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Lottery Calculator

Lottery Combination Generator

Count the distinct combinations any lottery's rules allow. Enter the main-number and bonus-ball pools to see the total combinations, the jackpot odds for one ticket, and — if you enter a ticket price — the illustrative cost of covering every combination.

Enter 0 for a lottery with no bonus ball.

Used only for the illustrative full-coverage cost.

Worked Examples

Powerball (5/69 + 1/26): C(69, 5) = 11,238,513 white-ball combinations × 26 Powerballs = 292,201,338 total.

Mega Millions (5/70 + 1/24): C(70, 5) = 12,103,014 × 24 = 290,472,336 total.

Classic 6/49: C(49, 6) = 13,983,816 total — 1 in 13,983,816 jackpot odds.

These figures are computed at build time with the same engine that powers the calculator above — the combination math lives in one place.

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

How many combinations does Powerball have?

C(69, 5) = 11,238,513 ways to choose the white balls, each pairable with 26 Powerballs: 292,201,338 total combinations, or 1 in 292,201,338 jackpot odds.

How many combinations does Mega Millions have?

C(70, 5) = 12,103,014 white-ball combinations × 24 Mega Balls = 290,472,336 total, or 1 in 290,472,336 jackpot odds.

How is the combination count calculated?

With the combinations formula C(n, r) = n! / (r! × (n−r)!), computed here with a stable multiplicative method — no factorial recursion. The bonus ball multiplies the main-ball combinations because it is drawn from a separate pool.

Does knowing the combination count help me win?

No. It only describes the size of the possibility space. Every combination has exactly the same probability in every drawing, so counting them changes nothing about your chances.

What does the 'cost to cover every combination' figure mean?

It is a plain multiplication — total combinations × ticket price — shown for mathematical illustration. Covering every combination is not practically possible (sales cutoffs, logistics, and the chance of splitting a jackpot with another winner), so treat it as arithmetic, not a plan.

Why do bonus balls multiply the total instead of adding?

Each main-ball combination can pair with every possible bonus ball. With 11,238,513 white-ball combinations and 26 Powerballs, the total is 11,238,513 × 26 — one independent choice multiplied by the other.