Lottery Odds Calculator

Choose a game or enter your own lottery format. The calculator gives the exact probability of matching a chosen number of balls — as “1 in X”, as a percentage and in words.

Game

Picking a game fills in its format. Changing any number below switches to “Custom lottery”.

Numbers in the pool (N)

How many numbers the balls are drawn from, e.g. 49.

Numbers drawn (D)

How many numbers the machine draws, e.g. 6 in Lotto or 20 in Keno.

Numbers you pick (P)

How many numbers you mark on one line of the ticket.

Exact matches (m)

Exactly how many of your numbers should be among the drawn ones.

Second number pool

Some lotteries draw a second, separate set of numbers. The two pools are independent, so their probabilities multiply.

Odds: 1 in 13,983,816

Probability: —
In words: —

What do these numbers mean?

Result for the settings above: 1 in 13,983,816. It updates as soon as any field changes.
We compute it from the formula shown below — not from a prediction model and not from draw history.
The result describes a single draw. It does not accumulate over consecutive games: the chance is the same every time.
The calculator computes, it does not advise. It does not point to numbers and does not say how much to play.

The numbers come from the formula and the values you typed above. They are not a forecast — no calculator changes the probability of a single draw.

How do I use this page?

Fill in the fields in the form above — the result recomputes at once, with no page reload.
Under the result you will find the interpretation scale, if the calculator has one: it says which range your value fell into.
The formula we use is shown lower on this page — you can check the arithmetic yourself.
To compute the same for another game or variant, change it in the select field — prices and pools update automatically.

What this page does not do: It does not point to numbers to play and does not predict a draw — every draw is independent of the previous ones.

Formula

P(m) = C(D, m) × C(N − D, P − m) ÷ C(N, P) · two pools: P = P₁ × P₂

N is the pool size, D the numbers drawn, P the numbers you pick and m the exact number of matches. C(n, k) is the binomial coefficient. This is the hypergeometric distribution: it counts the tickets with exactly m matches and divides them by all possible tickets. With two independent pools, as in Eurojackpot, the two probabilities are multiplied.

Theory — how is the lottery odds calculator computed?

The calculator lets you pick a ready-made game or enter your own lottery format, and returns the exact probability of matching a chosen number of balls as “1 in X”. For a given format, it counts how many of all possible tickets have exactly that number of matches and divides this by the total number of possible tickets. In Lotto 6 of 49, the chance of matching all six numbers is exactly 1 in 13,983,816. This is an exact calculation, not an estimate.

Frequently asked questions

What are the odds of winning the Lotto jackpot?

In Lotto 6/49 the odds of matching all six numbers are exactly 1 in 13,983,816 — the number of ways to choose 6 numbers out of 49.

Why does the calculator say “exactly” and not “at least”?

Because the hypergeometric formula gives the probability of one exact number of matches. For “at least three” add up the rows for three, four, five and six matches — the hypergeometric distribution calculator does this for you as P(X ≥ k).

Can I calculate the odds for a lottery from my country?

Yes. Choose “Custom lottery” and enter the pool size and how many numbers are drawn and picked. If the lottery draws an extra number from a separate pool, switch on the second pool.

Lottery Odds Calculator

Formula

Read more

Frequently asked questions

See also

Keno Odds Calculator

Lottery Syndicate Calculator

Lottery System Calculator

My saved selections

Notifications after draws