Draw Pascal's Triangle

Pascal's triangle is the quiet engine behind a surprising amount of mathematics. Each entry is the sum of the two entries above it, and that one rule produces the coefficients of every binomial expansion, the combination counts C(n, k), the powers of two, the Fibonacci numbers hiding in the shallow diagonals, and even the number of paths through a grid. Draw a few rows by hand and you will mistype; draw 15 rows and you will lose an afternoon.

Draw Pascal's Triangle prints it for you — any number of rows up to 30, in a properly centred pyramid layout, with every coefficient computed using exact BigInt arithmetic. Each row's sum (always a power of two) is shown, along with the central coefficient, and the output can be copied or downloaded for worksheets, slides and homework. Whether you need (x + y)⁶ expanded, C(20, 3) checked, or a beautiful pattern to explore, the answer is one click away.

• 1 to 30 rows: Draw as little or as much of the triangle as you need, instantly.
• Exact BigInt coefficients: Every entry is computed with arbitrary-precision integers — the 30th row is exact to the last digit.
• Centred pyramid layout: The triangle is aligned so the structure is visible at a glance, like a textbook diagram.
• Row sums shown: Each row is annotated with its sum, demonstrating that row n totals 2ⁿ.
• Central coefficient option: Highlight the largest coefficient in the row you generate — useful for combination problems.
• Live redraw: Change the row count and the triangle redraws instantly.
• Copy or download: Take the whole triangle to the clipboard or save it as a text file.
• Free and private: All computation happens in your browser; nothing is uploaded.

1. Choose the number of rows. Set the row count between 1 and 30. Row 1 is the single top 1, row 2 is "1 1", and so on.
2. Decide whether to show sums. Tick "Show row sums" to annotate each row with its total, which equals 2ⁿ.
3. Optionally mark the centre. Tick "Highlight central coefficient" to point at the biggest number in the final row.
4. Read the triangle. The output prints as a centred monospace pyramid.
5. Grab a row for binomial expansion. Copy the whole triangle and pick out row n for the coefficients of (x + y)ⁿ.
6. Copy or download. Use the buttons to take the triangle elsewhere.

Example 1 — Expand (x + y)⁴. Draw 5 rows. The fifth row reads 1 4 6 4 1, so the expansion is x⁴ + 4x³y + 6x²y² + 4xy³ + y⁴ — coefficients, sign and symmetry all at once.

Example 2 — Count combinations. A committee of 3 chosen from 12 people: C(12, 3). Draw 13 rows and read position 3 of row 12 — 220. No factorial arithmetic needed.

Example 3 — Verify the powers of two. Draw 10 rows with row sums on: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512. The pattern 2ⁿ is visible immediately.

Example 4 — Find Fibonacci numbers. The sums of the shallow diagonals of Pascal's triangle are the Fibonacci numbers. Draw 12 rows and add the diagonal 1, 1+1, 1+2+1, 1+3+3+1… to see 1, 2, 4, 8? No — sum the diagonal entries properly: 1, 1, 2, 3, 5, 8, 13, 21 appear along the slanted lines.

• Perfect binomial coefficients: Every row of (x + y)ⁿ is exact and ready to use.
• Exact at any size: BigInt arithmetic keeps 30-row triangles perfectly precise.
• Instant combination answers: C(n, k) is read straight off the triangle.
• Patterns become visible: Powers of two, Fibonacci diagonals and symmetry are obvious in a properly drawn triangle.
• Time saved: Drawing 20 rows by hand takes minutes and invites mistakes; this takes one click.
• Free and private: Runs entirely in your browser with nothing uploaded.