Pascal's Triangle Calculator
Any row of Pascal's triangle and the binomial expansion.
Enter your values
ⓘ Live results
Results
- Row 7
- 1, 7, 21, 35, 35, 21, 7, 1
- C(7, 3)
- 35
- Row sum
- 128
- Largest entry
- 35
- Expansion of (a + b)ⁿ
- a^7b^0 + 7a^6b^1 + 21a^5b^2 + 35a^4b^3 + 35a^3b^4 + 21a^2b^5 + 7a^1b^6 + a^0b^7
Quick answer
Row n of Pascal's triangle holds the binomial coefficients C(n, 0) through C(n, n), and every entry is the sum of the two above it.
C(n, k) = n! ÷ (k!(n − k)!)
How to use the Pascal's Triangle Calculator
- 1Enter the row number, counting the single 1 at the top as row 0.
- 2Enter a position k to pull one coefficient out.
- 3Use the row directly as the coefficients of a binomial expansion.
Worked example
Using the values the calculator loads with:
Inputs
- Row number n7
- Position k in the row3
Results
- Row 71, 7, 21, 35, 35, 21, 7, 1
- C(7, 3)35
- Row sum128
- Largest entry35
- Expansion of (a + b)ⁿa^7b^0 + 7a^6b^1 + 21a^5b^2 + 35a^4b^3 + 35a^3b^4 + 21a^2b^5 + 7a^1b^6 + a^0b^7
Frequently asked questions
Why does each row sum to 2ⁿ?
Because it counts every possible subset of n items — each item is either in or out.
Where do the Fibonacci numbers hide?
Along the shallow diagonals: sum the diagonal entries and you get 1, 1, 2, 3, 5, 8 and so on.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.