running Product

Calculate a cumulative product of a list of numbers.

Find the Maximal Number

Find the largest number in a number sequence.

Find the Minimal Number

Find the smallest number in a number sequence.

Calculate the Factorial

Find the factorial of a number.

Generate Number Bigrams

Create a list of digit bigrams from a number.

Generate Number Trigrams

Create a list of digit trigrams from a number.

Generate Number N-grams

Create a list of digit ngrams from a number.

Analyze a Number

Report how many digits appear how many times.

Convert a Number to an Ordinal

Convert a cardinal number to an ordinal number.

Convert an Ordinal to a Number

Convert an ordinal number to a cardinal number.

Convert a Number to Words

Express a number in English words.

Convert Words to a Number

Rewrite English words to numbers.

Convert a Number to Roman Number

Convert Arabic numerals to Roman numerals.

Convert a Roman Number to Regular Number

Convert Roman Numerals to Arabic numerals.

Generate Negafibonacci Numbers

Calculate a series of extended Fibonacci numbers.

Generate Fibonacci Primes

Find numbers that are both Fibonacci numbers and primes.

Fibonacci Number Test

Check if a number is a Fibonacci number.

Fibonacci Prime Test

Check if a number is both a Fibonacci number and a prime.

Construct Fibonacci Words

Create a sequence of Fibonacci words.

Construct Tribonacci Words

Create a sequence of Tribonacci words.

Generate Negalucas Numbers

Calculate a series of extended Lucas numbers.

Generate Lucas Primes

Calculate a series of extended Lucas numbers.

Lucas Prime Test

Check if a number is both a Lucas number and a prime.

Invert a Matrix

Find the inverse of a number matrix.

Calculate the Trace of a Matrix

Find the sum of main diagonal elements of a matrix.

Calculate the Eigenvalues of a Matrix

Find the eigenvalues of a matrix.

Multiply Matrices

Compute the product of two matrices.

Add Matrices

Compute the sum of two matrices.

Subtract Matrices

Compute the difference of two matrices.

Generate Moser de Bruijn Numbers

Calculate a sequence of Moser-Bruijn numbers.

Generate Kolakoski Numbers

Calculate a sequence of Oldenburger-Kolakoski numbers.

Generate Gijswijt Numbers

Calculate a sequence of self-describing Gijswijt numbers.

Generate Rudin-Shapiro Numbers

Calculate a sequence of Rusin-Shapiro numbers.

Generate Baum-Sweet Numbers

Calculate a sequence of Baum-Sweet numbers.

Generate Thue-Morse Sequence

Calculate members of Thue-Morse number series.

Generate Perfect Numbers

Create a list of perfect numbers.

Generate Almost Perfect Numbers

Create a list of almost perfect numbers.

Generate Excessive Number Sequence

Calculate a sequence of abundant numbers.

Generate Deficient Number Sequence

Calculate a sequence of deficient numbers.

Calculate Dragon Curve Numbers

Generate a list of paperfolding sequence numbers.

Generate Composite Numbers

Create a list of numbers that are not prime.

Test if a Number is Perfect

Check if the given number is a perfect number.

Test if a Number is Abundant

Check if the given number is an abundant number.

Test if a Number is Deficient

Check if the given number is a deficient number.

Calculate Greatest Common Divisor

Find the GCD of two or more numbers.

Calculate Least Common Multiple

Find the LCM of two or more numbers.

Generate a Sequence of Squares

Create a list of squares of numbers.

Generate a Sequence of Cubes

Create a list of cubes of numbers.

Calculate the Modulo

Find the modulus of a number.

Group Number Digits

Group together digits of a number.

Split a Number into Digits

Create a list of digits from a number.

Printf Numbers

Apply sprintf or printf function to numbers.

Palindrome Number Test

Test if the given number is a palindrome.

Create a Palindrome Number

Given a number, add digits to it so that it becomes a palindrome.

Create Zalgo Numbers

Let Zalgo destroy your numbers.

Mirror a Number

Create a mirror copy of a number.

Reverse a Number

Reverse the order of digits of a number.

Rotate a Number

Cyclically rotate digits of a number to the left or right.

Increase All Digits in a Number

Add one to every digit in a number.

Decrease All Digits in a Number

Subtract one from every digit in a number.

Calculate Percentages

Find x% of a number.

Generate Natural Numbers

Create a list of natural numbers.

Generate Rational Numbers

Create a list of rational numbers.

Generate Real Numbers

Create a sequence of real numbers.

Generate Complex Numbers

Create a list of complex numbers.

Generate Binary Numbers

Create a sequence of binary numbers.

Generate Pairs of Numbers

Create a sequence of number pairs.

Convert a Fraction to a Decimal

Convert a fraction to a decimal number.

Convert a Decimal to a Fraction

Convert a decimal number to a fraction.

Convert a Binary Number to Octal Number

Convert a base two number to base eight number.

Convert a Binary Number to Decimal Number

Convert a base two number to base ten number.

Convert a Binary Number to Hex Number

Convert a base two number to base sixteen number.

Convert a Octal Number to Binary Number

Convert a base eight number to base two number.

Convert a Octal Number to Decimal Number

Convert a base eight number to base ten number.

Convert a Octal Number to Hex Number

Convert a base eight number to base sixteen number.

Convert a Decimal Number to Binary Number

Convert a base ten number to base two number.

Convert a Decimal Number to Octal Number

Convert a base ten number to base eight number.

Convert a Decimal Number to Hex Number

Convert a base ten number to base sixteen number.

Convert a Hex Number to Binary Number

Convert a base sixteen number to base two number.

Convert a Hex Number to Octal Number

Convert a base sixteen number to base eight number.

Convert a Hex Number to Decimal Number

Convert a base sixteen number to base ten number.

Convert Any Number to Any Base

Convert any number in any base to any other base.

Change Number's Mantissa

Change the significand of a number.

Change Number's Base

Change the base of a number.

Change Number's Exponent

Change the power of a number.

Numberwang Number Test

Test if the given number is numberwang.

Subscribe!
Never miss an update

Cool!

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

Cool!