Lottery Odds Calculator

Calculate the odds of winning a lottery jackpot from the numbers you pick and the pool size, with the odds of matching fewer numbers. Example: choosing 5 of 69 plus 1 of 26 gives odds of 1 in 292,201,338.

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Numbers in the main pool

Numbers you pick from the main pool

Numbers in the bonus pool (0 for none)

How to use the Lottery Odds Calculator

Enter the size of the main number pool and how many numbers you pick.
Enter the size of the bonus pool, or 0 if there is none.
Press Calculate for the jackpot odds and smaller matches.

Formula and method

Number of combinations C(n, k) = n! / (k! x (n – k)!). With a bonus ball from a pool of b, odds = C(n, k) x b. The chance of matching exactly j of k picks is C(k, j) x C(n – k, k – j) / C(n, k).

Worked example: pick 5 of 69 plus 1 of 26

Step	Result
C(69, 5)	11,238,513
Times 26 bonus numbers	292,201,338
Odds	1 in 292,201,338

Odds of common lottery formats

Format	Odds of the jackpot
6 of 49	1 in 13,983,816
5 of 69 + 1 of 26	1 in 292,201,338
6 of 59	1 in 45,057,474
5 of 70 + 1 of 25	1 in 302,575,350
5 of 39	1 in 575,757

Understanding the odds

Odds of 1 in 292 million are far lower than the odds of being struck by lightning in a year. Every combination is equally likely, so picking birthdays or patterns does not help, though popular picks can mean sharing a prize.

Frequently asked questions

How do I calculate lottery odds?

Count the possible combinations with C(n, k) and multiply by the bonus pool size.

What are the odds of winning Powerball?

1 in 292,201,338 for the jackpot.

Does picking different numbers help?

No. Every combination is equally likely.

Do past draws affect the odds?

No, each draw is independent.

Does buying more tickets help?

It raises your chance in proportion to the number of unique tickets.

What are the odds of 6 of 49?

1 in 13,983,816.

Sources

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Effortless Math Team

11 minutes ago