Pascal Triangle Row Calculator

Work out pascal triangle row instantly with clear inputs, formula shown and shareable results.

About Pascal Triangle Row Calculator

Row n of Pascal's triangle holds the binomial coefficients C(n, 0) through C(n, n), each the sum of the two entries above it. The row always totals 2ⁿ.

Formulas

Pascal entry

entry(n, k) = C(n, k) = n! / (k!(n−k)!)

Row sum

Σₖ C(n, k) = 2ⁿ

Worked example

With the default values below, Pascal Triangle Row Calculator returns Entry at that position of 15. Change any input above and every figure here is recalculated in your browser.

Inputs used

Row number (top row is 0)accepts 0–40: 6
Entry position in the row (first is 0)accepts 0–40: 2

Results

Entry at that position: 15
Whole row: 1, 6, 15, 20, 15, 6, 1
Row total 2ⁿ: 64
Entries in the row: 7

Step by step

1Values used
2Pascal entry
3Row sum
4Entry at that position= 15
5Whole row= 1, 6, 15, 20, 15, 6, 1
6Row total 2ⁿ= 64
7Entries in the row= 7

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to whole numbers, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What is row 6?

1, 6, 15, 20, 15, 6, 1 — totalling 64 = 2⁶.

Why is each entry the sum of the two above?

Because C(n, k) = C(n−1, k−1) + C(n−1, k): a subset either contains the new element or it does not.