Lottery Probability Calculator
Result
Calculate exact lottery jackpot probability and 1-in-N odds for uniform draws without replacement and optional independent bonus outcomes.
Formula
- Calculate the probability of matching one winning unordered k-number combination drawn uniformly without replacement from n numbers. An optional bonus multiplier b represents independent equally likely bonus outcomes, with exactly one winning option. Enter integers 1 ≤ k ≤ n and b ≥ 1. The primary result is probability, followed by 1-in-N odds. This does not predict future drawings or improve winning chances.
- The main inputs are Pool n, Pick k, Bonus pool multiplier. Enter them in the units and format shown in the calculator.
- Keep comparable quantities in compatible units whenever the formula combines or compares them.
- Changing any input above recalculates the result with the same calculation engine used by this page.
Example: Lottery Probability
- Pool n: 49
- Pick k: 6
- Bonus pool multiplier: 1
For a uniform 6-of-49 lottery with one winning combination and bonus multiplier 1: C(49,6) = 13,983,816; Probability = 1 / 13,983,816 ≈ 0.00000007151123842 (0.00000715112%); odds = 1 in 13,983,816.
Sample result: Calculating…
Frequently asked questions
What does bonus multiplier mean?
It is the number of equally likely independent bonus outcomes; exactly one is winning. Use 1 if there is no bonus draw.
Does order matter?
No. The model treats selections as unordered, without replacement.
Does this predict the lottery?
No. It only calculates probability under the stated uniform and independent assumptions.
What does the Lottery Probability calculate?
Calculate exact lottery jackpot probability and 1-in-N odds for uniform draws without replacement and optional independent bonus outcomes.
Which values should I enter?
Enter Pool n, Pick k, Bonus pool multiplier using the units and format shown beside each field.
What formula does this calculator use?
The calculator uses the following relationship: Probability = 1 / [C(n,k) × b], where C(n,k) = n! / [k!(n−k)!] and b is the number of independent equally likely bonus outcomes. Odds: 1 in C(n,k) × b..