# Lotto Odds Calculator

The Lotto Odds Calculator enables users to calculate the odds of winning the jackpot and additional prize levels for any given lottery.

To use the calculator, type in the number matrix, select the number of prize tiers and tick whether the lottery includes a bonus ball. If the lottery includes a bonus number, additional options will appear specifying the bonus variables. Alternatively, select a lottery from the Popular Lotteries dropdown menu to automatically display the odds table.

Lotto Odds Calculator
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:
Numbers Matched
Calculated Odds
Show/Hide Calculations
6 Main Numbers
1 in 10,737,573

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(47,6)
C(6,6) × C(47-6, 6-6)
Substitute: n for 47 (number of balls in the main pool)
r for 6 (balls drawn from the main pool)
m for 6 (balls to be matched from the main pool)
47!
6! × (47-6)!

6!
6! × (6-6)!
×
41!
0! x (41-0)!
Expand: C(47,6) = 47! ÷ (6! × (47-6)!)
C(6,6) = 6! ÷ (6! × (6-6)!)
C(47-6, 6-6) = 41! ÷ (0! × (41-0)!)
! means 'Factorial' eg: 47! = 47 × 46 × 45 ... × 1
Note: 0! = 1
10,737,573
1 × 1
Simplify: 47! ÷ (6! × (47-6)!) = 10,737,573
6! ÷ (6! × (6-6)!) = 1
41! ÷ (0! × (41-0)!) = 1
10,737,573
1
=
10,737,573
Calculate: 10,737,573 ÷ (1 × 1) = 10,737,573
5 Main Numbers + BonusBall
1 in 1,789,596

The odds for this prize level are directly influenced by the BonusBall. Since the BonusBall 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(47,6)
6 - 5
47 - 6
×
C(6,5) × C(47-6, 6-5)
Substitute: n for 47 (number of balls in the main pool)
r for 6 (balls drawn from the main pool)
m for 5 (balls to be matched from the main pool)
47!
6! × (47 - 6)!

6 - 5
47 - 6
×
6!
5! × (6 - 5)!
×
41!
1! × (41 - 1)!
Expand: C(47,6) = 47! ÷ (6! × (47-6)!)
C(6,5) = 6! ÷ (5! × (6-5)!)
C(47-6, 6-5) = 41! ÷ (1! × (41-1)!)
! means 'Factorial' eg: 47! = 47 × 46 × 45 ... × 1
Note: 0! = 1
10,737,573
0.0244 × 6 × 41
Simplify: 47! ÷ (6! × (47-6)!) = 10,737,573
(6-5) ÷ (47-6) = 0.0244
6! ÷ (5! × (6-5)!) = 6
41! ÷ (1! × (41-1)!) = 41
10,737,573
6
=
1,789,596
Calculate: 10,737,573 ÷ (0.0244 × 6 × 41) = 1,789,596
5 Main Numbers
1 in 44,740

The odds for this prize level are indirectly influenced by the BonusBall. Therefore the variables associated with the main ball pool and those associated with the separate BonusBall pool must be taken into account in order to calculate the correct odds, hence 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(47,6)
47 - 6 - 6 + 5
47 - 6
×
C(6,5) × C(47-6, 6-5)
Substitute: n for 47 (number of balls in the main pool)
r for 6 (balls drawn from the main pool)
m for 5 (balls to be matched from the main pool)
47!
6! × (47 - 6)!

47 - 6 - 6 + 5
47 - 6
×
6!
5! × (6 - 5)!
×
41!
1! × (41 - 1)!
Expand: C(47,6) = 47! ÷ (6! × (47-6)!)
C(6,5) = 6! ÷ (5! × (6-5)!)
C(47-6, 6-5) = 41! ÷ (1! × (41-1)!)
! means 'Factorial' eg: 47! = 47 × 46 × 45 ... × 1
Note: 0! = 1
10,737,573
0.9756 × 6 × 41
Simplify: 47! ÷ (6! × (47-6)!) = 10,737,573
(47-6-6+5) ÷ (47-6) = 0.9756
6! ÷ (5! × (6-5)!) = 6
41! ÷ (1! × (41-1)!) = 41
10,737,573
240
=
44,740
Calculate: 10,737,573 ÷ (0.9756 × 6 × 41) = 44,740
4 Main Numbers + BonusBall
1 in 17,896

The odds for this prize level are directly influenced by the BonusBall. Since the BonusBall 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(47,6)
6 - 4
47 - 6
×
C(6,4) × C(47-6, 6-4)
Substitute: n for 47 (number of balls in the main pool)
r for 6 (balls drawn from the main pool)
m for 4 (balls to be matched from the main pool)
47!
6! × (47 - 6)!

6 - 4
47 - 6
×
6!
4! × (6 - 4)!
×
41!
2! × (41 - 2)!
Expand: C(47,6) = 47! ÷ (6! × (47-6)!)
C(6,4) = 6! ÷ (4! × (6-4)!)
C(47-6, 6-4) = 41! ÷ (2! × (41-2)!)
! means 'Factorial' eg: 47! = 47 × 46 × 45 ... × 1
Note: 0! = 1
10,737,573
0.0488 × 15 × 820
Simplify: 47! ÷ (6! × (47-6)!) = 10,737,573
(6-4) ÷ (47-6) = 0.0488
6! ÷ (4! × (6-4)!) = 15
41! ÷ (2! × (41-2)!) = 820
10,737,573
600
=
17,896
Calculate: 10,737,573 ÷ (0.0488 × 15 × 820) = 17,896
4 Main Numbers
1 in 918

The odds for this prize level are indirectly influenced by the BonusBall. Therefore the variables associated with the main ball pool and those associated with the separate BonusBall pool must be taken into account in order to calculate the correct odds, hence 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(47,6)
47 - 6 - 6 + 4
47 - 6
×
C(6,4) × C(47-6, 6-4)
Substitute: n for 47 (number of balls in the main pool)
r for 6 (balls drawn from the main pool)
m for 4 (balls to be matched from the main pool)
47!
6! × (47 - 6)!

47 - 6 - 6 + 4
47 - 6
×
6!
4! × (6 - 4)!
×
41!
2! × (41 - 2)!
Expand: C(47,6) = 47! ÷ (6! × (47-6)!)
C(6,4) = 6! ÷ (4! × (6-4)!)
C(47-6, 6-4) = 41! ÷ (2! × (41-2)!)
! means 'Factorial' eg: 47! = 47 × 46 × 45 ... × 1
Note: 0! = 1
10,737,573
0.9512 × 15 × 820
Simplify: 47! ÷ (6! × (47-6)!) = 10,737,573
(47-6-6+4) ÷ (47-6) = 0.9512
6! ÷ (4! × (6-4)!) = 15
41! ÷ (2! × (41-2)!) = 820
10,737,573
11,700
=
918
Calculate: 10,737,573 ÷ (0.9512 × 15 × 820) = 918
3 Main Numbers + BonusBall
1 in 688

The odds for this prize level are directly influenced by the BonusBall. Since the BonusBall 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(47,6)
6 - 3
47 - 6
×
C(6,3) × C(47-6, 6-3)
Substitute: n for 47 (number of balls in the main pool)
r for 6 (balls drawn from the main pool)
m for 3 (balls to be matched from the main pool)
47!
6! × (47 - 6)!

6 - 3
47 - 6
×
6!
3! × (6 - 3)!
×
41!
3! × (41 - 3)!
Expand: C(47,6) = 47! ÷ (6! × (47-6)!)
C(6,3) = 6! ÷ (3! × (6-3)!)
C(47-6, 6-3) = 41! ÷ (3! × (41-3)!)
! means 'Factorial' eg: 47! = 47 × 46 × 45 ... × 1
Note: 0! = 1
10,737,573
0.0732 × 20 × 10,660
Simplify: 47! ÷ (6! × (47-6)!) = 10,737,573
(6-3) ÷ (47-6) = 0.0732
6! ÷ (3! × (6-3)!) = 20
41! ÷ (3! × (41-3)!) = 10,660
10,737,573
15,600
=
688
Calculate: 10,737,573 ÷ (0.0732 × 20 × 10660) = 688
3 Main Numbers
1 in 54

The odds for this prize level are indirectly influenced by the BonusBall. Therefore the variables associated with the main ball pool and those associated with the separate BonusBall pool must be taken into account in order to calculate the correct odds, hence 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(47,6)
47 - 6 - 6 + 3
47 - 6
×
C(6,3) × C(47-6, 6-3)
Substitute: n for 47 (number of balls in the main pool)
r for 6 (balls drawn from the main pool)
m for 3 (balls to be matched from the main pool)
47!
6! × (47 - 6)!

47 - 6 - 6 + 3
47 - 6
×
6!
3! × (6 - 3)!
×
41!
3! × (41 - 3)!
Expand: C(47,6) = 47! ÷ (6! × (47-6)!)
C(6,3) = 6! ÷ (3! × (6-3)!)
C(47-6, 6-3) = 41! ÷ (3! × (41-3)!)
! means 'Factorial' eg: 47! = 47 × 46 × 45 ... × 1
Note: 0! = 1
10,737,573
0.9268 × 20 × 10,660
Simplify: 47! ÷ (6! × (47-6)!) = 10,737,573
(47-6-6+3) ÷ (47-6) = 0.9268
6! ÷ (3! × (6-3)!) = 20
41! ÷ (3! × (41-3)!) = 10,660
10,737,573
197,600
=
54
Calculate: 10,737,573 ÷ (0.9268 × 20 × 10660) = 54
2 Main Numbers + BonusBall
1 in 72

The odds for this prize level are directly influenced by the BonusBall. Since the BonusBall 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(47,6)
6 - 2
47 - 6
×
C(6,2) × C(47-6, 6-2)
Substitute: n for 47 (number of balls in the main pool)
r for 6 (balls drawn from the main pool)
m for 2 (balls to be matched from the main pool)
47!
6! × (47 - 6)!

6 - 2
47 - 6
×
6!
2! × (6 - 2)!
×
41!
4! × (41 - 4)!
Expand: C(47,6) = 47! ÷ (6! × (47-6)!)
C(6,2) = 6! ÷ (2! × (6-2)!)
C(47-6, 6-2) = 41! ÷ (4! × (41-4)!)
! means 'Factorial' eg: 47! = 47 × 46 × 45 ... × 1
Note: 0! = 1
10,737,573
0.0976 × 15 × 101,270
Simplify: 47! ÷ (6! × (47-6)!) = 10,737,573
(6-2) ÷ (47-6) = 0.0976
6! ÷ (2! × (6-2)!) = 15
41! ÷ (4! × (41-4)!) = 101,270
10,737,573
148,200
=
72
Calculate: 10,737,573 ÷ (0.0976 × 15 × 101270) = 72

Approx. Overall Odds*: 1 in 29

Odds for popular lotteries:

### How to use the Lotto Odds Calculator

Enter the number of balls to be drawn Enter the total number of balls from which these are drawn Choose the total number of prize levels the lottery has, eg: Match 6, Match 5, Match 4 and Match 3 would be 4 levels If the lottery includes 'bonus' numbers eg: a Powerball, tick the "include bonus balls" box 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 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.

*Please note, the overall odds of winning a prize does not take into account the chance of winning guaranteed prizes (for lotteries that offer them), because the odds of winning a raffle prize fluctuates based on how many tickets were purchased for each draw.