Lottery Odds Calculator
Work out the real odds of any lottery: the jackpot, matching fewer numbers, and how many tickets you'd need for a meaningful chance. Pick a real lottery or enter your own numbers. Every answer shows the exact combination count.
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See how your odds change with more tickets. They still barely move.
Check your lottery's current rules before relying on these numbers. Formats change from time to time.
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Practice questions
Five fresh questions each time, with worked answers. Teachers can print them as a worksheet with an answer key, or save it as a PDF from the print window.
How lottery odds are actually worked out
A lottery ticket is a combination: the order you write the numbers in doesn't matter, and once a ball is drawn it isn't drawn again. So the number of possible tickets is C(n, r), the number of ways to choose r numbers from n, with no repeats and no order.
Powerball draws 5 main numbers from 69, plus 1 Powerball from a separate pool of 26. The main numbers alone give C(69, 5) = 11,238,513 combinations. Multiply by the 26 possible Powerballs and you get 292,201,338 total combinations, so a single ticket has a 1 in 292,201,338 chance of the jackpot.
The formula
Combinations = C(n, r) × C(b, k)
n is the main pool, r is how many you pick from it, b is the bonus pool, and k is how many bonus numbers you pick. If there's no bonus draw, leave that part out entirely.
Real lottery odds
| Lottery | Format | Jackpot odds |
|---|---|---|
| Powerball (US) | 5 from 69, plus 1 from 26 | 1 in 292,201,338 |
| Mega Millions (US) | 5 from 70, plus 1 from 25 | 1 in 302,575,350 |
| EuroMillions | 5 from 50, plus 2 from 12 | 1 in 139,838,160 |
| UK Lotto | 6 from 59 | 1 in 45,057,474 |
| Classic 6 from 49 | 6 from 49 | 1 in 13,983,816 |
UK Lotto used to draw from 49 balls, giving odds of 1 in 13,983,816. In October 2015 the pool was expanded to 59 balls, making the jackpot roughly three times harder to win in exchange for bigger rollovers. It's a good example of how a small change to n has a large effect on C(n, r).
Why more tickets barely help
Buying 10 Powerball tickets, each with different numbers, gives you 10 in 292,201,338, which is about 1 in 29,220,134. That's ten times better, and still a chance smaller than being dealt a royal flush. Buying every single combination would guarantee a win, but for Powerball that's over 292 million tickets at $2 each, far more than any realistic jackpot.
Matching fewer numbers
Lotteries pay smaller prizes for partial matches. For a 6 from 49 draw, matching all 6 is 1 in 13,983,816, but matching just 3 is far more common, about 1 in 57. The chance of matching exactly k of the r numbers drawn, from a pool of n, is C(r, k) × C(n−r, r−k) divided by C(n, r): choose k of the winning numbers and the rest from the numbers that weren't drawn.
Mistakes people make
Thinking "hot" and "cold" numbers matter. Each draw is independent of the last. A number that hasn't appeared in months is exactly as likely as one drawn last week.
Confusing the jackpot odds with the odds of winning something. Powerball's overall odds of winning any prize are about 1 in 24.9, because most prizes only need a few matches. The jackpot is the rarest tier by a huge margin.
Assuming picking unpopular numbers changes your odds. It doesn't change your chance of winning, only how much you'd share the jackpot with other winners if you did.
How we calculate
Every combination count uses exact whole-number arithmetic (JavaScript BigInt), so the numbers shown are exact, however large. The match-table probabilities are computed directly from the hypergeometric distribution, the same maths used on the card probability calculator for drawing hands from a deck. Every number in the reference table was checked against official lottery odds pages. If you spot a mistake, let us know and we'll correct it and note the change here.
References
- Sheldon Ross, A First Course in Probability, 10th edition, Pearson, 2019.
- Official Powerball, Mega Millions, EuroMillions and UK National Lottery odds pages, checked September 2026.
- National Weather Service, "How Dangerous Is Lightning?", weather.gov/safety/lightning-odds, checked September 2026. Source for the lightning comparison in the reality check above.
Related calculators
- Combinations and Permutations Calculator, the full counting toolkit this page is built from
- Birthday Problem Calculator, another famously surprising probability
- Card Probability Calculator, for poker hand odds using the same maths
- Probability Calculator, the full set of tools
Questions people ask
What are the odds of winning the Powerball jackpot?
1 in 292,201,338. That comes from C(69, 5) × 26, the ways to pick 5 main numbers from 69 times the 26 possible Powerballs.
Does buying more tickets meaningfully improve my odds?
It improves them proportionally, but the numbers are so large that even 1,000 tickets leaves you at roughly 1 in 292,000 for Powerball, still very unlikely.
Do certain numbers come up more often?
No, not for a fair, properly run lottery. Each draw is independent, so past results don't affect future ones.
Why did UK Lotto's odds get worse in 2015?
The main pool grew from 49 to 59 balls, which increases C(n, r) sharply. That single change made the jackpot about three times harder to win.