Lottery Odds Calculator
Calculate the odds of winning a lottery jackpot from the number pool, how many numbers are drawn, and an optional bonus ball.
How it works
Total combinations = C(pool, drawn) × C(bonus pool, bonus drawn) · Jackpot odds = 1 in that total · where C(n,k) = n! ÷ [k!(n−k)!]
A lottery jackpot requires matching an unordered set of numbers, so the count of possible tickets is a combination, C(n, k). A separate bonus ball (like the Powerball) multiplies the main combinations by the bonus pool's own combinations, which is why games with an extra ball have such astronomically long odds. Because order does not matter, C(n, k) is far smaller than the number of ordered arrangements — but still enormous for real lotteries.
Worked example
A 6-from-49 game: C(49, 6) = 13,983,816, so the jackpot odds are 1 in about 14 million. Add a bonus ball drawn from a separate pool of 10 and you multiply by C(10, 1) = 10, giving roughly 1 in 140 million.
Sources: Combination — Wikipedia · Lottery mathematics — Wikipedia
Frequently asked questions
Why does a bonus ball make winning so much harder?
The bonus ball comes from its own pool, so its combinations multiply the main odds. Adding a 1-from-26 Powerball to a 5-from-69 game multiplies ~11.2 million by 26, giving about 1 in 292 million — the extra ball alone makes it 26 times harder.
Does buying more tickets meaningfully improve my odds?
Only linearly, and from a tiny base. Buying 10 tickets in a 1-in-14-million game moves you to 10 in 14 million — still effectively zero. It is spending, not a strategy.
Are these odds for the jackpot or any prize?
These are the jackpot (match-all) odds. Lower-tier prizes for matching some of the numbers are much more likely, and their odds are computed from partial-match combinations, which this calculator does not break out.
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This calculator is for educational purposes. Double-check important results before acting on them.