ConverterHub

Lottery Odds Calculator

Find your chance of winning the lottery.

Result

1 : 13,983,816
13,983,816

How it is calculated

A lottery draw where the order of the numbers does not matter is counted with combinations: C(n, k) = n! / (k! × (n − k)!), where n is the total count of balls in the pool and k is how many numbers you pick. The tool computes it with the multiplicative form, so large factorials are never formed, and shows the number of possible combinations and the odds of one ticket winning as 1 in that number. Both inputs must be whole numbers, k cannot be greater than n, and n is limited to 90. The result is the chance of matching all the main numbers only. Bonus balls, lower prizes, games with a separate pool (such as a star or power number) and tickets with several lines are not included.

Worked example

In a game where you pick 6 numbers from 49, n = 49 and k = 6. C(49, 6) = (49 × 48 × 47 × 46 × 45 × 44) / (6 × 5 × 4 × 3 × 2 × 1) = 10,068,347,520 / 720 = 13,983,816 combinations. A single ticket therefore has odds of 1 : 13,983,816 of matching all six numbers. Buying 10 different tickets improves the chance to 10 in 13,983,816, which is still roughly 1 in 1.4 million.

Try this example →

Common mistakes

  • Applying the result to a game that has a second pool (bonus or star number); the odds of the full game are the product of both pools.
  • Entering the number of tickets or the numbers already drawn instead of the pool size and picks.
  • Believing that numbers which have not come up recently are "due"; each draw is independent.
  • Confusing odds for the jackpot with odds of winning any prize, which are much better but not given here.
  • Using a game where order matters, such as a three-digit game in which 123 differs from 321, where the count is a different formula.

About this calculator

This calculator uses the combinations formula (n choose k, written C(n,k) = n!/(k!(n-k)!)) to work out how many possible number combinations exist in a lottery, and inverts that figure to give the odds of any single ticket matching the winning numbers. It accounts for whether a bonus/power ball is drawn from a separate pool, which multiplies the total combinations and long odds even further.

It's used by lottery players comparing the odds of different games (a 6/49 draw versus a 5/70 game with a separate power ball, for example), and by anyone wanting to understand, in concrete terms, just how unlikely a jackpot win actually is — often expressed as 1 in tens or hundreds of millions.

Was this helpful?

You can pick up to 3 reactions.

Comments (0)

  • Be the first to comment.

Popular calculators

Loan Calculator

Monthly payment, total interest and full amortization schedule.

Percentage Calculator

Percent change, percent of, and ratio calculations.

Discount Calculator

Calculate final price, savings, and discount amount.

BMI Calculator

Body mass index from height and weight (metric or imperial).

Age Calculator

Compute your exact age in years, months and days from a birth date.

Compound Interest Calculator

Calculate the final amount and interest earned with compounding.

All Calculators