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Pascal's Triangle Calculator.

Generate one row of Pascal's triangle using exact integer coefficients.

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01

Set your values

Results update as you type.

row: 5

row

0.000000
coefficients: 1, 5, 10, 10, 5, 1

coefficients

1, 5, 10, 10, 5, 1

Results update automatically as you type.

Use Cases

Binomial expansion

Quickly get the coefficients for expanding (a+b)^n without manual calculation. Each row corresponds to the coefficients of the expansion.

Example: For (x+y)^5, row 5 gives 1, 5, 10, 10, 5, 1.

Combinatorics and probability

Find the number of ways to choose k items from n (n choose k) by reading the k-th entry in row n. Useful for probability problems and counting.

Example: Row 6, entry 2 is 15, so C(6,2)=15.

Frequently Asked Questions

What is Pascal's triangle?
Pascal's triangle is a triangular array of numbers where each number is the sum of the two directly above it. The rows are numbered starting from 0, and each row contains the coefficients of the binomial expansion (a+b)^n.
How do I use this calculator?
Simply enter the row number (0–50) you want to generate. The calculator will display the exact coefficients for that row. For example, row 4 gives 1, 4, 6, 4, 1.
What can I use a row of Pascal's triangle for?
Rows of Pascal's triangle are used in algebra for binomial expansions, in combinatorics to find combinations (n choose k), and in probability for binomial distributions. They also appear in patterns like Fibonacci numbers and powers of 2.

Tips & Common Mistakes

Tips

  • Remember that row numbers start at 0, so row 0 is just '1'.
  • Each row has n+1 entries, where n is the row number.
  • The sum of all numbers in row n equals 2^n.
  • Use the calculator to verify your manual calculations or to explore patterns.

Common Mistakes to Avoid

  • Entering a row number greater than 50, which is outside the calculator's range.
  • Confusing row numbers: row 1 is '1 1', not '1'.
  • Assuming the first entry is 0; it is always 1.

Last updated: August 13, 2026