Lottery Odds Calculator
The ticket, priced in combinations — what any pick-N matrix really pays in odds, how many ways the drum can land, and how long one ticket a week really waits.
Lottery Odds Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Results are a model, not a quotation — an institution's own figures govern.
- Every input is an assumption; change one and the answer changes with it.
- Rounding is applied only at the display layer, so totals may differ by a cent from a statement that rounds each line.
In short: Five from 69 plus one from 26: the jackpot odds are 1 in 292,201,338 — C(69,5) = 11,238,513 lines times 26 Powerballs. One ticket twice a week, the jackpot arrives about every 2,809,628 years. The combinatorics are exact; the ticket remains a tax on hope.
Formula
ways = C(pool, picks) × C(bonus pool, bonus picks); wait in years = ways ÷ 104 draws a year
Lottery odds are combinatorics with a drum: the count of ways to draw your picks is C(pool, picks), and a bonus ball multiplies it by the bonus drum's own count. The two American giants run 5-from-69-plus-1-from-26 (1 in 292,201,338) and 5-from-70-plus-1-from-25 (1 in 302,575,350). The perspective line is the honest one: one ticket per drawing, twice a week, is 104 shots a year — divide the ways by 104 and the wait shows up in years. None of this is a reason to play or not to play; it is the price tag. The tax side of the same ticket lives on the lottery tax page.
Worked Example
- Enter the main pool and how many numbers you mark.
- Enter the bonus drum — or set it to 0 for none.
- Read the odds, the ways, and the wait.
Defaults: 69 pool, 5 picks, 26 bonus, 1 bonus pick — 1 in 292,201,338, about 2,809,628 years at two tickets a week.
Strengths & Limits Of This Model
Where this engine is strong
- Runs entirely in your browser — no figure you type is transmitted or stored.
- Shows the full working, so every number can be traced and challenged.
- Free, unmetered and free of affiliate incentives.
Where it stops
- Generalised assumptions cannot capture every individual circumstance.
- Jurisdiction-specific rules and mid-year changes may not be reflected.
- A model output is not a substitute for a professional review of your position.
Practical Use Cases
Jackpot math
the drum, counted exactly
Office pools
what a share really buys
Small games
the odds nobody prints
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Lottery Odds Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
What are the actual Powerball odds?
Five numbers from 69 plus one Powerball from 26: C(69,5) = 11,238,513 ways to draw the five, times 26 bonus balls = 292,201,338. The published line — 1 in 292.2 million — is exactly this arithmetic. Matching the five without the bonus is 1 in 11,688,053.52 because the bonus ball then has 25 wrong ways and 1 right one to sit in.
How are these odds calculated?
Combinations: C(n,k) = n! ÷ (k!(n−k)!) — the count of unordered k-subsets of an n-pool. Five from 69 is 69×68×67×66×65 ÷ 120 = 11,238,513. The bonus drum multiplies: ×26 for Powerball. Order never matters in these games, which is why combinations and not permutations price the ticket.
What are the Mega Millions odds?
5 from 70 plus 1 from 25: C(70,5) = 12,103,014 times 25 = 302,575,350 — 1 in 302.6 million, slightly worse than Powerball's jackpot despite the similar headline. Set the fields to 70, 5, 25, 1 and this page reproduces it exactly. The any-prize odds run near 1 in 24 for both games — driven by the small-prize tiers, not the jackpot.
Does buying more tickets help?
Linearly, honestly: 10 tickets make it 10 times as likely and still practically impossible — 10 in 292,201,338 is about 1 in 29.2 million. The wait card drops from 2.8 million years to 280,963. The only move that changes the RATIO of your life spent waiting meaningfully is not playing a game priced at 50 cents of hope per dollar of EV.
Do 'lucky numbers' or patterns change the odds?
Not the odds — every combination is equally likely, including 1-2-3-4-5. Patterns change something real but different: the PAYOUT, because popular picks (birthdays, sequences) share the jackpot with more people when they win. Play 1-2-3-4-5 and you are pricing an equal chance at a smaller split. The drum has no memory and no taste.
Is the wait number a promise?
It is an average, not a promise — the expected years between jackpots at 104 tickets a year. A jackpot can arrive on the first ticket (1 in 292,201,338 of that) or never in ten lifetimes; averages describe the mountain, not your hike. The honest reading: the wait is so far past a human scale that the ticket's value is the daydream, and the daydream costs two dollars.
Can this price a raffle or a small state game?
Yes — the fields take any matrix: a 5-from-39 fantasy game with no bonus ball is C(39,5) = 575,757, and the wait card drops to about 5,536 years at two tickets a week. Small games are the only place the odds reach a human scale, and even there the expected value of a two-dollar ticket rarely crosses a dollar. The combinatorics are the same; only the honesty of the prize table varies.
Why does the bonus ball multiply the odds so hard?
Because the bonus drum is an independent draw: matching five main numbers AND the bonus means clearing both hurdles, and probabilities of independent events multiply. The bonus turns 11,238,513 into 292,201,338 — a factor of 26 from a single extra ball. It is the cheapest-looking field on the card and by far the most expensive in odds.