About the Pascal's Triangle Generator
Pascal's triangle is a pattern of numbers in which every number is the sum of the two directly above it. The edges are all ones. Its rows give the coefficients of binomial expansions and the numbers of combinations, and it hides many other patterns. This generator builds as many rows as you ask for, up to 60, using exact big-number arithmetic. Type the number of rows and the Pascal's triangle appears at once, with a few related figures underneath, and you can copy the result with one tap. The sums run in your browser, so nothing you enter is uploaded.
Updated October 2026
How to use the Pascal's Triangle Generator
- 1Enter the number of rows.
- 2Pick the units or options from the menus if the Pascal's triangle tool offers them.
- 3Read the Pascal's triangle in the large result box.
- 4Look at the extra rows for related figures.
- 5Press Copy result to keep the answer.
When you need the Pascal's triangle
Students use the triangle to expand brackets, to count combinations and to study probability, since row n lists the chances of getting 0, 1, 2 and so on heads in n − 1 coin tosses, after dividing by the row sum.
The triangle hides the Fibonacci numbers in its shallow diagonals, the powers of 11 in its rows and the triangular numbers along a diagonal. Teachers use it to show how one simple rule can contain many patterns.
How the Pascal's triangle is worked out
Each entry is the sum of the two above it. Row n (counting the top row as row 1) has n entries and sums to 2 to the power n − 1. Entry k of row n is the combination C(n − 1, k − 1). Eight rows end with 1, 7, 21, 35, 35, 21, 7, 1, which adds up to 128 = 2⁷. The fifth row, 1 4 6 4 1, gives the coefficients of (a + b)⁴.
Every answer on this page comes from that one rule, so you can check any result by hand with a calculator. The figures shown underneath, such as other units, are conversions of the same answer.
- Exact big numbers
- Up to 60 rows
- Row sum and largest entry shown
Mistakes to avoid with Pascal's triangle
Rows grow quickly: the middle entry of row 60 has 17 digits, so the display scrolls sideways on a narrow screen. Copy the text to a document if you want to keep it. Counting rows from 0 is also common, so check which convention your book uses.
On phone and computer
On a phone, type into the boxes one after another and read the Pascal's triangle underneath; Copy result puts it on the clipboard for a message or a note. On a computer the inputs sit on the left and the answer on the right, so you can change one figure and watch the Pascal's triangle move. The pascal's triangle generator works the same on both. Each row holds binomial numbers, so Permutation and Combination Calculator and Binomial Distribution Calculator use them. Fibonacci Calculator finds the pattern along diagonals, and Factorial Calculator shows where the numbers come from.
Features
- Rows count from 1 here
- Edges are ones
- Row sums are powers of 2
- Clear messages when the Pascal's triangle inputs make no sense
- Copy the result with one tap
- Private: nothing is uploaded
Frequently asked questions
How do I calculate Pascal's triangle?
Each entry is the sum of the two above it. Row n (counting the top row as row 1) has n entries and sums to 2 to the power n − 1. Entry k of row n is the combination C(n − 1, k − 1). Eight rows end with 1, 7, 21, 35, 35, 21, 7, 1, which adds up to 128 = 2⁷. The fifth row, 1 4 6 4 1, gives the coefficients of (a + b)⁴.
What is the formula for Pascal's triangle?
Each entry is the sum of the two above it. Row n (counting the top row as row 1) has n entries and sums to 2 to the power n − 1. Entry k of row n is the combination C(n − 1, k − 1). The pascal's triangle generator applies it exactly and rounds only the displayed answer to six significant figures.
How do I use Pascal's triangle to expand (a + b)^n?
Take row n + 1 of the triangle (counting the top row as row 1). Its numbers are the coefficients of the terms.
What is the sum of a row?
2 raised to the power of the row number minus one. The first row sums to 1, the second to 2, the third to 4.
What is the largest number the tool can show?
With 60 rows, the largest entry is the middle number of row 60, 59,132,290,782,430,712, shown exactly.
Is this pascal's triangle generator free and private?
Yes. It is free, needs no account and runs in your browser, so the numbers you type are not uploaded or stored.