Probability · Combinations · Bonus balls
Lottery Calculator
Calculate your real odds of winning any lottery with hypergeometric math used in official disclosures. Free, no sign-up, with presets for Powerball, Mega Millions, EuroMillions, UK Lotto, Lotto Max, and Set for Life.
Lottery odds calculator
Luck or logic?
Five quick checks on how lottery odds are modeled — no trick questions, just clear statistics.
1. In a typical lotto line, order of the numbers on your ticket matters for matching the draw.
2. The count “how many ways to choose 6 numbers from 49” is written as:
3. If every ticket is equally likely, buying more tickets:
4. The hypergeometric setup for “m matches out of r drawn from a pool of n” uses:
5. A tool that outputs odds from pool size and draw rules:
Quick answer
A lottery calculator computes the real probability of winning using the hypergeometric formula: Odds = C(n,r) / [C(r,m) × C(n−r,r−m)]. In a 6/49 game, jackpot odds are 1 in 13,983,816.
How to calculate lottery odds
Lottery odds use combinations, written as C(n, r), where order does not matter.
C(n, r) = n! / [r! × (n − r)!]
Odds = C(n, r) / [C(r, m) × C(n − r, r − m)]
Example 6/49 jackpot: C(49,6)=13,983,816 and favorable outcomes=1, so odds are 1 in 13,983,816. Example matching 3 in 6/49 is about 1 in 57.
Lottery odds calculator for popular games
Powerball odds calculator
5/69 + 1/26. Jackpot: 1 in 292,201,338. Any prize: ~1 in 24.9.
Mega Millions odds calculator
5/70 + 1/25. Jackpot: 1 in 302,575,350. Any prize: ~1 in 24.
EuroMillions odds calculator
5/50 + 2/12. Jackpot: 1 in 139,838,160. Any prize: ~1 in 13.
UK Lotto odds calculator
6/59. Jackpot: 1 in 45,057,474. Any prize: ~1 in 9.3.
Lotto Max odds calculator
7/50. Jackpot: 1 in 33,294,800 per selection.
Set for Life odds calculator
5/47 + 1/10. Top prize: 1 in 15,339,390.
Texas lottery odds calculator
Lotto Texas jackpot: 1 in 25,827,165. Texas Two Step jackpot: 1 in 1,832,600.
Pick 3 and Pick 4 lottery calculator
Pick 3/Pick 4 use digit draws where repeats are allowed, so hypergeometric math does not apply.
| Play type | Odds |
|---|---|
| Pick 3 Straight | 1 in 1,000 |
| Pick 3 Box (6-way) | 1 in 167 |
| Pick 4 Straight | 1 in 10,000 |
| Pick 4 Box (24-way) | 1 in 417 |
If I buy multiple lottery tickets, what are my odds?
Chances scale linearly with unique tickets: odds become approximately Total Combinations divided by tickets bought.
| Powerball tickets | Approximate jackpot odds |
|---|---|
| 1 | 1 in 292,201,338 |
| 100 | 1 in 2,922,013 |
| 1,000 | 1 in 292,201 |
| 1,000,000 | 1 in 292 |
Lottery prediction calculator — why no algorithm works
No tool can predict independent random draws. Hot/cold numbers and pattern matching do not change base probability. The gambler's fallacy is believing overdue numbers are due.
Lottery statistics — hot and cold numbers
Frequency charts describe history, not future outcomes. They can be interesting, but they do not provide predictive power in fair audited draws.
Expected value of a lottery ticket
For most mainstream lotteries, expected value is negative after taxes, cash-value discount, and split-jackpot risk. Play for entertainment, not investment return.
Lottery odds by country and region
US
Powerball, Mega Millions, and state lotteries use draw-based combination rules.
UK
UK Lotto, EuroMillions, Set for Life, and Thunderball each have different pools and bonus structures.
Canada
Lotto Max and Lotto 6/49 are major draw-based games.
Australia
Saturday Lotto and Powerball Australia use distinct formats from US games.
India — Dear Lottery
Dear Lottery is raffle-style in many cases; use 1 ÷ sold tickets, not hypergeometric draw odds.
Bonus balls
From the remaining pool. After r main balls, one extra ball may be drawn from the n − r balls not used in the main draw. A typical “five + bonus” story multiplies the chance of exactly m − 1 main hits by 1 / (n − r) when one bonus ball is drawn and must be your one remaining ticket number.
From a separate bonus pool. Some games draw additional numbers from a second pool (same hypergeometric structure). If the bonus draw is independent of the main draw, combined odds multiply: (1 in main) × (1 in bonus line).
If you do win — taxes, annuity, and lump sum
US: federal withholding applies on larger wins; state tax varies; lump sum is typically lower than advertised annuity headline.
UK/Canada/Australia: winnings are generally tax-free, but income earned from proceeds can still be taxable depending on jurisdiction.
This tool calculates probability only. Confirm payout/tax rules with your lottery operator and tax advisor.
Frequently asked questions
How do I calculate the probability of winning a 6/49 lottery jackpot?
Use combinations: C(49, 6) = 13,983,816. One exact jackpot combination means jackpot odds are 1 in 13,983,816. For non-jackpot tiers, favorable outcomes are C(6, m) × C(43, 6 − m).
What are the odds of winning Powerball?
Powerball jackpot odds are 1 in 292,201,338 for matching 5 numbers from 69 plus 1 Powerball from 26. Overall odds of winning any listed prize are roughly 1 in 24.9.
How do I calculate Mega Millions odds?
Mega Millions jackpot odds are 1 in 302,575,350. You can derive it from C(70,5) × 25.
Can lottery calculators predict winning numbers?
No. Draws are independent random events, so past draws do not predict future outcomes. Hot/cold systems and pattern tools do not create a mathematical edge.
If I buy 100 lottery tickets, what are my odds?
Odds improve linearly with unique tickets. For Powerball, 100 tickets moves from 1 in 292,201,338 to about 1 in 2,922,013.
How do I calculate EuroMillions jackpot odds?
Use C(50,5) × C(12,2) = 139,838,160, so jackpot odds are 1 in 139,838,160.
Does this tool work for Pick 3 or Pick 4?
No. Pick 3/Pick 4 use independent digit draws where repetition is allowed, so their odds are based on permutation-style rules, not hypergeometric draws.
Can I use this calculator for UK Lotto, Lotto Max, or Set for Life?
Yes. Use the presets or enter custom values for draw-style games like UK Lotto, Lotto Max, and Set for Life.
Does this tool work for Dear Lottery or raffle-style games?
No. Raffle-style lotteries use pre-printed tickets. Odds are simply 1 divided by the number of sold tickets in that series.
Is the lottery a good investment?
Generally no. Expected value is usually negative after ticket cost, tax effects, annuity discounting, and split-jackpot risk.
Can lottery winnings be directly deposited?
Many lottery operators allow direct deposit for smaller claims, but limits and procedures vary by jurisdiction.
Can you buy lottery tickets with a debit card?
Often yes where lottery sales are legal, but acceptance rules vary by state/country and retailer.
Is this lottery calculator free?
Yes. It is free with no sign-up, no email, and no usage limits.
Before you play — responsible gambling resources
- US: National Council on Problem Gambling — 1-800-GAMBLER
- UK: GamCare — 0808 8020 133
- Canada: Responsible Gambling Council — responsiblegambling.org
- Australia: Gambling Help Online — 1800 858 858
This calculator exists to explain odds clearly, not to encourage play.