Health Lottery Odds Calculator

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Calculate Lotto Odds

Balls to be drawn: Total number of prize levels:
From a pool of: Tick to include bonus balls:
Bonus balls to be drawn: Prize levels that involve
matching a bonus ball:
Bonus ball name:
Odds for Popular Lotteries:

Calculated Odds
Numbers Matched Odds Show Working Out +
5 Main Numbers (Jackpot) 1 in 2,118,760.000 Show/Hide ›

The odds for this prize level are not influenced by any 'Bonus Balls' and only the variables associated with the main ball pool are required to calculate the correct odds. The following formula is therefore used (Please note: calculations have been rounded):

C(n,r)
C(r,m)
×
C(n-r,r-m)
C(n,r) = Odds of correctly choosing r balls from n
n = Number of balls in the main pool
r = Balls drawn from the main pool
m = Balls to be matched from the main pool
C(50,5)
C(5,5)
×
C(50-5,5-5)
Substitute:
n for 50 (number of balls in the main pool)
r for 5 (balls drawn from the main pool)
m for 5 (balls to be matched from the main pool)
50!
5! × (50 - 5)!
5!
5! × (5 - 5)!
×
45!
0! × (45 - 0)!
Expand:
C(50,5) = 50! ÷ (5! × (50-5)!)
C(5,5) = 5! ÷ (5! × (5-5)!)
C(50-5,5-5) = 45! ÷ (0! × (45-0)!)
! means 'Factorial' eg: 50! = 50 × 49 × 48 ... × 1
Note: 0! = 1
2,118,760
1 × 1
Simplify:
50! ÷ (5! × (50-5)!) = 2,118,760
5! ÷ (5! × (5-5)!) = 1
45! ÷ (0! × (45-0)!) = 1
2,118,760 = 2,118,760.000
1
Calculate:
2,118,760 ÷ (1 × 1) = 2,118,760.000
4 Main Numbers + Bonus Ball 1 in 423,752.000 Show/Hide ›

The odds for this prize level are directly influenced by the Bonus Ball. Since the Bonus Ball is drawn from the same pool as the main numbers, the following formula is used (Please note: calculations have been rounded):

C(n,r)
r - m
n - r
× C(r,m) × C(n-r,r-m)
C(n,r) = Odds of correctly choosing r balls from n
n = Number of balls in the main pool
r = Balls drawn from the main pool
m = Balls to be matched from the main pool
C(50,5)
5 - 4
50 - 5
× C(5,4) × C(50-5,5-4)
Substitute:
n for 50 (number of balls in the main pool)
r for 5 (balls drawn from the main pool)
m for 4 (balls to be matched from the main pool)
50!
5! × (50 - 5)!
5 - 4
50 - 5
×
5!
4! × (5 - 4)!
×
45!
1! × (45 - 1)!
Expand:
C(50,5) = 50! ÷ (5! × (50-5)!)
C(5,4) = 5! ÷ (4! × (5-4)!)
C(50-5,5-4) = 45! ÷ (1! × (45-1)!)
! means 'Factorial' eg: 50! = 50 × 49 × 48 ... × 1
Note: 0! = 1
2,118,760
0.0222 × 5 × 45
Simplify:
50! ÷ (5! × (50-5)!) = 2,118,760
(5-4) ÷ (50-5) = 0.0222
5! ÷ (4! × (5-4)!) = 5
45! ÷ (1! × (45-1)!) = 45
2,118,760 = 423,752.000
5
Calculate:
2,118,760 ÷ (0.0222 × 5 × 45) = 423,752.000
4 Main Numbers 1 in 9,630.727 Show/Hide ›

The odds for this prize level are indirectly influenced by the Bonus Ball. Even though this prize level only involves matching 4 main numbers, the fact that you can also match 4 main numbers and a Bonus Ball means the odds of matching 4 main numbers alone are increased. Since the Bonus Ball is also drawn from the same pool as the main numbers, the following formula is used (Please note: calculations have been rounded):

C(n,r)
n - r - r + m
n - r
× C(r,m) × C(n-r,r-m)
C(n,r) = Odds of correctly choosing r balls from n
n = Number of balls in the main pool
r = Balls drawn from the main pool
m = Balls to be matched from the main pool
C(50,5)
50 - 5 - 5 + 4
50 - 5
× C(5,4) × C(50-5,5-4)
Substitute:
n for 50 (number of balls in the main pool)
r for 5 (balls drawn from the main pool)
m for 4 (balls to be matched from the main pool)
50!
5! × (50 - 5)!
50 - 5 - 5 + 4
50 - 5
×
5!
4! × (5 - 4)!
×
45!
1! × (45 - 1)!
Expand:
C(50,5) = 50! ÷ (5! × (50-5)!)
C(5,4) = 5! ÷ (4! × (5-4)!)
C(50-5,5-4) = 45! ÷ (1! × (45-1)!)
! means 'Factorial' eg: 50! = 50 × 49 × 48 ... × 1
Note: 0! = 1
2,118,760
0.9778 × 5 × 45
Simplify:
50! ÷ (5! × (50-5)!) = 2,118,760
(50-5-5+4) ÷ (50-5) = 0.0222
5! ÷ (4! × (5-4)!) = 5
45! ÷ (1! × (45-1)!) = 45
2,118,760 = 9,630.727
220
Calculate:
2,118,760 ÷ (0.9778 × 5 × 45) = 9,630.727
3 Main Numbers + Bonus Ball 1 in 4,815.364 Show/Hide ›

The odds for this prize level are directly influenced by the Bonus Ball. Since the Bonus Ball is drawn from the same pool as the main numbers, the following formula is used (Please note: calculations have been rounded):

C(n,r)
r - m
n - r
× C(r,m) × C(n-r,r-m)
C(n,r) = Odds of correctly choosing r balls from n
n = Number of balls in the main pool
r = Balls drawn from the main pool
m = Balls to be matched from the main pool
C(50,5)
5 - 3
50 - 5
× C(5,3) × C(50-5,5-3)
Substitute:
n for 50 (number of balls in the main pool)
r for 5 (balls drawn from the main pool)
m for 3 (balls to be matched from the main pool)
50!
5! × (50 - 5)!
5 - 3
50 - 5
×
5!
3! × (5 - 3)!
×
45!
2! × (45 - 2)!
Expand:
C(50,5) = 50! ÷ (5! × (50-5)!)
C(5,3) = 5! ÷ (3! × (5-3)!)
C(50-5,5-3) = 45! ÷ (2! × (45-2)!)
! means 'Factorial' eg: 50! = 50 × 49 × 48 ... × 1
Note: 0! = 1
2,118,760
0.0444 × 10 × 990
Simplify:
50! ÷ (5! × (50-5)!) = 2,118,760
(5-3) ÷ (50-5) = 0.0444
5! ÷ (3! × (5-3)!) = 10
45! ÷ (2! × (45-2)!) = 990
2,118,760 = 4,815.364
440
Calculate:
2,118,760 ÷ (0.0444 × 10 × 990) = 4,815.364
3 Main Numbers 1 in 223.970 Show/Hide ›

The odds for this prize level are indirectly influenced by the Bonus Ball. Even though this prize level only involves matching 3 main numbers, the fact that you can also match 3 main numbers and a Bonus Ball means the odds of matching 3 main numbers alone are increased. Since the Bonus Ball is also drawn from the same pool as the main numbers, the following formula is used (Please note: calculations have been rounded):

C(n,r)
n - r - r + m
n - r
× C(r,m) × C(n-r,r-m)
C(n,r) = Odds of correctly choosing r balls from n
n = Number of balls in the main pool
r = Balls drawn from the main pool
m = Balls to be matched from the main pool
C(50,5)
50 - 5 - 5 + 3
50 - 5
× C(5,3) × C(50-5,5-3)
Substitute:
n for 50 (number of balls in the main pool)
r for 5 (balls drawn from the main pool)
m for 3 (balls to be matched from the main pool)
50!
5! × (50 - 5)!
50 - 5 - 5 + 3
50 - 5
×
5!
3! × (5 - 3)!
×
45!
2! × (45 - 2)!
Expand:
C(50,5) = 50! ÷ (5! × (50-5)!)
C(5,3) = 5! ÷ (3! × (5-3)!)
C(50-5,5-3) = 45! ÷ (2! × (45-2)!)
! means 'Factorial' eg: 50! = 50 × 49 × 48 ... × 1
Note: 0! = 1
2,118,760
0.9556 × 10 × 990
Simplify:
50! ÷ (5! × (50-5)!) = 2,118,760
(50-5-5+3) ÷ (50-5) = 0.0444
5! ÷ (3! × (5-3)!) = 10
45! ÷ (2! × (45-2)!) = 990
2,118,760 = 223.970
9,460
Calculate:
2,118,760 ÷ (0.9556 × 10 × 990) = 223.970
2 Main Numbers + Bonus Ball 1 in 223.970 Show/Hide ›

The odds for this prize level are directly influenced by the Bonus Ball. Since the Bonus Ball is drawn from the same pool as the main numbers, the following formula is used (Please note: calculations have been rounded):

C(n,r)
r - m
n - r
× C(r,m) × C(n-r,r-m)
C(n,r) = Odds of correctly choosing r balls from n
n = Number of balls in the main pool
r = Balls drawn from the main pool
m = Balls to be matched from the main pool
C(50,5)
5 - 2
50 - 5
× C(5,2) × C(50-5,5-2)
Substitute:
n for 50 (number of balls in the main pool)
r for 5 (balls drawn from the main pool)
m for 2 (balls to be matched from the main pool)
50!
5! × (50 - 5)!
5 - 2
50 - 5
×
5!
2! × (5 - 2)!
×
45!
3! × (45 - 3)!
Expand:
C(50,5) = 50! ÷ (5! × (50-5)!)
C(5,2) = 5! ÷ (2! × (5-2)!)
C(50-5,5-2) = 45! ÷ (3! × (45-3)!)
! means 'Factorial' eg: 50! = 50 × 49 × 48 ... × 1
Note: 0! = 1
2,118,760
0.0667 × 10 × 14,190
Simplify:
50! ÷ (5! × (50-5)!) = 2,118,760
(5-2) ÷ (50-5) = 0.0667
5! ÷ (2! × (5-2)!) = 10
45! ÷ (3! × (45-3)!) = 14,190
2,118,760 = 223.970
9,460
Calculate:
2,118,760 ÷ (0.0667 × 10 × 14,190) = 223.970

Overall Odds: 1 in 108.177

Please note, some lotteries have irregular prize levels, therefore the odds calculated may not be 100% accurate.


How to use the Lotto Odds Calculator


  1. Enter the number of balls to be drawn
  2. Enter the total number of balls from which these are drawn
  3. Choose the total number of prize levels the lottery has, eg: Match 6, Match 5, Match 4 and Match 3 would be 4 levels
  4. If the lottery includes 'bonus' numbers eg: a Powerball, tick the "include bonus balls" box
  5. If the box has been ticked, a dropdown menu will appear in a similar style to the original fields. Enter the number of 'bonus' numbers to be drawn, the size of the pool it/they are drawn from, and the amount of prize levels that involve matching the bonus number. Finally, select the name of the bonus number from the remaining dropdown box
  6. Click the "Calculate Odds" button to view the odds, or to start again, click Reset.

Alternatively you can choose a lottery from the "Popular Lotteries" dropdown menu at the bottom of the form to quickly input the variables for your chosen lottery and auto-display the odds table.

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