Powerball Odds Calculator (Jackpot and All Tiers)
Calculate Powerball odds for jackpot and all 9 prize tiers.
Multiple-ticket math, expected value at any jackpot size, and the math against you.
Powerball draws 5 white balls from 1-69 plus 1 red Powerball from 1-26. Jackpot odds:
P(jackpot) = 1 / (C(69,5) × 26) = 1 / 292,201,338
Where C(69,5) = 69! / (5! × 64!) = 11,238,513 white-ball combinations.
You are about 25 times more likely to be killed by lightning in your lifetime (1 in 12 million) than to win the Powerball jackpot (1 in 292 million) on a single ticket.
All nine prize tiers and their probabilities (US Powerball):
| Match | Prize | Odds | Probability |
|---|---|---|---|
| 5+PB | Jackpot | 1 in 292,201,338 | 0.0000003% |
| 5 | $1,000,000 | 1 in 11,688,053 | 0.0000086% |
| 4+PB | $50,000 | 1 in 913,129 | 0.000110% |
| 4 | $100 | 1 in 36,525 | 0.00274% |
| 3+PB | $100 | 1 in 14,494 | 0.00690% |
| 3 | $7 | 1 in 580 | 0.173% |
| 2+PB | $7 | 1 in 701 | 0.143% |
| 1+PB | $4 | 1 in 92 | 1.087% |
| 0+PB | $4 | 1 in 38 | 2.602% |
Overall odds of winning ANY prize: 1 in 24.9 (about 4%).
Expected value of a $2 Powerball ticket. EV depends on jackpot size, taxes, and number of tickets sold (which affects split probability). Without considering jackpot splits or taxes:
EV = Σ(Probability × Prize) - Cost
At a $50M jackpot, EV is about -$1.30 (you lose $1.30 per $2 ticket on average). At a $1B jackpot, EV approaches break-even before taxes. Once you account for split probability (millions of tickets sold means jackpot might be split among multiple winners) and taxes (24% federal withholding plus state, plus the 50% lump-sum discount), Powerball is mathematically a losing bet at every realistic jackpot size.
The “lump sum vs annuity” choice. Powerball pays jackpot two ways:
- 30-year graduated annuity: face value, payments grow ~5% per year
- Lump sum: ~50% of advertised jackpot, paid upfront
If you take the $1B advertised jackpot:
- Lump sum: ~$500M before taxes, ~$320M after federal/state taxes
- Annuity: $1B over 30 years, ~$24M-$66M per year, after taxes roughly $640M total over 30 years
The annuity wins on total dollars but lump sum wins on present value (especially if you can earn 5%+ annually). Most winners take lump sum because of the inflation-and-investment-flexibility argument.
Multiple ticket math. Buying N tickets multiplies your odds linearly:
- 1 ticket: 1 in 292M
- 10 tickets: 1 in 29.2M
- 100 tickets: 1 in 2.92M
- 1,000 tickets: 1 in 292,000
- 1 million tickets: 1 in 292
Even a million tickets ($2M cost) gives you a 0.34% chance of the jackpot. Pooling syndicates work this way — split cost, split winnings.
The “guaranteed win” myth. Buying every possible combination of 292 million tickets at $2 each costs $584 million — more than most jackpots advertised. Even when the advertised jackpot exceeds that cost, you must consider:
- Lump sum is ~50% of advertised
- Taxes take another ~37%
- Split probability if multiple winners
- Time and logistics of buying that many tickets
- States limit retailer ticket sales per draw
Mathematically, “guaranteed win” Powerball strategies have lost real money the few times they have been attempted at scale.
Why people play anyway. EV math is irrelevant to most lottery purchasers. The $2 buys a few days of “what if I won” daydreaming. As an entertainment expense the math works fine. As an investment it does not.
Worked example. A $400M advertised jackpot.
- Lump sum: $200M
- After federal 37% tax: $126M
- After 5% state tax: $120M
- Probability of winning jackpot on 1 ticket: 1 / 292.2M
- EV from jackpot alone: $120M / 292.2M = $0.41
- EV from lower tier prizes: ~$0.32
- Total EV: $0.73 against $2 ticket cost = -$1.27 per ticket
You lose $1.27 in expected value per ticket. A 100-ticket purchase loses $127 in EV. The bigger the jackpot, the smaller (but never zero, never positive in real terms) the loss.