Pascal's Triangle

Binomial coefficients in Pascal's triangle

About this calculator

The Pascal's Triangle Calculator builds the triangle of binomial coefficients row by row and highlights any cell C(n, k) together with the two cells above it. It shows how Pascal's rule C(n, k) = C(n−1, k−1) + C(n−1, k) generates each entry, the binomial-coefficient formula n! / (k!(n−k)!), and the row sum 2ⁿ. Useful for combinatorics, the binomial theorem, and probability.

How to use the Pascal's Triangle calculator

  1. Enter the values for your problem into the input fields.
  2. Read the result — it updates instantly as you type.
  3. Check the formula and the visual explanation to follow how the answer was found.
  4. Copy the page URL to share the exact calculation.

Common examples

  • Row 4 is 1 4 6 4 1 — the coefficients of (a + b)⁴
  • C(4, 2) = 6 = C(3, 1) + C(3, 2) = 3 + 3 (Pascal's rule)
  • The edges are all 1: C(n, 0) = C(n, n) = 1
  • Each row sums to a power of two: row 4 sums to 16 = 2⁴
  • Every row reads the same forwards and backwards: C(n, k) = C(n, n−k)

Frequently asked questions

How does the Pascal's Triangle calculator work?

Enter your values and the calculator applies the exact mathematical method for this problem, showing the result together with the formula it used. Everything is computed with high-precision arithmetic, so the answer you see is not limited by ordinary floating-point rounding.

When would I use the Pascal's Triangle calculator?

It is useful for homework and exam preparation, for checking work done by hand, and whenever a step in a larger problem needs this calculation done quickly and reliably.

How accurate are the results?

Calculations run at 30 significant digits of precision internally. Displayed values are rounded for readability, but the underlying result is far more precise than a typical hand or pocket-calculator computation.

Can I share a specific calculation with someone else?

Yes. Every value you enter updates the URL, so copying the address bar and sharing the link reopens the exact same calculation for whoever clicks it.