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Lottery Odds Calculator

Work out lottery odds instantly with clear inputs, formula shown and shareable results.

About Lottery Odds Calculator

The number of possible tickets is C(pool, pick), and the number matching exactly the required count is C(pick, match) x C(pool - pick, pick - match). A 6 from 49 jackpot is one in 13,983,816, and because the count is a combination, adding a single ball to the pool raises the odds by roughly 15%.

Formulas

Total combinations

total = C(pool, pick) = pool! / (pick! x (pool - pick)!)

Matching combinations

ways = C(pick, match) x C(pool - pick, pick - match)

Worked example

With the default values below, Lottery Odds Calculator returns Odds are one in of 13,983,816. Change any input above and every figure here is recalculated in your browser.

Inputs used

Numbers you pickaccepts 1–20
6
Numbers in the poolaccepts 2–90
49
Numbers you need to matchaccepts 1–20
6

Results

Odds are one in
13,983,816
Chance of winning
0.00000715%
Total possible tickets
13,983,816
Tickets that would win
1

Step by step

  1. 1Values used
  2. 2Total combinations
  3. 3Matching combinations
  4. 4Odds are one in= 13,983,816
  5. 5Chance of winning= 0.00000715
  6. 6Total possible tickets= 13,983,816
  7. 7Tickets that would win= 1

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is the Lottery Odds figure worked out?

total = C(pool, pick) = pool! / (pick! x (pool - pick)!). The number of possible tickets is C(pool, pick), and the number matching exactly the required count is C(pick, match) x C(pool - pick, pick - match).

Why does this matter?

A 6 from 49 jackpot is one in 13,983,816, and because the count is a combination, adding a single ball to the pool raises the odds by roughly 15%.

What do I need to enter?

Enter numbers you pick, numbers in the pool, numbers you need to match. The defaults shown are a realistic worked example — swap in your own figures to get a result you can use.

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