Lottery Odds Calculator
Work out the odds of winning a lottery from the number pool and how many you must match.
Last updated · View algorithm, constants and default inputs (JSON)
About this calculator
The calculator counts possible combinations for a simple draw where order does not matter and all numbers are drawn from one pool. The multi-ticket probability assumes every ticket is a different combination, so duplicate tickets add no chance; if tickets exceed all combinations, only the distinct combinations are counted. It does not model prize tiers, taxes or expected value.
Worked example
calculated with the default values below
Numbers in the pool 49 · Numbers you must match 6 · Tickets bought 1 · Price per ticket 2 $ Possible combinations 13,983,816 · Distinct tickets counted 1 · Probability per ticket 0.0000071511 % · Probability with all your tickets 0.00000715 % · Total spent 2.00 $
Disclaimer
These calculators give general estimates for information and entertainment. Platform algorithms, metrics and definitions change without notice, and none of these results are official figures from the platforms named.
Implementation source
This record describes the implementation used by this page. It is not independent validation. External references, when available, support only the stated formula or definition; estimates and custom rules retain their own assumptions.
Formula and variables
C(n,k) = n! ÷ (k!(n−k)!); p = 1 ÷ C(n,k); p_all = min(tickets,C(n,k)) ÷ C(n,k)
- n
- pool size
- k
- numbers selected
- C(n,k)
- possible combinations
- tickets
- tickets purchased
- p
- probability per ticket
- p_all
- probability across distinct combinations
Ticket probability assumes a simple draw with no order and distinct combinations. Multiple-ticket probability counts at most C(n,k) unique combinations; ticket spend still uses all tickets. Jackpot-only model; no prizes, taxes or expected value.
Frequently asked questions
How does the calculator handle multiple tickets?
It assumes tickets use different number combinations and counts no more than the total number of possible combinations. Duplicate tickets do not increase the chance of winning; ticket spend still includes every ticket. It models the jackpot only.