Lottery Odds Calculator
Calculate the exact odds of winning any lottery game
Formula:
Odds = C(n,r) × C(b,p)Lottery Configuration
Enter the lottery format
Main Numbers
Bonus Ball (Optional)
Odds Results
Your lottery odds breakdown
Jackpot Odds
1 in 292.2M
292,201,338 total combinations
Probability: 0.34 in 1M
Main Combinations
11,238,513
Bonus Combinations
26
Est. Any Prize
1 in 5.8M
Prize Tier Odds
Match 5 + Bonus
1 in 292.2M
Match 5 only
1 in 11.7M
Match 4 + Bonus
1 in 913.1K
Match 4 only
1 in 36.5K
Match 3 + Bonus
1 in 14.5K
Match 3 only
1 in 580
Match 2 + Bonus
1 in 701
Match 2 only
1 in 28
Important: Lottery games have a significant house edge (typically 40-50%). The expected value of a ticket is usually negative. Play responsibly and only with money you can afford to lose.
Popular Lottery Formats
Load common lottery configurations
Combinations Formula
How lottery odds are calculated
C(n,r) = n! / (r! × (n-r)!)
n = Total balls in the pool
r = Numbers you pick
! = Factorial (e.g., 5! = 5×4×3×2×1)
C(n,r) = Total possible combinations
Quick Answer
TL;DR summary
Lottery odds are calculated using combinations: C(n,r) = n! / (r!(n-r)!). For Powerball (5/69 + 1/26): C(69,5) × C(26,1) = 11,238,513 × 26 = 292,201,338. Your chance of winning the jackpot is 1 in 292.2 million - you're more likely to be struck by lightning twice.
Key Facts About Lottery Odds
Important things to know
- Powerball jackpot odds: 1 in 292,201,338 (matching 5 white + 1 red)
- Mega Millions jackpot odds: 1 in 302,575,350 (matching 5 white + 1 gold)
- Overall odds of winning ANY Powerball prize: 1 in 24.87
- Adding a bonus ball multiplies the total combinations significantly
- Buying 100 tickets only changes odds from 1:292M to 100:292M (still negligible)
- Lottery expected value is typically -40% to -50% (house edge)
- State lotteries are mathematically worse than most casino games
Frequently Asked Questions
Common lottery odds questions
How are lottery odds calculated?
Lottery odds use the combinations formula: C(n,r) = n! / (r!(n-r)!). For a game where you pick r numbers from n total numbers, this formula calculates all possible combinations. For games with bonus balls, multiply the main combinations by the bonus ball combinations.
Why are lottery odds so bad?
Lotteries need to fund prizes, operating costs, and state revenue - typically only 50-60% of ticket sales go to prizes. The large jackpot odds are necessary to create exciting prize pools. The mathematical expected value of a lottery ticket is usually -40% to -50%, worse than almost any casino game.
Does buying more tickets improve my odds significantly?
Mathematically yes, but practically no. Buying 100 Powerball tickets changes your odds from 1 in 292 million to 100 in 292 million (still 0.000034%). You would need to buy millions of tickets to have meaningful odds, which would cost more than most jackpots.
What are the odds of matching some numbers but not all?
Partial match odds are much better. In Powerball: matching 5 numbers (no Powerball) is 1 in 11.7 million, matching 4 + Powerball is 1 in 913,000, and matching just the Powerball is 1 in 38. These tiers make up the majority of winners.
Are some number combinations luckier than others?
No. Every combination has exactly the same probability of being drawn. "1-2-3-4-5-6" has the same odds as any other combination. However, popular numbers (birthdays, patterns) mean more people might share your jackpot if you win.
How this works
Calculations follow the published mathematics of the game — combinatorics for cards, probability theory for dice, and expected-value accounting for wagers. Results are verified against independent references (primarily Wizard of Odds). No calculation here is an opinion or recommendation; it is arithmetic applied to the rules of the game.
What this tool can’t do
When to consult a professional
This tool computes probability and expected value. It is not a betting system and cannot predict the outcome of any individual wager. If gambling is causing problems for you or someone you know, call the National Problem Gambling Helpline at 1-800-GAMBLER.
Sources
- [1]Wizard of Odds — Michael Shackleford, ASAIndustrywizardofodds.comAccessed Apr 21, 2026
Actuary; widely cited casino-game probability reference. Used for house-edge and EV verification.
- [2]National Council on Problem GamblingOfficial sourcencpgambling.orgAccessed Apr 21, 2026
Responsible-gambling guidance and 1-800-GAMBLER helpline.
Joseph OrdunaFounder & Software Engineer
Full-stack software engineer specializing in embedded systems, web architecture, and AI/ML. Founder of Practical Web Tools. Built the gesture-controlled drone IP acquired by KD Interactive (Aura Drone, sold on Amazon).