Free lottery odds calculator
Work out your real chance of a lottery jackpot from just two numbers — the pool size and how many numbers you pick — using the combinations formula C(n, k). A classic 6-from-49 draw returns 1 in 13,983,816, and every figure is updated live, as you type.
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What are lottery odds?
Your lottery odds are the chance that the numbers you pick exactly match the numbers drawn. This lottery odds calculator works it out from just two inputs — the pool size (how many numbers the draw chooses from) and how many numbers you pick — and reports the result as a clean "1 in X" figure. For a classic 6-from-49 draw it returns 1 in 13,983,816.
The odds depend only on how many distinct equally-likely combinations of numbers exist. Every ticket is one combination out of that total, so "1 in X" simply means there are X possible tickets and exactly one of them is the winner. The maths behind X is the combinations formula, written C(n, k) or nCk — the same counting tool used across probability, poker hands, and statistics.
How to calculate lottery odds (the nCr combinations formula)
Because the order numbers are drawn in does not matter, lottery odds use combinations, not permutations. The number of ways to choose k items from n is the binomial coefficient C(n, k), read "n choose k":
The calculator avoids huge factorials by multiplying iteratively — it builds C(n, k) as (n ÷ 1) × ((n−1) ÷ 2) × ((n−2) ÷ 3) × … for k terms — but the answer is identical to the factorial formula above. Try it with the lottery number generator if you want to see nCr and nPr side by side.
- Step 1 — pool size n: count the numbers the draw selects from (e.g. 49).
- Step 2 — pick count k: count the numbers you choose (e.g. 6).
- Step 3 — apply C(n, k): compute n! / (k!·(n−k)!) to get the number of possible tickets.
- Step 4 — read the odds: your chance of the jackpot is 1 in that number.
A worked example: 6 from 49
Marco plays a classic 6/49 lottery and wants to know his real chance of the jackpot. He enters pool size 49 and numbers to pick 6. Here is exactly how the calculator gets to its answer.
Step 1 — Set up C(49, 6)
With n = 49 and k = 6, the formula is C(49, 6) = 49! / (6! × 43!). Rather than expand the full factorials, cancel the 43! and keep only the top six terms.
Step 2 — Multiply the six top terms
Step 3 — Read the odds
There are 13,983,816 possible 6-number tickets, and exactly one wins the jackpot. The calculator prints 1 in 13,983,816 with the note "Chance of matching 6 out of 49" — Marco's odds on a single ticket are just under 1 in 14 million.
Why order doesn't matter (combinations vs permutations)
If the order of the drawn numbers mattered, you would use permutations P(n, k) = n! / (n−k)!, which counts every ordering separately. For 6 from 49 that would be 10,068,347,520 ordered sequences — far more than the combination count.
But a lottery ticket {3, 17, 42, 19, 8, 31} wins whether those numbers are drawn in that order or any other. Each set of 6 numbers can be arranged in 6! = 720 different orders, all of which are the same ticket. Dividing the 10,068,347,520 permutations by 720 collapses them down to the 13,983,816 distinct combinations the calculator uses.
Real lottery jackpot odds compared
The table below shows the single-pool combination C(n, k) for popular game formats — the number this calculator returns when you enter that pool size and pick count. The bigger the pool and the more numbers you pick, the longer the odds.
| Game format | Pool (n) | Pick (k) | Main-pool odds = 1 in C(n, k) |
|---|---|---|---|
| Pick 3 of 10 (toy example) | 10 | 3 | 1 in 120 |
| Small 6/42 game | 42 | 6 | 1 in 5,245,786 |
| 6/45 game (e.g. Australia, Saturday Lotto) | 45 | 6 | 1 in 8,145,060 |
| Classic 6/49 (Lotto, EuroMillions-style main) | 49 | 6 | 1 in 13,983,816 |
| Powerball main pool, 5 of 69 (no Powerball) | 69 | 5 | 1 in 11,238,513 |
| Mega Millions main pool, 5 of 70 (no Mega Ball) | 70 | 5 | 1 in 12,103,014 |
These are main-pool combinations only — exactly what this tool computes. US Powerball and Mega Millions add a separate bonus ball, which makes the official jackpot odds far longer (see the next section).
Bonus balls, Powerball, and Mega Millions
Games like US Powerball and Mega Millions draw from two separate pools: a set of main (white) balls plus one extra ball from its own pool. Because the two draws are independent, you multiply the odds of each to get the overall jackpot odds.
So to estimate a two-pool game with this calculator, compute the main pool here (enter 69 and 5 for Powerball → 1 in 11,238,513), then multiply by the size of the bonus-ball pool yourself. The official Powerball jackpot odds are 1 in 292,201,338 and Mega Millions are 1 in 302,575,350.
What the odds mean for a ticket's value
Odds of 1 in 13,983,816 are hard to picture, so a comparison helps: you are roughly as likely to win a 6/49 jackpot on one ticket as you are to flip a fair coin and get heads about 24 times in a row. The odds are fixed by the combinations — they do not improve with "lucky" numbers, birthdays, or the previous draw's results, because every combination is equally likely.
- Each combination is equally likely. 1-2-3-4-5-6 has exactly the same chance as any "random-looking" ticket.
- Buying more tickets scales odds linearly: 10 distinct tickets in a 6/49 game move you from 1 in 13,983,816 to about 1 in 1,398,382 — still extremely long.
- Expected value compares the prize × probability against the ticket price; for almost every lottery the expected value is negative, which is why it's a game of chance, not an investment.
This section is descriptive probability, not financial advice. Lotteries are designed so the house edge is large; treat any ticket as paid entertainment with a tiny chance of a prize, never as a savings or income strategy.
Common lottery odds questions
What are the odds of winning a 6/49 lottery?
1 in 13,983,816 on a single ticket. That is C(49, 6) — the number of distinct 6-number combinations from 49 numbers — and exactly one of them is the jackpot winner.
Does this calculator include the Powerball or bonus ball?
No. It computes the main-pool combination C(n, k) only. For Powerball, entering pool 69 and pick 5 returns 1 in 11,238,513; the official 1 in 292,201,338 jackpot odds come from multiplying that by the 26 separate Powerball numbers.
Do lucky numbers or past draws change my odds?
No. Every combination is equally likely on every draw, and draws are independent, so previous results and "hot" or "cold" numbers have no effect. Picking 1-2-3-4-5-6 has identical odds to any other ticket.
How this calculator works and sources
This lottery odds calculator applies the combinations formula C(n, k) = n! / (k!·(n−k)!) exactly, computing it iteratively for speed and rounding to a whole number of tickets, then reporting 1 in that figure. The maths runs entirely in your browser — nothing is sent anywhere. The 6/49 value of 13,983,816, the Powerball jackpot odds of 1 in 292,201,338, and the Mega Millions odds of 1 in 302,575,350 are standard, well-documented combinatorics figures.
Wikipedia — Lottery mathematics: the combinations formula and the 13,983,816-ticket 6/49 result.Powerball — official prize chart and jackpot odds (1 in 292,201,338).Minnesota Lottery — Figuring the Odds: how lottery probabilities are calculated.Frequently asked questions about the free lottery odds calculator
About this lottery odds calculator
This lottery odds calculator runs entirely in your browser — your pool size and pick count never leave your device. It applies the combinations formula C(n, k) = n! / (k!·(n−k)!), computing it iteratively for speed, and reports your single-ticket jackpot odds as a clean "1 in X" figure. It covers the main number pool only and does not add a Powerball or bonus ball.
Find more tools on the everyday calculators shelf or browse the full calculators directory. To generate a set of numbers to play, try the lottery number generator.