What this calculator does
Beer pong cups are stacked in a triangle, and a triangle of any size follows the same rule: the number of cups in a rack with n cups along the back row is n(n+1)/2, the nth triangular number. The familiar 10-cup pyramid is just the case where n is 4, since 4 + 3 + 2 + 1 = 10.
Not every house or tournament plays the same rack size. Some games use 6 cups a side for a faster round, others stretch to a bigger rack for a longer game. This calculator takes whatever back-row size you actually play with and works out cups per side and the total needed for both ends of the table.
The formula
Cups per side is the sum of every row from 1 up to the number of cups along the back, which has the closed form n(n+1)/2. Doubling that figure accounts for both sides of the table, since each side racks its own identical triangle.
| Term | Meaning |
|---|---|
| n | The number of cups along the back row, which sets the size of the triangle. |
| Cups per side | The total cups in one triangle rack: n(n+1)/2. |
| Total cups | Cups per side counted twice, once for each end of the table. |
The inputs explained
| Field | What to enter |
|---|---|
| Cups along the back row (rack size) | The number of cups along the back row of the rack you play with (4 gives the standard 10-cup triangle). |
When to use it
Buying cups before a party
Knowing the exact count needed for both sides, rather than guessing, means arriving with the right number of cups instead of running short mid-game or buying a pack far larger than needed.
Agreeing house rules before playing
Groups that play 6-cup games rather than the standard 10-cup pyramid can check the total either format actually needs before setting up.
Running a tournament with a non-standard rack
A larger or smaller triangle changes the total cup count fast, since the count grows roughly with the square of the back-row size, so it is worth checking before ordering supplies for several tables.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How many cups does each rack size need?
The cup count for a range of common triangle sizes, from a quick 2-cup game up to a stretched 10-cup pyramid.
Questions
How many cups are in a standard beer pong rack?
The usual pyramid has a back row of 4 cups, giving 4 + 3 + 2 + 1 = 10 cups per side, 20 cups in total across both ends of the table.
Why does the cup count grow so much faster than the back row?
Cups per side is a triangular number, n(n+1)/2, which grows roughly with the square of n. Doubling the back row from 4 to 8 does not double the cups, it roughly quadruples them, from 10 to 36 per side.
What is a 6-cup game?
Some groups rack a smaller triangle with a back row of 3, giving 6 cups per side and 12 in total, for a shorter game with fewer cups to clear.
Is this the same maths as other triangular arrangements?
Yes. Any triangle stacked the same way, whether cups, bowling pins or a stack of cans, uses the identical n(n+1)/2 formula. The triangle number calculator covers that formula generally, for any n and in either direction.
For the general version of this formula, including checking whether a given total is a triangular number, see the triangle number calculator.