MATH · LOTTERY ODDS
Lottery Odds Calculator
Calculate exact lottery prize-tier odds for any pool size. See "1 in X" probability and percentage for the jackpot and every lower prize tier — configurable for Powerball, Mega Millions, or any lottery.
| Tier | Odds | Probability |
|---|---|---|
| Match 5 + Powerball (Jackpot) | 1 in 292,201,338 | 3.422e-7% |
| Match 5 (no Powerball) | 1 in 11,688,054 | 0.000008556% |
| Match 4 + Powerball | 1 in 913,129 | 0.000110% |
| Match 4 (no Powerball) | 1 in 36,525 | 0.002738% |
| Match 3 + Powerball | 1 in 14,494 | 0.006899% |
| Match 3 (no Powerball) | 1 in 580 | 0.172484% |
| Match 2 + Powerball | 1 in 701 | 0.142587% |
| Match 2 (no Powerball) | 1 in 28 | 3.5647% |
| Match 1 + Powerball | 1 in 92 | 1.0872% |
| Match 1 (no Powerball) | 1 in 4 | 27.1806% |
| Powerball only | 1 in 38 | 2.6093% |
Odds are calculated mathematically from the pool sizes you enter. Actual lottery rules may differ slightly from this model. Purchasing lottery tickets does not improve your statistical odds.
About This Calculator
Every lottery ticket is a combinatorics problem. This calculator shows you the exact mathematical odds for every prize tier — jackpot, match-5, match-4, and so on — for any pool size you configure. The default is Powerball (69 white balls, pick 5, plus 26 power balls), but you can adjust the numbers to match Mega Millions, EuroMillions, or any other lottery.
How It Works
Enter the total white ball pool size, how many balls are drawn (the "pick"), and the power ball pool size. The calculator uses C(n,k) combinatorics (combinations without replacement) to compute the exact number of ways to win each tier and divides by the total possible ticket combinations (C(pool, pick) × power ball count) to get the probability.
The Formula
Total = C(n, k) × p Win (j white + PB) = C(k,j) × C(n−k, k−j) Odds = Total ÷ Wins
- n
- White ball pool size
- k
- White balls drawn (pick size)
- p
- Power ball pool size
- j
- Number of white balls matched in this tier (0 ≤ j ≤ k)
Frequently Asked Questions
- What are the odds of winning Powerball?
- With the default Powerball configuration (69 white balls, pick 5, 26 power balls), the jackpot odds are 1 in 292,201,338. The total ticket combinations are C(69,5) × 26 = 11,238,513 × 26.
- How do prize-tier odds work?
- Each tier is defined by how many white balls you match and whether you match the power ball. Matching fewer white balls is more likely because there are more ways to partially match than to match all. The power ball adds an additional factor of 1 (match) or p−1 (miss).
- Why use C(n,k) and not n!/k!(n−k)! directly?
- C(n,k) is the same formula but computed multiplicatively, which is far more numerically stable for large n — this calculator uses the same BigInt-guarded algorithm as the Permutation and Combination calculator to avoid silent Infinity.
- Can I use this for lotteries without a power ball?
- Set the power ball pool to 1. This means there is exactly one "power ball" option, which is always "correct", effectively removing the bonus ball from the calculation.