What Is the Mega Millions Odds Calculator?
Mega Millions is a US multi-state lottery in which you pick 5 white-ball numbers from a pool (traditionally 1-70) plus one gold "Mega Ball" from a separate pool (traditionally 1-25). This calculator computes the probability of matching all numbers and winning the jackpot, expressed as a "1 in N" figure. It is configurable, so you can model rule changes or other lotteries simply by adjusting the pool sizes.
How to Use It
Enter the total number of white balls in the pool, how many white balls you must pick, and the number of Mega Balls. The defaults reflect the standard US Mega Millions matrix. Press calculate to see the exact number of possible combinations and your odds of hitting the jackpot with a single ticket.
The Formula Explained
The white-ball combinations follow the "n choose k" formula, since order does not matter: \(C(n,k) = \frac{n!}{k!\cdot(n-k)!}\). The single Mega Ball is a straightforward 1-in-m chance. Total jackpot combinations are the product of the two, and the odds are the reciprocal.
$$\text{Jackpot odds} = \frac{1}{\dbinom{\text{white total}}{\text{white pick}} \times \text{mega total}}$$
Worked Example
With 70 white balls choosing 5:
$$C(70,5) = \frac{70\cdot69\cdot68\cdot67\cdot66}{5\cdot4\cdot3\cdot2\cdot1} = \frac{1{,}452{,}361{,}680}{120} = 12{,}103{,}014$$Multiply by 25 Mega Balls:
$$12{,}103{,}014 \times 25 = 302{,}575{,}350$$So your jackpot odds are 1 in 302,575,350.
FAQ
Are these the official odds? Yes — 1 in 302,575,350 matches the published US Mega Millions jackpot odds for the 70/25 matrix.
Does buying more tickets help? Each distinct ticket adds one chance, so 10 tickets give roughly 10 in 302,575,350. The improvement is real but tiny.
Why is order ignored? Lottery draws are evaluated as a set of numbers, not a sequence, which is why combinations (not permutations) are used.
