Lottery Odds Calculator
Odds Are a Combinatorics Problem, Not a Feeling
Every lottery format — pick 6 from 49, pick 5 from 70 plus a bonus ball — reduces to the same combinatorics question: how many distinct unordered groups of numbers can be drawn from the pool, since any one of those groups is equally likely to be the winning one. This calculator computes that count directly for any pick-size and pool-size combination, plus an optional bonus-ball pool multiplied in when the game includes one.
The Formula
Total Combinations = C(n, r) × Bonus Pool Size (if applicable)
Here n is the total pool of numbers and r is how many are drawn. If the game includes a separate bonus ball (drawn from its own pool), the base combination count is multiplied by the bonus pool size, since each of the main combinations can pair with any bonus number.
Where This Matters
- Comparing games objectively — two lotteries with similar jackpots can have very different odds depending on pool size and pick count, and this is the only way to compare them on equal footing.
- Understanding why one extra number in the pool matters so much — combinations grow combinatorially, not linearly, so a pool of 49 versus 59 numbers changes total combinations by a large multiple, not a small percentage.
- Sizing up a custom or workplace pool game — for informal number-pool games with non-standard pick sizes, this calculates the real odds rather than relying on intuition.
| Format | Total combinations |
|---|---|
| Pick 6 from 44 | 7,059,052 |
| Pick 5 from 59 | 5,006,386 |
| Pick 6 from 49 | 13,983,816 |
| Pick 5 from 69 + 1 from 26 (Powerball format) | 292,201,338 |
| Pick 5 from 70 + 1 from 25 (Mega Millions format) | 302,575,350 |
How to Use This Calculator
- Enter the total numbers in the pool (e.g. 49).
- Enter the numbers you pick (e.g. 6).
- Enter the bonus ball pool size if the game has a separate bonus draw (enter 0 if none).
- Select Calculate for the total combinations and the probability of matching all numbers with one ticket.
Related Calculations
See the exact combination math with the Lottery Combination Calculator, or check whether a ticket has positive expected value with the Lottery Expected Value Calculator.