What formula does this use?

It uses the binomial coefficient C(n, k) = n! / (k! × (n−k)!), which counts how many ways you can choose k numbers from a pool of n without regard to order.

How does the bonus ball change the odds?

When enabled, the total combinations multiply by C(bonus_pool, bonus_picks) — the number of ways the bonus drum can be drawn. If only one bonus ball is drawn this is just the bonus pool size, so Powerball (5 from 69 + 1 from 26) gives C(69,5) × 26 = 292,201,338. If several are drawn, use the combination: EuroMillions (5 from 50 + 2 Lucky Stars from 12) gives C(50,5) × C(12,2) = 2,118,760 × 66 = 139,838,160.

Why does order not matter?

Most lotteries pay out based on which numbers you matched, not the sequence in which they were drawn. So choosing {1,2,3,4,5} is the same winning ticket regardless of draw order — hence combinations, not permutations.

How accurate are the results?

The calculator uses JavaScript BigInt for factorials to avoid floating-point overflow on large pools, so the combination count is exact. The displayed probability is then computed as a standard floating-point number.

What is the 1-in-X odds format?

It means you have 1 winning combination out of X equally likely tickets. For example, 1-in-292,201,338 means buying one ticket gives roughly a 0.000000342% chance of winning the jackpot.

Lottery Odds Calculator

Enter your lottery parameters to instantly see the exact odds of winning — with or without a bonus ball.

Lottery Parameters

Main pool size (total numbers to pick from)

Numbers drawn (how many you pick)

Bonus ball / Powerball drum

Enable for lotteries with a separate ball drawn from a second pool.

Common lotteries

Set your lottery parameters and click Calculate Odds.

Summary

This calculator uses the combinations formula C(n,k) = n! / (k! × (n−k)!) to compute the exact number of possible ticket combinations and the probability of matching all drawn numbers. For lotteries with a separate bonus drum, the total odds are C(main_pool, main_picks) × C(bonus_pool, bonus_picks). When only one bonus ball is drawn (Powerball, Mega Millions) this reduces to × bonus_pool; when several are drawn (e.g. EuroMillions draws 2 Lucky Stars from 12) the bonus factor is C(12,2) = 66.

How it works

Enter the size of the main number pool (e.g. 69 for Powerball).
Enter how many numbers are drawn from that pool (e.g. 5).
Optionally enable a bonus drum, then enter its pool size and how many bonus numbers are drawn (e.g. 26 and 1 for Powerball, or 12 and 2 for EuroMillions Lucky Stars).
The calculator applies C(n,k) to count all possible combinations.
Your odds are displayed as a 1-in-X ratio plus the exact decimal probability.

Use cases

Verify the official odds for Powerball, Mega Millions, or EuroMillions jackpots.
Compare how adding a bonus drum multiplies the odds.
Understand how changing pool size affects ticket combinations.
Teach combinations and probability in a math or statistics class.
Evaluate smaller local lottery games against national jackpots.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu