Lottery Odds Calculator
Calculate exact winning probabilities for any lottery game. See every prize tier from jackpot to the smallest match.
Select a Lottery Game
Total Combinations
292,201,338
Jackpot Odds
1 in 292,201,338
Prize Tiers
11
All Prize Tiers
Odds for every possible match level
| Match | Odds |
|---|---|
| Match 5 + PowerballJackpot | 1 in 292,201,338 |
| Match 5 main only | 1 in 11,688,053 |
| Match 4 + Powerball | 1 in 913,129 |
| Match 4 main only | 1 in 36,525 |
| Match 3 + Powerball | 1 in 14,494 |
| Match 3 main only | 1 in 579 |
| Match 2 + Powerball | 1 in 701 |
| Match 2 main only | 1 in 28 |
| Match 1 + Powerball | 1 in 91 |
| Match 1 main only | 1 in 3 |
| Match Powerball only | 1 in 38 |
How It Works
This calculator uses the combination formula C(n, k) = n! / (k!(n-k)!) to compute exact odds for every match tier. All arithmetic is performed with BigInt to avoid rounding errors on large factorials.
Interpretation
“1 in X” means that, on average, you would need X tickets to achieve that match level once. Each ticket is an independent event — past draws do not influence future ones.
Understanding Lottery Mathematics
Every lottery draw is governed by combinatorics — the branch of mathematics that counts the number of ways to choose items from a set. The core formula is the combination function C(n, k), which tells you how many unique groups of k items can be selected from a pool of n. Because order does not matter in lottery draws, combinations (not permutations) are the correct calculation.
Powerball Example
| Component | Calculation | Result |
|---|---|---|
| Main numbers (5 from 69) | C(69, 5) | 11,238,513 |
| Powerball (1 from 26) | × 26 | 26 |
| Jackpot odds | 1 in 292,201,338 |
Lower prize tiers are calculated by finding the number of ways to match some of the drawn numbers while simultaneously mismatching the rest. For instance, matching exactly 3 of 5 main numbers requires choosing 3 winners from the 5 drawn (C(5, 3)) and 2 losers from the 64 undrawn (C(64, 2)), then dividing by the total combinations.
This calculator uses BigInt arithmetic to handle the very large factorials involved, ensuring every result is exact rather than a floating-point approximation. Whether you play Powerball, Mega Millions, EuroMillions, UK Lotto, or a custom format, the math is computed precisely in your browser.
Frequently Asked Questions
How are lottery odds calculated?
Lottery odds are calculated using the mathematical combination formula C(n,k) = n! / (k!(n-k)!). For example, Powerball requires matching 5 numbers from 69, giving C(69,5) = 11,238,513 main-ball combinations. Multiply by the 26 possible Powerballs and the jackpot odds are 1 in 292,201,338.
What is the difference between odds and probability?
Probability expresses the chance of an event as a fraction between 0 and 1. Odds express it as a ratio, such as "1 in 292 million." Both convey the same information in different formats. Our calculator displays odds in the "1 in X" format because it is the most intuitive for lottery players.
Which lottery has the best odds of winning the jackpot?
Among major lotteries, games with smaller number pools have better jackpot odds. For example, a 6/49 format like UK 49s has far better odds than Powerball or Mega Millions. However, smaller-pool games typically offer smaller jackpots. Use the calculator above to compare exact odds across every supported game.
Do my odds improve if I buy more tickets?
Yes, each unique ticket gives you one additional chance. Buying 10 tickets makes you 10 times more likely to win than buying 1. However, even 10 tickets for Powerball gives you roughly a 1 in 29 million chance — still extremely unlikely. The expected value of a lottery ticket is almost always negative.
What are the odds of matching some but not all numbers?
Partial-match odds are calculated by combining the ways to choose the correct numbers from the drawn set with the ways to choose incorrect numbers from the remaining pool. Our calculator shows every prize tier so you can see exactly how likely each partial match is.
Does choosing your own numbers change the odds?
No. Every combination has the same probability of being drawn whether you pick the numbers yourself or use a quick pick. Choosing less-popular numbers does not improve your odds of winning, but it can reduce the chance of splitting a jackpot with other winners.