Pascal's Triangle Calculator
Any row of Pascal's triangle and the binomial expansion.
Enter your values
Enter the row number n you are working with.
Enter the position k in the row you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- 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)!)
At a glance
| What it does | Any row of Pascal's triangle and the binomial expansion. |
|---|---|
| Category | Math |
| Inputs needed | Row number n, Position k in the row |
| Main output | Row 7 |
| Formula | C(n, k) = n! ÷ (k!(n − k)!) |
| Cost | Free — no sign-up, no download |
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.
Inputs explained
- Row number n
- Enter the row number n you are working with.
- Position k in the row
- Enter the position k in the row you are working with.
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.
What do I need to enter into the Pascal's Triangle Calculator?
Just 2 values: row number n, position k in the row. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Pascal's Triangle Calculator work out the 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. It applies the formula C(n, k) = n! ÷ (k!(n − k)!) and shows the working so you can check each step by hand.
Is the Pascal's Triangle Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.