Lottery Odds Calculator

How Lottery Odds Work

Lottery odds measure how likely you are to match a specific number of balls drawn from a pool. The calculation uses combinations to count total possible draws versus winning draws. For a standard 6/59 lottery, the jackpot odds are 1 in 45,057,474. See also the Permutation and Combination Calculator and Probability Calculator.

Lottery Odds Formula

$$\text{Odds} = \frac{C(n, r)}{C(r, m) \times C(n-r, r-m)}$$

Where $n$ is the pool size, $r$ is balls drawn, and $m$ is the number of matches.

Example: 6/49 Lottery Jackpot

For a 6/49 game matching all 6 numbers: $C(49, 6) = 13{,}983{,}816$. With $m = 6$, the winning combinations equal 1, giving odds of 1 in 13,983,816.

Related Tools

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• Implied Probability Calculator
• Hypergeometric Distribution Calculator