Pascal's Triangle Calculator

Your details

Triangle mode shows the full triangle layout. Entry mode finds one specific cell. Row-sum mode gives the total of all numbers in a row.
How many rows to generate, counting from row 0. Max 20 rows.
rows
Row index, starting from 0. Row 0 is just "1".
C(n, k)Medium coefficient
20

The binomial coefficient at row n, column k

Row sum64
Row maximum20
Triangle rowsRow 0: 1 Row 1: 1 1 Row 2: 1 2 1 Row 3: 1 3 3 1 Row 4: 1 4 6 4 1 Row 5: 1 5 10 10 5 1 Row 6: 1 6 15 20 15 6 1
C(n, k)20
Row sum64
Row max20

First 7 rows of Pascal's triangle

  • The triangle has 7 rows (row 0 through row 6).
  • Row 6 sums to 2^6 = 64.
  • Every interior entry equals the sum of the two entries directly above it in the previous row.
  • Rows are symmetric: C(n, k) = C(n, n-k) for every position.

Next stepSwitch to Entry mode to look up any individual binomial coefficient C(n, k).

 = Powered by OnlyCalculators