Room for ChanceThe science of chance

Free interactive tool

Lottery Combinations Calculator

Count exact unordered combinations, with an optional separate number pool. Includes US and UK game presets.

Inputs and results stay in this page. These tools set no cookies, save no browser preferences and send no input data to our server. A CSV downloads only when you request it. Displayed probabilities are rounded; combination counts use exact integer arithmetic.

Understand the result

How Many Lottery Combinations Are There? The C(n,k) Formula explains the derivation and common interpretation errors. Compare it with the published 1-2-3 versus 2-6-9: exact enumeration and one million draws.

Exact C(n,6) counts as the pool grows, displayed on a logarithmic vertical axis. Markers identify 49, 59 and 90. This figure concerns six selected labels; five-label games use their own displayed formulas.
Figure 1. Exact C(n,6) counts as the pool grows, displayed on a logarithmic vertical axis. Markers identify 49, 59 and 90. This figure concerns six selected labels; five-label games use their own displayed formulas.
Download SVGDownload PNG

Related game generators

Generate a valid line for a game without treating this calculation as a prediction.

Powerball generatorEuroMillions generator

Explore all ten tools · See reproducible experiments