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Pascal's triangle generator

Generate Pascal's triangle to any depth, with exact big-integer entries. Each number is the sum of the two above it, and row n holds the binomial coefficients — the coefficients of (a+b)ⁿ. The triangle hides the Fibonacci numbers, powers of two, and the Sierpinski pattern.

Related tools

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Pascal's triangle generator is free to use as often as you like, directly from this page. You will find it under Sequences & series, with Angle Bisector Calculator (triangle) and Equilateral triangle calculator for the neighbouring cases.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What is Pascal's triangle generator?

Generate Pascal's triangle to any depth, with exact big-integer entries. Each number is the sum of the two above it, and row n holds the binomial coefficients — the coefficients of (a+b)ⁿ. The triangle hides the Fibonacci numbers, powers of two, and the Sierpinski pattern.

What does a concrete case look like?

n = 5 → 1, 5, 10, 10, 5, 1 — the tool shows every step in between, not just the final figure.

When would I actually use this?

Finding the nth term without listing every one before it, summing a long run in one step, and recognising which family a sequence belongs to.

What is the most common mistake?

Starting the index at the wrong end. Whether the first term is a₀ or a₁ shifts every result by one position, and the two conventions are both common.

How is Pascal's triangle generator different from Angle Bisector Calculator (triangle)?

They sit next to each other but answer different questions: Angle Bisector Calculator (triangle) is the one to open when you need it to enter the three sides or the three vertices and get the length of each internal angle bisector, the incenter, the inradius, and the exact point where every bisector cuts the opposite side. The angle bisector theorem is the heart of it: the bisector splits the opposite side in the ratio of the two adjacent sides. The triangle inequality is checked before anything is computed, and the triangle is drawn with its three bisectors. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Equilateral triangle calculator is the closest one after this: Compute the area, height and perimeter of an equilateral triangle from its side.

What else is worth having open alongside it?

General Triangle Solver and Triangle area calculator (Heron's formula) — they come up in the same task often enough to be worth a second tab.

Where do the figures come from?

The closed forms are the standard ones, and the tool states the indexing convention it uses so a result can be compared against a textbook without ambiguity.

Further reading

All guides →
How-toHow to Find the Area of a Triangle: Base × Height and Heron's FormulaTwo reliable ways to find a triangle's area: half base times height when you know the height, and Heron's formula when you only know the three sides.ExplainerFibonacci and the Golden RatioThe Fibonacci sequence adds each pair of terms to make the next; the ratio of neighboring terms homes in on the golden ratio φ ≈ 1.618. See how, and where the pattern turns up.ExplainerThe Flat Pattern of a Cone Is a Sector, Not a CircleRoll a 50 mm cone 80 mm tall and its pattern is a 190.8° slice of a 94 mm circle. Flatten a nearly cylindrical lampshade and the pattern radius runs to 839 mm — the shallower the taper, the further away the apex.ExplainerA 1 % Drop Rate Does Not Mean One Hundred RunsAt 1 %, a hundred attempts give you 63.4 % — not certainty. Ninety per cent takes 230 attempts and ninety-nine takes 459, and more than a third of players are still empty-handed at a hundred.ExplainerWhat Is a Z-Score? Standard Deviations Above the MeanA z-score is z = (x − μ) / σ — how many standard deviations a value sits from the mean. Learn how to compute it, read the standard normal curve, and turn it into a percentile.How-toHow to Find the Distance Between Two PointsUse the distance formula d = √((x₂−x₁)² + (y₂−y₁)²) to measure the straight-line distance between two points on a plane, with a worked example and the midpoint too.