Lottery Odds Calculator

Find your exact odds of winning the jackpot for any pick-k-from-n lottery — with or without a bonus ball — using the combination formula C(n,k).

Quick Facts

Method
Combinations: total tickets = C(n,k) × (bonus pool, if any)
Order does not matter, so we count combinations, not permutations.

Your Results

Calculated
Odds of jackpot (one ticket)
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1 in this many
Probability per ticket
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Chance of winning
Odds with your tickets
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Across all tickets bought
Distinct combinations
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Total possible tickets

Ready

Enter your lottery's rules and press Calculate.

How the Lottery Odds Calculator works

To win a lottery jackpot you have to match every number the machine draws. Because the order in which the balls come out does not matter, the number of different tickets that could possibly be drawn is a combination, written C(n, k) or "n choose k". Your odds of holding the winning ticket are simply 1 divided by that count.

The formula

If a game asks you to pick k numbers from a pool of n, the number of possible tickets is:

C(n, k) = n! / ( k! × (n − k)! )

Your odds of winning the jackpot with a single ticket are 1 in C(n, k), and your probability is 1 / C(n, k). If the game also draws a separate bonus ball (a Powerball or "extra" ball) from its own pool of m numbers, you must match that too, so the total number of tickets becomes C(n, k) × m.

Why order does not matter

If order mattered you would use permutations, which are much larger. But a lottery ticket like {4, 8, 15, 16, 23, 42} is the same winning ticket no matter what sequence the balls are drawn in. Dividing the permutation count by k! removes those duplicate orderings, which is exactly what the combination formula does.

Common reference points

  • 6 from 49 (classic Lotto): C(49, 6) = 13,983,816 → about 1 in 14 million.
  • 6 from 59 (UK Lotto): C(59, 6) = 45,057,474 → about 1 in 45 million.
  • US Powerball (5 from 69, plus 1 Powerball from 26): C(69, 5) × 26 = 11,238,513 × 26 = 292,201,338 → about 1 in 292 million.
  • US Mega Millions (5 from 70, plus 1 Mega Ball from 25): C(70, 5) × 25 = 12,103,014 × 25 = 302,575,350 → about 1 in 303 million.

Buying more tickets

Each additional distinct ticket adds one more chance out of the fixed total. If C(n, k)×m is the total number of tickets and you buy T of them, your odds improve to 1 in C(n, k)×m / T. Buying 10 tickets in a 1-in-14-million game gives roughly 1 in 1.4 million — better, but still overwhelmingly unlikely.

Frequently Asked Questions

What is C(n, k) and how do I read it?
C(n, k), read "n choose k", is the number of ways to choose k items from n when order doesn't matter. For a lottery it is the count of every possible ticket. Your jackpot odds are 1 in that number. For example C(49, 6) = 13,983,816, so a 6-from-49 game gives odds of 1 in 13,983,816.
Do the odds change from draw to draw or if numbers are "due"?
No. Each draw is independent and every combination is equally likely every time. Numbers that haven't appeared recently are not "due" — the balls have no memory. Picking 1-2-3-4-5-6 has exactly the same odds as any other combination; the only reason to avoid popular patterns is that if they do win you'd share the prize with more people.
Does buying more tickets meaningfully improve my chances?
Only in proportion to how many you buy against an enormous denominator. Ten distinct tickets in a 1-in-14-million game give about 1 in 1.4 million. To guarantee a jackpot you would have to buy every combination — nearly 14 million tickets — which usually costs far more than the prize after taxes and the risk of splitting it.

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