Pascals Triangle Calculator

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Pascal's Triangle Calculator

Generate Pascal's Triangle rows and review its common number patterns in a clean layout.

Last updated: March 2026 | By ForgeCalc Engineering

Pascal's Triangle Generator

Binomial coefficients

Generation Steps

1.Start with a 1 at the top.
2.Each edge of the triangle is 1.
3.Each inner value is the sum of the two values above it.
4.Generate 6 rows of Pascal's Triangle.
Rows Displayed
6

Rows 1 through 6

1
1
1
1
2
1
1
3
3
1
1
4
6
4
1
1
5
10
10
5
1

What Is Pascal's Triangle?

Pascal's Triangle is a triangular array of binomial coefficients where each value is the sum of the two values directly above it.

How to Build Pascal's Triangle

  1. Start with a top row containing a single 1.
  2. Place 1s along the edges of each new row.
  3. Fill the middle values by adding the two numbers above.
  4. Continue for the number of rows you want.
each entry = sum of the two above

Worked Example

Example: the fifth row is 1, 4, 6, 4, 1.

1 4 6 4 1

Frequently Asked Questions

What does each row represent?

Each row contains the binomial coefficients for a power of (x + y).

Why are the edges always 1?

Because there is only one way to choose zero or all items.

Does it relate to probability?

Yes. It is heavily used in combinations and probability problems.

How many rows can I generate?

This calculator caps the view at 15 rows for readability.

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