Lottery
Calculate lottery odds instantly — enter pool size, balls drawn, and target matches. Get jackpot probability, prize tier breakdown, and interactive charts for any lottery format.
About This Calculator
Our lottery odds calculator helps you understand the true probability of winning any lottery game. Whether you play the Powerball, Mega Millions, EuroMillions, state lotteries in India, or local raffles, this tool computes the exact odds using the combination formula from probability theory. Simply enter the total number of balls in the pool, how many balls are drawn, and how many numbers you want to match to see your chances.
The calculation uses the hypergeometric distribution formula: the probability of matching m numbers when r numbers are drawn from a pool of n is C(r,m) × C(n−r,r−m) / C(n,r). The odds are expressed as 1 in X, where X is the number of combinations containing exactly m matches divided by the total number of possible combinations. This is the same mathematics used by all major lotteries worldwide.
The results include a full breakdown table showing odds and probability for every possible match level from 0 to the number of balls drawn, so you can see how the odds change as you aim for different prize tiers. The interactive chart visualizes the probability distribution across match levels.
Regional Notes
India: State lotteries operate in Kerala, Punjab, Sikkim, Nagaland, and others. Most use a 6/49 format. Winnings are taxed at 30% under Section 194B plus 4% cess for prizes over ₹10,000.
US: Powerball uses 5/69 + 1/26, Mega Millions uses 5/70 + 1/25. Federal withholding is 24% and state taxes vary from 0% to 13%. Top marginal rate can reach 37%.
UK: The National Lottery uses a 6/59 format. All lottery winnings are tax-free in the UK, making it one of the most favorable jurisdictions for lottery players.
Frequently Asked Questions
How do I calculate lottery odds?
Lottery odds are calculated using combinations. For a game where you pick r numbers from a pool of n, the probability of matching exactly m numbers is C(r, m) × C(n−r, r−m) / C(n, r). This calculator automates this formula for any lottery format.
What are the odds of winning a 6/49 lottery jackpot?
The odds of winning a standard 6/49 lottery jackpot (matching all 6 numbers) are 1 in 13,983,816. Matching 5 numbers has odds of 1 in 55,491, matching 4 numbers is 1 in 1,033, and matching 3 numbers is 1 in 57.
How do lotteries work in India?
Lotteries in India are regulated by state governments under the Public Gambling Act. States like Kerala, Punjab, and Sikkim operate official lotteries. Winnings are subject to a flat 30% tax plus cess under Section 194B, and prizes above ₹10,000 have TDS deducted before payout.
How are lottery winnings taxed in the US?
US lottery winnings are subject to 24% federal withholding tax, plus additional tax based on your income bracket (up to 37%). State taxes vary from 0% (Texas, Florida) to 13% (Arizona). Most states also withhold state tax. The effective tax rate can exceed 50% in high-tax states.
Are lottery winnings taxable in the UK?
Lottery winnings in the UK are completely tax-free. The National Lottery and other UK lotteries do not charge tax on prizes, and winners are not required to declare winnings as income. This makes UK lotteries more attractive compared to US or Indian lotteries where significant taxes apply.
What is the difference between odds and probability?
Probability is the chance of winning expressed as a value between 0 and 1, while odds compare the number of winning outcomes to losing outcomes. For example, a 1 in 13,983,816 probability equals odds of 1:13,983,815 against winning. This calculator shows both measures.
Can lottery odds be improved by buying more tickets?
Buying more tickets does improve your odds linearly. For a 1 in 14 million lottery, buying 10 tickets gives you 10 in 14 million odds (1 in 1.4 million). However, the expected value remains negative, and the probability of winning any significant prize is still extremely low.
Do lotteries use bonus balls and how do they affect odds?
Some lotteries include bonus balls drawn from the remaining pool or a separate bonus pool. Bonus balls create additional prize tiers, typically giving players who matched most numbers a chance at a better prize. The odds improve slightly for lower tiers but the jackpot odds remain the same.