Lottery Odds Calculator – Powerball and Mega Millions, Exact
No charts copied from anyone, and no hope sold. This page counts the combinations itself — every prize tier of Powerball and Mega Millions, worked out live from the real structure of each game — and then shows you exactly what any set of numbers you pick is up against. Bring your lucky numbers if you like. The maths will treat them exactly like every other combination, because that is precisely what the draw does.
Your game and your numbers
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What those numbers are up against
The honest totals
The truth about your numbers
Your combination: 7, 14, 21, 28, 35 and Powerball 12. Its jackpot odds are 1 in 292,201,338 — exactly the same as every other combination of the 292,201,338 there are. No set of numbers is luckier than another, and the draw has no memory of what won last week or what your family plays.
What a typical ticket actually does: it matches an average of 0.36 of the five white balls, and 67.8% of tickets match no white ball at all. Most tickets lose — the tier table below shows exactly how that is built into the game.
- Jackpot odds are counted exactly, not estimated: the default game gives 1 in 292,201,338.
- Buying more tickets scales the chance, but the guide works through what more tickets actually do — the odds barely move.
- Expected value is shown without illusions: a jackpot’s headline size is not its expected return.
- Every prize tier, counted exactly
- Pairs well with this calculation
- Lottery odds in three steps
- How the lottery odds calculator works
- Going deeper
- Mega Millions, counted the same way
- What buying more tickets actually does
- Expected value, without illusions
- How long would you have to play to expect a jackpot?
- Frequently asked questions
Every prize tier, counted exactly
Powerball has nine ways to win. For each one, the calculator counts how many of the 292,201,338 combinations land there — that count, divided into the total, is the odds. Nothing is rounded until the final display.
| Match | Winning combinations | Chance | Odds |
|---|---|---|---|
| 5 + Powerball | 1 | 0.00000034% | 1 in 292,201,338 |
| 5 | 25 | 0.00000856% | 1 in 11,688,054 |
| 4 + Powerball | 320 | 0.00010951% | 1 in 913,129 |
| 4 | 8,000 | 0.002738% | 1 in 36,525 |
| 3 + Powerball | 20,160 | 0.006899% | 1 in 14,494 |
| 3 | 504,000 | 0.1725% | 1 in 579.8 |
| 2 + Powerball | 416,640 | 0.1426% | 1 in 701.3 |
| 1 + Powerball | 3,176,880 | 1.0872% | 1 in 91.98 |
| 0 + Powerball | 7,624,512 | 2.6093% | 1 in 38.32 |
| Any prize | 11,750,538 | 4.0214% | 1 in 24.87 |
Read the jackpot row slowly: of the 292,201,338 combinations, exactly one takes the top prize, while 7,624,512 of them — matching nothing but the Powerball — take the smallest. The tiers in between are where the game spends most of its winning tickets, which is why small prizes feel common and large ones feel impossible. Both feelings are just this table.
The one idea underneath all of it
Odds are a division, not a prophecy: the combinations that land in a tier, divided by every combination there is. Count honestly and the mystery disappears — what is left is a game whose biggest prize is priced at one combination in nearly three hundred million, and whose smallest prizes are common enough to keep the ticket feeling alive. Knowing the count does not beat the game, but it does mean the game never fools you.
Pairs well with this calculation
The rest of the chance and odds shelf.
Lottery odds in three steps
Fix the game structure
Powerball draws 5 white balls from 69 and 1 Powerball from 26. Mega Millions draws 5 from 70 and 1 Mega Ball from 25. Those four numbers are the whole game — everything else is counting.
Count every combination
The white balls can be chosen in C(69, 5) = 11,238,513 ways for Powerball. Multiply by the 26 bonus balls and there are 292,201,338 combinations a single ticket can be — and exactly one of them is the jackpot.
Count each tier, then divide
For every prize tier, count the combinations that land in it: some of your numbers drawn, the rest drawn from the numbers you did not pick. Tier odds are that count divided into the total. Add the tiers together and you get the chance of winning anything at all.
How the lottery odds calculator works
odds of a tier = total combinations ÷ combinations in that tier
The jackpot, counted. Five white balls from 69 can be chosen in C(69, 5) = 11,238,513 ways. The Powerball adds a factor of 26, giving 11,238,513 × 26 = 292,201,338 combinations. One of them matches all five white balls and the Powerball, so the jackpot odds are 1 in 292,201,338 — the anchor figure this calculator reproduces exactly.
One tier, counted in full. Matching exactly 3 white balls plus the Powerball: choose which 3 of your 5 numbers hit, C(5, 3) = 10 ways; the other 2 white balls must come from the 64 numbers you did not pick, C(64, 2) = 2,016 ways; and the Powerball must be the 1 right ball of 26. Total: 10 × 2,016 × 1 = 20,160 winning combinations, so the odds are 292,201,338 ÷ 20,160 — 1 in 14,494.
Winning anything. Add up the winning combinations of all nine tiers — 1 + 25 + 320 + 8,000 + 20,160 + 504,000 + 416,640 + 3,176,880 + 7,624,512 = 11,750,538 — and divide into the total: 11,750,538 of 292,201,338 combinations win something, a 4.0214 percent chance, or 1 in 24.87 per ticket.
Mega Millions is the same count with different pools. Five from 70 gives C(70, 5) = 12,103,014 ways, times 25 Mega Balls = 302,575,350 combinations — a slightly steeper jackpot than Powerball, partly repaid by a slightly better any-prize chance of 1 in 23.99. Switch the game at the top of the calculator and every tier is recounted from the new pools.
Going deeper
The draw is a machine mixing balls; it cannot know that 7 is your anniversary or that 4, 8, 15, 16, 23 came from a television show. Every one of the 292,201,338 combinations is exactly as likely as every other, including the ones that look absurd: 1, 2, 3, 4, 5 with Powerball 6 has precisely the same chance as your carefully chosen spread. Pattern, meaning and history change nothing about the odds — they are properties of the counting, not of the numbers.
Where your choice does matter is the payout side, through sharing. Jackpots are split between everyone holding the winning combination, and players do not choose uniformly: date-based numbers only ever use 1 to 31, sequences and patterns are played by thousands, and famous combinations are held by crowds. Win on a crowded combination and the same jackpot is sliced more ways. You cannot improve your odds by choosing — but a combination nobody else plays at least keeps a win whole. That is the only honest edge a picked number can offer.
Numbers this large stop meaning anything, so compare them with other long shots you can count the same way. Being dealt a royal flush in five-card poker is 1 in 649,740 — rare enough to be a lifetime story for most players, and still about 450 times more likely than the Powerball jackpot. Flipping a coin and landing 28 heads in a row is 1 in 268,435,456: slightly more likely than winning Powerball, and nobody expects to do it by trying harder.
Time makes the same point. Powerball draws three times a week, roughly 156 draws a year. One ticket in every draw gives an expected wait of 292,201,338 plays for the jackpot to find your combination — about 1.9 million years of buying a ticket for every single draw. The jackpot does get won, regularly, because hundreds of millions of combinations are sold; it is the crowd that beats the odds, never the individual ticket. That, in one sentence, is the whole economics of the game.
Mega Millions, counted the same way
Powerball’s counting is worked in full in the guide above. Mega Millions follows the same method with different matrix numbers: five white balls drawn from 70, and one Mega Ball drawn from 25. The white balls can be chosen in combinations of 70 taken five at a time, which is 12,103,014 ways, and multiplying by the 25 possible Mega Balls gives 302,575,350 combinations a single ticket can be, against Powerball’s 292,201,338. The Mega Millions jackpot is therefore harder by the ratio of the two totals, 302,575,350 divided by 292,201,338, which is 1.0355, or about 3.6 percent more combinations to beat. The table below counts all nine Mega Millions prize tiers by the same method the guide above uses for Powerball: choose which of your numbers hit, choose the rest from the numbers you did not pick, and multiply by the bonus-ball factor where the tier requires the Mega Ball.
| Mega Millions tier | Winning combinations | Odds |
|---|---|---|
| 5 white balls plus Mega Ball (jackpot) | 1 | 1 in 302,575,350 |
| 5 white balls, no Mega Ball | 24 | 1 in 12,607,306 |
| 4 white balls plus Mega Ball | 325 | 1 in 931,001 |
| 4 white balls, no Mega Ball | 7,800 | 1 in 38,792 |
| 3 white balls plus Mega Ball | 20,800 | 1 in 14,547 |
| 3 white balls, no Mega Ball | 499,200 | 1 in 606 |
| 2 white balls plus Mega Ball | 436,800 | 1 in 693 |
| 1 white ball plus Mega Ball | 3,385,200 | 1 in 89 |
| No white balls, Mega Ball only | 8,259,888 | 1 in 37 |
Add the nine tiers together and 12,610,038 of the 302,575,350 combinations win something, so the chance of winning any Mega Millions prize on one ticket is 12,610,038 divided by 302,575,350, which is 4.17 percent, or odds of 1 in 24.0. Powerball’s corresponding figure, worked out on the page itself, is 11,750,538 winning combinations out of 292,201,338, which is 4.02 percent, or 1 in 24.87. The two games are therefore close on the small prizes and far apart only at the top: a Mega Millions ticket is slightly more likely to win something, and slightly less likely to win the jackpot, than a Powerball ticket. Neither fact makes either game a better investment, for the reason the next section gives, but it does settle the bar-room question of which game is harder: at the jackpot, Mega Millions, by about three and a half percent; at any prize, Powerball, by a fraction of a percent in the other direction.
One counting subtlety is worth stating because it traps even careful readers of tier tables. Matching two white balls without the Mega Ball, or one white ball without it, wins nothing in Mega Millions, and those combinations are correctly absent from the table above. A table that included them would count 10,483,200 combinations for two white balls alone and 81,244,800 for one white ball alone, and would arrive at a wildly wrong overall figure near 1 in 2.9. The official tier list is the definition of winning, not the combinatorics alone: the counting method gives the size of every tier, but only the game’s published prize structure decides which tiers pay. The same caution applies to Powerball, whose nine tiers are the ones this page counts, and to any lottery whose matrix you look up elsewhere.
What buying more tickets actually does
Buying more tickets improves your chances exactly linearly for the jackpot and less than linearly for winning anything, and the difference between those two statements is the whole psychology of lottery tickets. For the jackpot, each distinct combination you hold is one more of the 292,201,338 possible combinations, so ten tickets give you ten chances in 292,201,338, which is odds of 1 in 29,220,134, and a hundred tickets give odds of 1 in 2,922,013. The table below shows the jackpot odds for one, ten, a hundred and a thousand distinct Powerball tickets, alongside the chance of winning any prize at all with that many tickets, computed as one minus the chance that every ticket loses.
| Distinct tickets, one draw | Jackpot odds | Chance of any prize |
|---|---|---|
| 1 | 1 in 292,201,338 | 4.02% |
| 10 | 1 in 29,220,134 | 33.66% |
| 100 | 1 in 2,922,013 | 98.35% |
| 1,000 | 1 in 292,201 | Over 99.99% |
Read the two columns together and the trap becomes visible. With a hundred tickets you are almost certain, at 98.35 percent, to win something, which feels like the odds have collapsed in your favour, while your jackpot odds are still 1 in 2,922,013, which is to say still effectively impossible for any practical purpose. The any-prize column saturates because most winning combinations are small prizes, and buying many tickets quickly covers the dense bottom of the prize structure; the jackpot column never saturates at any affordable scale, because it is a single combination among hundreds of millions. A thousand tickets still leave you at 1 in 292,201 for the jackpot, and covering every combination would need 292,201,338 tickets, before even considering whether buying, storing and checking that many tickets were logistically possible or whether the jackpot would then have to be shared.
Playing the same numbers every week changes nothing about any single draw, and playing different numbers every week changes nothing either. Each draw is independent: the balls have no memory of last week’s numbers, of your birthday, or of how long it has been since a number last appeared. What does change with repetition is the count of chances you have bought, and the count grows so slowly against these denominators that it is barely visible: one ticket a week for fifty years is 2,600 tickets, each still facing 1 in 292,201,338 in its own draw, and the chance of at least one jackpot across all 2,600 draws is about 2,600 divided by 292,201,338, which is 0.00089 percent, still under one-thousandth of one percent. The draws do not accumulate into a certainty. The honest way to think about a lottery ticket is as entertainment with a known, tiny chance attached, not as a savings plan with a delayed payout.
Expected value, without illusions
The expected value of a ticket is the sum over all tiers of the chance of landing in that tier times the prize for that tier, minus the price of the ticket. For ordinary jackpots that sum is below the ticket price, which is the precise sense in which lotteries are a bad investment and a fair entertainment purchase at the same time: the price buys a small chance at a large prize plus the enjoyment of imagining it, and the mathematics says the chance alone is worth less than the price. The expected value rises with the jackpot, because the jackpot term dominates the sum, and at very large jackpots it can approach or even pass the ticket price on paper. That paper figure is not the real figure, for three reasons that all point the same way.
First, the jackpot is usually advertised as an annuity total, paid over decades, while the cash alternative is substantially smaller; expected value computed on the annuity figure overstates what a winner actually receives if they take cash, which most do. Second, taxes take a large share of a jackpot win, and the tax treatment depends on the winner’s jurisdiction and circumstances, so a pre-tax expected value is not a spendable figure. Third, and most importantly at large jackpots, the prize may be split: when a jackpot grows, more tickets are sold, more combinations are covered, and the chance that someone else holds the same winning combination rises, so the expected share of the jackpot falls even as the headline jackpot rises. A calculation that ignores splitting, taxes and the annuity discount will flatter every large jackpot, sometimes past the break-even point, and that flattery is the closest thing the lottery world has to a winning system. There is none: no selection of numbers, no pattern of play, and no frequency of purchase changes the odds of any ticket, and any system that claims otherwise is selling something other than mathematics.
Popular numbers deserve a final note, because they are the one place where choice does matter, though not in the way players hope. Choosing numbers above 31, or an unpatterned spread, does not change your chance of winning; every combination is equally likely, as the FAQ above stresses. It can change what you receive if you win, because birthdays and patterns are popular choices, and a popular winning combination is more likely to be shared with other winners. The effect is on the prize, not the probability, and it is the only sense in which number selection has any consequence at all. Play the numbers you enjoy, in the knowledge that the draw does not care, and that the only strategy with a mathematical basis is to spend no more than the entertainment is worth to you.
How long would you have to play to expect a jackpot?
Odds of 1 in 292,201,338 are hard to feel, but waiting times make them tangible. The expected number of tickets to the first jackpot, if every ticket is a distinct combination in an independent draw, is 292,201,338 tickets: that is the mean of the geometric distribution, one divided by the chance per ticket. At one ticket a week, buying 292,201,338 tickets takes 5,619,257 years. At a hundred tickets a week, every week without fail, it takes 56,193 years. Those are not exaggerations for effect; they are the divisions, 292,201,338 divided by 52 and by 5,200, and they are the reason no playing frequency available to a human lifetime moves the jackpot from impossible to plausible. A lifetime of weekly tickets, 2,600 of them, is less than nine-thousandths of one percent of the expected wait.
The median wait is shorter than the mean, and the difference is itself instructive. Half of all hypothetical players buying distinct combinations would hit a jackpot within about 202.5 million tickets, because the chance of at least one win across that many tickets is one minus the chance that every ticket loses, which reaches 50 percent at roughly 202.5 million tickets, not at 292.2 million. The mean is longer than the median because the distribution has a long tail: a minority of players wait enormously longer than average, pulling the mean up. Neither figure should encourage more spending, since both describe waits measured in millions of tickets, and both assume distinct combinations, which a player choosing birthday numbers or patterns does not guarantee. The waiting-time view leads to the same conclusion as the odds view, by a road that is harder to argue with: a jackpot is not a plan that patience will eventually redeem, but an event so unlikely that no human schedule of play brings it within reach.
Odds versus probability: the same number, two wordings
Visitors ask for both wordings, and the page answers both, but they are one number written two ways. A probability of 1 in 292,201,338 is the fraction of tickets that win. Odds against, in the betting sense, are 292,201,337 to 1. The calculator shows the probability form because it feeds directly into expected value: probability times prize, summed over tiers.
Why the jackpot size never moves the odds
A jackpot grows when draws roll over, and every rollover brings a wave of extra tickets. None of that changes the combinations. The pool is fixed at 292,201,338 for Powerball and 290,472,336 for Mega Millions, so the odds per ticket are identical whether the jackpot is $20 million or $1 billion. What grows with the jackpot is the expected value, and even that is cut by tax, the cash discount, and the chance of splitting.
Frequently asked questions
What are the odds of winning the Powerball jackpot?
1 in 292,201,338 for a single combination. The count comes straight from the game: there are C(69, 5) = 11,238,513 ways to choose the five white balls, and 26 possible Powerballs, so 11,238,513 × 26 = 292,201,338 combinations in total — and exactly one of them is the jackpot combination. Your combination, a quick pick, and the numbers 1, 2, 3, 4, 5 with Powerball 6 all carry exactly the same 1 in 292,201,338.
What are the odds of winning any Powerball prize?
1 in 24.87 — a 4.0214 percent chance per play. That figure adds up all nine prize tiers, from matching the Powerball alone (1 in 38.32) to the jackpot. Most of that chance sits in the smallest tiers: matching just the Powerball, or one white ball plus the Powerball, together account for the bulk of all winning tickets.
Do my own numbers have better odds than a quick pick?
No. Every combination of five white balls plus a bonus ball is equally likely to be drawn, whether you chose it, a machine chose it, or it spells out your birthday. What your choice can change is how many other players are likely to hold the same combination: numbers based on dates only use 1 to 31, the most crowded corner of the ticket, so a jackpot won on date numbers is more likely to be shared. The odds of winning stay identical either way.
Does buying more tickets improve my odds?
Yes — but only in proportion, and only if the tickets are different combinations. Each distinct combination is one more of the 292,201,338, so 100 different Powerball combinations give you 100 chances in 292,201,338, or 1 in 2,922,013, of holding the jackpot ticket. One hundred copies of the same combination are still just one combination, with the original 1 in 292,201,338.
Which is better, Powerball or Mega Millions?
For the jackpot, Powerball is fractionally less steep: 1 in 292,201,338 against Mega Millions at 1 in 302,575,350, because Mega Millions draws five from 70 white balls instead of 69. For winning anything at all the order flips: Mega Millions pays some prize on 1 in 23.99 plays (4.1676 percent) against Powerball at 1 in 24.87 (4.0214 percent). Either way, both games return less on average than a ticket costs — the odds on this page are simply the honest version of that.
How are these odds worked out?
By counting combinations, tier by tier. To match exactly three white balls and the Powerball, for example, you need 3 of your 5 numbers among the 5 drawn — C(5, 3) = 10 ways — the other 2 from the 64 numbers not drawn — C(64, 2) = 2,016 ways — and the 1 right Powerball from 26. That is 10 × 2,016 × 1 = 20,160 winning combinations out of 292,201,338, which is 1 in 14,494. Every figure on this page is counted the same way, by the calculator itself, not copied from a chart.
What are my odds if I play the same numbers every week?
Exactly the same, every week, as any other combination: 1 in 292,201,338 for a Powerball jackpot on each ticket, each draw. Draws are independent, and the balls have no memory of what won last week, of how long a number has been absent, or of how long you have been playing your numbers. Playing the same combination for years does not make it due, and switching numbers does not reset anything. What repetition buys is more chances in total, one per ticket per draw, and against a denominator of hundreds of millions that accumulation is slow: a ticket a week for fifty years is 2,600 chances, still a small fraction of one percent of the combinations.
Do more tickets for one draw beat one ticket for many draws?
For the jackpot, the expected number of wins is the same either way: a hundred tickets in one draw give a hundred chances at that draw’s jackpot, and one ticket in a hundred draws gives a hundred chances spread across draws, each at that draw’s jackpot. The distributions differ, not the expectation. A hundred tickets in one draw can only win that draw’s jackpot once in practice, since the winning combination can appear among them at most once if the tickets are distinct, while a hundred separate draws offer a hundred separate, independent shots. Neither arrangement improves on the other mathematically; the choice is about entertainment, not odds, and the total spent is what matters for your budget.
Is Mega Millions harder than Powerball?
At the jackpot, yes, by about 3.6 percent: Mega Millions has 302,575,350 combinations against Powerball’s 292,201,338, because five balls from 70 give 12,103,014 white-ball combinations against five from 69 giving 11,238,513, multiplied by 25 Mega Balls against 26 Powerballs. At any prize the comparison reverses by a fraction: Mega Millions pays on 12,610,038 combinations, or 1 in 24.0, against Powerball’s 11,750,538, or 1 in 24.87. The difference at the top is real but small beside the scale of both denominators; neither game is meaningfully easier to win than the other in any sense that should affect how much you spend.
What does 1 in 24.87 mean for a single ticket?
It means that one ticket has a 4.02 percent chance of winning any Powerball prize, because 11,750,538 of the 292,201,338 combinations pay something. It does not mean that buying 25 tickets guarantees a win, or that a win is due after 24 losing tickets. Each ticket is independent, so the chance of at least one win across 25 tickets is one minus the chance that all 25 lose, which is 64.16 percent, not 100 percent. The 1 in 24.87 figure is an average over all combinations, not a schedule: most tickets lose, a few win small prizes, and the jackpot remains one combination among hundreds of millions however many tickets you have bought before.
Does the UK Lotto have better odds than Powerball?
Yes, by a wide margin. The UK Lotto jackpot is 1 in 45,057,474 against Powerball at 1 in 292,201,338, because the UK game draws 6 from 59 while Powerball draws 5 from 69 plus a Powerball. The trade is prize size: fewer combinations mean a smaller prize pool.
Why did Mega Millions odds change in 2025?
Mega Millions changed its matrix in April 2025, moving the Mega Ball pool from 25 numbers to 24. That cut the combinations from 302,575,350 to 290,472,336, slightly improving jackpot odds while the ticket price rose to $5.
Can a lottery strategy beat the odds?
No strategy changes the combinations. Number selection, wheeling systems, and hot or cold numbers all buy the same probability per ticket. Wheeling buys more tickets, which improves odds only in proportion to the tickets bought.
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