Lottery Odds Calculator
Odds of winning any lottery — pick-N games, Powerball, Mega Millions, EuroMillions and custom formats. Shown as 1-in-N, probability and percent, with a perspective chart against real-world rare events.
What are lottery odds?
A lottery draws a small set of balls from a larger pool without repetition and without order mattering. That is the exact definition of a combination, counted by C(n, r) = n! / (r! · (n − r)!). The odds of any single ticket winning the jackpot are simply 1 in C(n, r) — because every possible combination is equally likely and only one of them is the winning set.
For lotteries with a bonus ball (Powerball, Mega Millions, EuroMillions), the bonus draw is independent of the main draw, so you multiply the two counts together. That is why jackpot odds jump from tens of millions to hundreds of millions the moment a bonus ball is added.
Lottery odds, piece by piece
Jackpot odds — pick r from n
A lottery draws r balls from a pool of n without replacement, and order doesn't matter — that is the exact definition of a combination. Every one of C(n, r) possible draws is equally likely, and only one matches your ticket, so your odds are 1 in C(n, r).
Partial match — m of r
For smaller prize tiers you want the probability of matching exactly m of the r drawn balls. Choose which m of your r numbers get matched, then the remaining r − m drawn balls must come from the n − r numbers you did not pick.
Bonus ball multiplier
Powerball, Mega Millions and EuroMillions draw an extra ball from a separate pool. Because the bonus draw is independent of the main draw, you simply multiply the two counts together — which is why jackpot odds jump from tens of millions into the hundreds of millions.
Odds, probability, and percent
Three ways of writing the same number: 1-in-N is the ratio, probability is 1/N as a decimal, and percent is that same number scaled by 100. Which form is 'best' depends on the audience — big-N odds are easiest to grasp as 1-in-N; small-p probabilities read better in scientific notation.
Why picking birthdays doesn't hurt your odds (a common myth)
Every combination the machine can draw is equally likely — the balls have no idea whether they are "spread out" or all under 32. The odds of a specific ticket winning are 1 in C(n, r) regardless of how you chose those numbers: quick-pick, birthdays, sequences like 1-2-3-4-5-6, patterns down the ticket — all identical.
What number choice does affect is share size if you win. Many players use birthdays (so numbers 1–31 are over-picked), lucky numbers like 7, and "random-looking" spreads. If the winning numbers happen to fit those patterns, you split the jackpot with more people. Picking numbers above 31, or letting the terminal quick-pick for you, doesn't improve whether you win — only how much you'd take home if you do.
Why past draws don't help — the gambler's fallacy
Every draw is independent. A ball that hasn't appeared for six months is not "due", and a hot number that's come up three weeks in a row isn't "on a roll". The probability that any specific ball is drawn is r / n on every single draw, with no memory of what came before. Systems that promise better odds by tracking overdue numbers are selling pattern-hunting where no pattern exists — the math is exactly the same as if you'd never looked at history at all.
Common mistakes
- Ignoring the bonus ball. C(69, 5) is only about 11 million — but the Powerball jackpot is 1 in 292 million because the bonus ball multiplies the odds by 26.
- Confusing "match r of r" with "match some of r". Partial-match odds use C(r, m) · C(n − r, r − m) — not 1. Skipping that gives odds that look far too long for smaller prize tiers.
- Treating multiple tickets as multiplicative. Buying two different tickets doubles your odds; it doesn't square the probability. Two in 14 million is still one in 7 million.
- Believing "random-looking" tickets are more likely to win. 1-2-3-4-5-6 has the exact same probability as any other 6-number combination.
Features of this calculator
- Works for any pick-N-from-M lottery, not just the famous ones.
- One-click presets for 6/49, Powerball (5/69 + 1/26), Mega Millions (5/70 + 1/25) and EuroMillions (5/50 + 2/12) — illustrative of published formats.
- Bonus-ball toggle with its own pool size and number-of-balls-drawn, for games like Powerball, Mega Millions and EuroMillions.
- Odds shown three ways: '1 in N', probability, and percentage — so the scale is unambiguous.
- Partial-match support: compute the odds of matching 3-of-5, 4-of-6, etc., not just the full jackpot.
- Perspective bar chart plotting your lottery's odds against real-world rare-event benchmarks on a log scale.
- Full show/hide step-by-step working using the C(r, m) · C(n − r, r − m) hypergeometric argument.
- Copy the summary as text or download the result card as a PNG.
Frequently asked questions
+What's the difference between odds and probability?
Probability is the fraction of favourable outcomes: 1/292,201,338 for Powerball. Odds "1 in N" is that same fraction inverted. This tool shows both so there's no ambiguity.
+Are lottery odds really the same every draw?
Yes. Balls are drawn independently each time, so every draw resets the probability. Whether last week's winning ticket had "lucky" numbers is irrelevant to this week's draw.
+Can I improve my odds with a system?
No. The only mathematically valid way to improve your odds of winning is to buy more distinct tickets — which scales linearly and gets uneconomical fast. Number patterns and hot/cold analyses don't change the underlying combinatorics.
+How is this different from a jackpot analyzer?
This calculator gives the mathematical odds of your ticket matching. A jackpot analyzer factors in the jackpot size, ticket price and expected number of winners to estimate expected value — that's a separate, harder calculation.