Lottery odds come from counting combinations. In a game where k balls are drawn from N and you pick k numbers, there are C(N, k) equally likely draws and only one matches your ticket exactly. For a 6/59 game that is 45,057,474 possible draws, so the jackpot odds are 1 in 45,057,474.
Smaller prizes need only some of your numbers to match. To match exactly m numbers, m of the drawn balls must come from your k numbers and the remaining k − m from the N − k numbers you did not pick, which gives the hypergeometric formula above. Many games add a bonus ball. In US games such as Powerball and Mega Millions it comes from a separate drum, which multiplies the jackpot odds by the size of that drum; in UK Lotto a bonus ball is drawn from the remaining main balls and only matters for the “5 + bonus” prize.
Choose a preset or describe your own game. The calculator lists every prize tier with its odds and probability, the overall chance of winning anything, the odds of the tier you select and how the chance grows if you play many draws. Formats were checked against the operators’ published rules in October 2026.
How to use the Lottery Odds Calculator
- Lottery
- Balls in the main pool (N)
- Balls drawn – numbers you pick (k)
- Bonus balls
- Balls in the bonus pool
- Bonus balls drawn
- Fewest main matches that win a prize
- Main numbers matched (for the selected tier) — Values above the number of balls drawn mean all of them.
- Bonus balls matched (for the selected tier) — Ignored for games without a bonus ball.
- Number of draws you play (one ticket each)
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
The tool multiplies hypergeometric probabilities for the main draw and the bonus draw. For a bonus ball drawn from the remaining main balls, the chance that it is one of your unmatched numbers is (k − m)/(N − k). “Any prize” adds up the tiers that pay a prize in the chosen game (for a custom game, every result with at least the minimum number of main matches).
Worked example
In a 6/59 game there are C(59, 6) = 45,057,474 tickets, so the jackpot odds are 1 in 45,057,474. To match exactly 5: choose 5 of your 6 numbers (6 ways) and 1 of the 53 others (53 ways): 318 winning tickets, odds 1 in 141,690. To match exactly 3: C(6, 3) × C(53, 3) = 20 × 23,426 = 468,520 tickets, odds 1 in 96.17. With UK Lotto’s bonus ball the 5-match tier splits: 6 of the 318 tickets also hold the bonus ball (1 in 7,509,579) and 312 do not (1 in 144,415).
Jackpot odds of major lotteries
| Game | Format | Jackpot odds | Any prize |
|---|---|---|---|
| Powerball | 5 of 69 + 1 of 26 | 1 in 292,201,338 | 1 in 24.87 |
| Mega Millions | 5 of 70 + 1 of 24 | 1 in 290,472,336 | 1 in 23.07 |
| EuroMillions | 5 of 50 + 2 of 12 | 1 in 139,838,160 | 1 in 12.97 |
| UK Lotto | 6 of 59 + bonus | 1 in 45,057,474 | 1 in 9.23 |
Formula
P(m main matches) = C(k, m) × C(N − k, k − m) ÷ C(N, k) · separate bonus pool: × C(b, j) × C(M − b, b − j) ÷ C(M, b) · jackpot odds = C(N, k) × C(M, b)
Worked example
Inputs — Lottery: Custom game; Balls in the main pool (N): 59; Balls drawn – numbers you pick (k): 6; Bonus balls: No bonus ball; Fewest main matches that win a prize: 3; Main numbers matched (for the selected tier): 6; Bonus balls matched (for the selected tier): 0; Number of draws you play (one ticket each): 1.
Results — Jackpot odds = 1 in 45,057,474; Game format = Your game: pick 6 of 59; Selected tier = 6 of 6 main numbers; Odds of the selected tier = 1 in 45,057,474; Probability of the selected tier = 2.219 × 10^-6%; Odds of winning any prize = 1 in 92.05.
Key terms
- Combination C(n, k)
- The number of ways to choose k items from n when order does not matter.
- Hypergeometric distribution
- The distribution of matches when drawing without replacement – the basis of lottery odds.
- Bonus ball
- An extra ball, drawn from a separate pool or from the remaining balls, that creates additional prize tiers.
- Odds of 1 in X
- A probability of 1/X; the expected number of attempts per win.
Frequently asked questions
What are the odds of winning the Powerball jackpot?
1 in 292,201,338: C(69, 5) = 11,238,513 white-ball combinations times 26 Powerballs. The odds of winning any prize are about 1 in 24.87.
What are the odds of winning Mega Millions?
Since the April 2025 change to 5 of 70 plus 1 of 24 Mega Balls, the jackpot odds are 1 in 290,472,336 and any prize is about 1 in 23.07.
What are the EuroMillions odds?
5 of 50 plus 2 of 12 Lucky Stars: the jackpot is 1 in 139,838,160 and any of the 13 prize tiers about 1 in 13.
What are the UK Lotto odds?
6 of 59: the jackpot is 1 in 45,057,474, 5 + bonus 1 in 7,509,579, 5 numbers 1 in 144,415, 4 numbers 1 in 2,180, 3 numbers 1 in 96.2 and 2 numbers (a free Lucky Dip) 1 in 10.3.
Do some numbers have better odds?
No. Every combination is equally likely. Avoiding popular numbers such as birthdays only reduces the chance of sharing a jackpot.
Does buying more tickets help?
Each extra different ticket adds one more combination: 10 tickets in a 6/59 draw give 10 in 45,057,474 – still about 1 in 4.5 million.
What is the formula for lottery odds?
Odds of matching m of k numbers = C(N, k) ÷ [C(k, m) × C(N − k, k − m)].