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Lottery Calculator

Lottery Odds Calculator

Calculate the odds for any lottery. Describe the game's number pools below — main numbers, bonus balls, ticket count, and ticket price — and get the possible combinations, the jackpot odds, the single-ticket probability, your chance with multiple tickets, and the expected tickets and cost for one win.

Numbers run from 1 to this value.

Enter 0 for a lottery with no bonus ball.

Leave blank if the price is unknown.

How Jackpot Odds Are Calculated

A lottery jackpot requires matching every number drawn. The number of possible combinations comes from the combinations formula C(n, r) = n! / (r! × (n−r)!), which counts how many ways r numbers can be chosen from a pool of n — order doesn't matter.

For example, Powerball asks for 5 white balls from 1–69: C(69, 5) = 11,238,513 possible white-ball combinations. Each of those can pair with any of 26 Powerballs, so 11,238,513 × 26 = 1 in 292,201,338. The calculator above performs this same derivation for whatever pools you enter — nothing is hard-coded.

The single-ticket probability is simply 1 divided by the combinations. With multiple tickets covering different combinations, the chance of at least one win is 1 − (1 − p)n, where p is the single-ticket probability and n is the ticket count. This assumes each ticket covers a different combination.

What the Results Mean

Possible combinations is the total number of distinct tickets the game can produce. Jackpot odds ("1 in X") is the same number expressed as odds.

Single-ticket probability is shown as a percentage with enough decimal places to stay nonzero — for example, a Powerball jackpot ticket is about 0.000000342%. Expected tickets for one win is the mathematical average (1 ÷ p) over an enormous number of plays. It is not a guarantee: buying that many tickets never assures a win, and roughly half of all players buying that many would still not have won.

Buying additional tickets increases the number of combinations covered, but the jackpot probability may remain extremely small.

Powerball and Mega Millions Jackpot Odds

For reference, here are the jackpot odds for the two national games, derived from their verified rules through the same engine:

Powerball

1 in 292,201,338

5/69 + 1/26 · $2 per play

Powerball odds calculator →

Mega Millions

1 in 290,472,336

5/70 + 1/24 · $5 per play

Mega Millions odds calculator →

How We Calculate

  1. Start with the selected lottery amount. Enter the advertised jackpot and the cash option (or choose the annuity to estimate one annual payment).

  2. Determine the cash or taxable amount. For a lump sum, the cash option is the taxable amount. For an annuity, each annual payment is taxed in the year it is received.

  3. Apply applicable federal tax rules. Lottery winnings are taxed as ordinary income. The calculator subtracts the standard deduction for your filing status, then applies that year's progressive federal tax brackets.

  4. Apply applicable state rules. The calculator applies the state's configured planning rate. States that do not tax lottery winnings show $0 state tax. Local and city taxes are not included.

  5. Calculate estimated total tax. Estimated federal and state taxes are added together for the total estimated tax liability.

  6. Calculate estimated take-home amount. Estimated total tax is subtracted from the taxable amount. This is an estimate of final liability — withholding shown separately is what may be held back when you are paid, and it is credited against this liability.

Results are estimates for informational purposes only — not tax, legal, or financial advice. Your actual tax bill depends on your full tax return, the lottery's rules, and the laws in effect when you claim the prize.

Frequently Asked Questions

What is a lottery number generator?

A lottery number generator is a random-number utility that picks a valid combination of numbers for a lottery's rules — for example, 5 numbers from 1–69 plus a bonus ball from 1–26. It is a convenience tool, not a prediction tool.

Are lottery numbers truly random?

The numbers this site's generator produces come from your browser's cryptographic random source (crypto.getRandomValues where available), which is suitable for picking unbiased random numbers. But 'random' here means unpredictable picks — it says nothing about which numbers will be drawn.

Can random numbers improve my odds?

No. Every valid combination has exactly the same probability of being drawn — 1 in 292,201,338 for a Powerball jackpot, for example. Randomly generated numbers do not improve the mathematical odds of winning and cannot predict future winning numbers.

How many lottery combinations can I generate?

You can never generate more unique combinations than mathematically exist: for a 'pick r from n' lottery that is C(n,r). The combination generator refuses requests that exceed the possible unique combinations instead of looping forever.

Can I generate Powerball numbers?

Yes — the Powerball number generator uses the verified 5/69 + 1/26 rules to produce sets of 5 sorted white-ball numbers plus a Powerball. The sets are random conveniences with no predictive value.

Can I generate Mega Millions numbers?

Yes — the Mega Millions number generator uses the verified 5/70 + 1/24 rules. Like every generated set, the results are random and carry no advantage over any other valid combination.

Can the generator predict winning numbers?

No, and no generator can. Each drawing is an independent random event: past results do not influence future ones, and there is no 'hot', 'cold', or 'due' number. This site deliberately offers no prediction features — only random generation.

Sources & References