# 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
5 Main Numbers + Powerball (Jackpot)
1 in 42,375,200

The odds for this prize level are directly influenced by the Powerball. Therefore the variables associated with the main ball pool and those associated with the separate Powerball 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)
C(r,m) × C(n-r, r-m)
×
C(t,b)
C(b,d) × C(t-b,b-d)
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
t = Number of balls in the bonus pool
b = Balls drawn from the bonus pool
d = Balls to be matched from the bonus pool
C(50,5)
C(5,5) × C(50-5, 5-5)
×
C(20,1)
C(1,1) × C(20-1, 1-1)
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)
t for 20 (number of balls in the bonus pool)
b for 1 (balls drawn from the bonus pool)
d for 1 (balls to be matched from the bonus pool)
50!
5! × (50-5)!

5!
5! × (5-5)!
×
45!
0! x (45-0)!
×
20!
1! × (20-1)!

1!
1! × (1-1)!
×
19!
0! × (19-0)!
Expand: C(50,5) = 50! ÷ (5! × (50-5)!)
C(5,5) = 5! ÷ (5! × (5-5)!)
C(50-5, 5-5) = 45! ÷ (0! × (45-0)!)
C(20,1) = 20! ÷ (1! × (20-1)!)
C(1,1) = 1! ÷ (1! × (1-1)!)
C(20-1, 1-1) = 19! ÷ (0! × (19-0)!)
! means 'Factorial' eg: 50! = 50 × 49 × 48 ... × 1
Note: 0! = 1
2,118,760
1 × 1
×
20
1 × 1
Simplify: 50! ÷ (5! × (50-5)!) = 2,118,760
5! ÷ (5! × (5-5)!) = 1
45! ÷ (0! × (45-0)!) = 1
20! ÷ (1! × (20-1)!) = 20
1! ÷ (1! × (1-1)!) = 1
19! ÷ (0! × (19-0)!) = 1
42,375,200
1
=
42,375,200
Calculate: (2,118,760 ÷ (1 × 1)) × (20 ÷ (1 × 1)) = 42,375,200
5 Main Numbers
1 in 2,230,274

The odds for this prize level are indirectly influenced by the Powerball. Even though this prize level only involves matching 5 main numbers, the fact that you can also match 5 main numbers and a Powerball means the odds of matching 5 main numbers alone are increased. Therefore the variables associated with the main ball pool and those associated with the separate Powerball 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)
C(r,m) × C(n-r, r-m)
×
C(t,b)
C(b,d) × C(t-b,b-d)
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
t = Number of balls in the bonus pool
b = Balls drawn from the bonus pool
d = Balls to be matched from the bonus pool
C(50,5)
C(5,5) × C(50-5, 5-5)
×
C(20,1)
C(1,0) × C(20-1, 1-0)
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)
t for 20 (number of balls in the bonus pool)
b for 1 (balls drawn from the bonus pool)
d for 0 (balls to be matched from the bonus pool)
50!
5! × (50-5)!

5!
5! × (5-5)!
×
45!
0! x (45-0)!
×
20!
1! × (20-1)!

1!
0! × (1-0)!
×
19!
1! × (19-1)!
Expand: C(50,5) = 50! ÷ (5! × (50-5)!)
C(5,5) = 5! ÷ (5! × (5-5)!)
C(50-5, 5-5) = 45! ÷ (0! × (45-0)!)
C(20,1) = 20! ÷ (1! × (20-1)!)
C(1,0) = 1! ÷ (0! × (1-0)!)
C(20-1, 1-0) = 19! ÷ (1! × (19-1)!)
! means 'Factorial' eg: 50! = 50 × 49 × 48 ... × 1
Note: 0! = 1
2,118,760
1 × 1
×
20
1 × 19
Simplify: 50! ÷ (5! × (50-5)!) = 2,118,760
5! ÷ (5! × (5-5)!) = 1
45! ÷ (0! × (45-0)!) = 1
20! ÷ (1! × (20-1)!) = 20
1! ÷ (0! × (1-0)!) = 1
19! ÷ (1! × (19-1)!) = 19
42,375,200
19
=
2,230,274
Calculate: (2,118,760 ÷ (1 × 1)) × (20 ÷ (1 × 19)) = 2,230,274
4 Main Numbers + Powerball
1 in 188,334

The odds for this prize level are directly influenced by the Powerball. Therefore the variables associated with the main ball pool and those associated with the separate Powerball 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)
C(r,m) × C(n-r, r-m)
×
C(t,b)
C(b,d) × C(t-b,b-d)
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
t = Number of balls in the bonus pool
b = Balls drawn from the bonus pool
d = Balls to be matched from the bonus pool
C(50,5)
C(5,4) × C(50-5, 5-4)
×
C(20,1)
C(1,1) × C(20-1, 1-1)
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)
t for 20 (number of balls in the bonus pool)
b for 1 (balls drawn from the bonus pool)
d for 1 (balls to be matched from the bonus pool)
50!
5! × (50-5)!

5!
4! × (5-4)!
×
45!
1! x (45-1)!
×
20!
1! × (20-1)!

1!
1! × (1-1)!
×
19!
0! × (19-0)!
Expand: C(50,5) = 50! ÷ (5! × (50-5)!)
C(5,4) = 5! ÷ (4! × (5-4)!)
C(50-5, 5-4) = 45! ÷ (1! × (45-1)!)
C(20,1) = 20! ÷ (1! × (20-1)!)
C(1,1) = 1! ÷ (1! × (1-1)!)
C(20-1, 1-1) = 19! ÷ (0! × (19-0)!)
! means 'Factorial' eg: 50! = 50 × 49 × 48 ... × 1
Note: 0! = 1
2,118,760
5 × 45
×
20
1 × 1
Simplify: 50! ÷ (5! × (50-5)!) = 2,118,760
5! ÷ (4! × (5-4)!) = 5
45! ÷ (1! × (45-1)!) = 45
20! ÷ (1! × (20-1)!) = 20
1! ÷ (1! × (1-1)!) = 1
19! ÷ (0! × (19-0)!) = 1
42,375,200
225
=
188,334
Calculate: (2,118,760 ÷ (5 × 45)) × (20 ÷ (1 × 1)) = 188,334
4 Main Numbers
1 in 9,912

The odds for this prize level are indirectly influenced by the Powerball. Even though this prize level only involves matching 4 main numbers, the fact that you can also match 4 main numbers and a Powerball means the odds of matching 4 main numbers alone are increased. Therefore the variables associated with the main ball pool and those associated with the separate Powerball 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)
C(r,m) × C(n-r, r-m)
×
C(t,b)
C(b,d) × C(t-b,b-d)
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
t = Number of balls in the bonus pool
b = Balls drawn from the bonus pool
d = Balls to be matched from the bonus pool
C(50,5)
C(5,4) × C(50-5, 5-4)
×
C(20,1)
C(1,0) × C(20-1, 1-0)
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)
t for 20 (number of balls in the bonus pool)
b for 1 (balls drawn from the bonus pool)
d for 0 (balls to be matched from the bonus pool)
50!
5! × (50-5)!

5!
4! × (5-4)!
×
45!
1! x (45-1)!
×
20!
1! × (20-1)!

1!
0! × (1-0)!
×
19!
1! × (19-1)!
Expand: C(50,5) = 50! ÷ (5! × (50-5)!)
C(5,4) = 5! ÷ (4! × (5-4)!)
C(50-5, 5-4) = 45! ÷ (1! × (45-1)!)
C(20,1) = 20! ÷ (1! × (20-1)!)
C(1,0) = 1! ÷ (0! × (1-0)!)
C(20-1, 1-0) = 19! ÷ (1! × (19-1)!)
! means 'Factorial' eg: 50! = 50 × 49 × 48 ... × 1
Note: 0! = 1
2,118,760
5 × 45
×
20
1 × 19
Simplify: 50! ÷ (5! × (50-5)!) = 2,118,760
5! ÷ (4! × (5-4)!) = 5
45! ÷ (1! × (45-1)!) = 45
20! ÷ (1! × (20-1)!) = 20
1! ÷ (0! × (1-0)!) = 1
19! ÷ (1! × (19-1)!) = 19
42,375,200
4,275
=
9,912
Calculate: (2,118,760 ÷ (5 × 45)) × (20 ÷ (1 × 19)) = 9,912
3 Main Numbers + Powerball
1 in 4,280

The odds for this prize level are directly influenced by the Powerball. Therefore the variables associated with the main ball pool and those associated with the separate Powerball 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)
C(r,m) × C(n-r, r-m)
×
C(t,b)
C(b,d) × C(t-b,b-d)
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
t = Number of balls in the bonus pool
b = Balls drawn from the bonus pool
d = Balls to be matched from the bonus pool
C(50,5)
C(5,3) × C(50-5, 5-3)
×
C(20,1)
C(1,1) × C(20-1, 1-1)
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)
t for 20 (number of balls in the bonus pool)
b for 1 (balls drawn from the bonus pool)
d for 1 (balls to be matched from the bonus pool)
50!
5! × (50-5)!

5!
3! × (5-3)!
×
45!
2! x (45-2)!
×
20!
1! × (20-1)!

1!
1! × (1-1)!
×
19!
0! × (19-0)!
Expand: C(50,5) = 50! ÷ (5! × (50-5)!)
C(5,3) = 5! ÷ (3! × (5-3)!)
C(50-5, 5-3) = 45! ÷ (2! × (45-2)!)
C(20,1) = 20! ÷ (1! × (20-1)!)
C(1,1) = 1! ÷ (1! × (1-1)!)
C(20-1, 1-1) = 19! ÷ (0! × (19-0)!)
! means 'Factorial' eg: 50! = 50 × 49 × 48 ... × 1
Note: 0! = 1
2,118,760
10 × 990
×
20
1 × 1
Simplify: 50! ÷ (5! × (50-5)!) = 2,118,760
5! ÷ (3! × (5-3)!) = 10
45! ÷ (2! × (45-2)!) = 990
20! ÷ (1! × (20-1)!) = 20
1! ÷ (1! × (1-1)!) = 1
19! ÷ (0! × (19-0)!) = 1
42,375,200
9,900
=
4,280
Calculate: (2,118,760 ÷ (10 × 990)) × (20 ÷ (1 × 1)) = 4,280
3 Main Numbers
1 in 225

The odds for this prize level are indirectly influenced by the Powerball. Even though this prize level only involves matching 3 main numbers, the fact that you can also match 3 main numbers and a Powerball means the odds of matching 3 main numbers alone are increased. Therefore the variables associated with the main ball pool and those associated with the separate Powerball 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)
C(r,m) × C(n-r, r-m)
×
C(t,b)
C(b,d) × C(t-b,b-d)
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
t = Number of balls in the bonus pool
b = Balls drawn from the bonus pool
d = Balls to be matched from the bonus pool
C(50,5)
C(5,3) × C(50-5, 5-3)
×
C(20,1)
C(1,0) × C(20-1, 1-0)
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)
t for 20 (number of balls in the bonus pool)
b for 1 (balls drawn from the bonus pool)
d for 0 (balls to be matched from the bonus pool)
50!
5! × (50-5)!

5!
3! × (5-3)!
×
45!
2! x (45-2)!
×
20!
1! × (20-1)!

1!
0! × (1-0)!
×
19!
1! × (19-1)!
Expand: C(50,5) = 50! ÷ (5! × (50-5)!)
C(5,3) = 5! ÷ (3! × (5-3)!)
C(50-5, 5-3) = 45! ÷ (2! × (45-2)!)
C(20,1) = 20! ÷ (1! × (20-1)!)
C(1,0) = 1! ÷ (0! × (1-0)!)
C(20-1, 1-0) = 19! ÷ (1! × (19-1)!)
! means 'Factorial' eg: 50! = 50 × 49 × 48 ... × 1
Note: 0! = 1
2,118,760
10 × 990
×
20
1 × 19
Simplify: 50! ÷ (5! × (50-5)!) = 2,118,760
5! ÷ (3! × (5-3)!) = 10
45! ÷ (2! × (45-2)!) = 990
20! ÷ (1! × (20-1)!) = 20
1! ÷ (0! × (1-0)!) = 1
19! ÷ (1! × (19-1)!) = 19
42,375,200
188,100
=
225
Calculate: (2,118,760 ÷ (10 × 990)) × (20 ÷ (1 × 19)) = 225
2 Main Numbers + Powerball
1 in 299

The odds for this prize level are directly influenced by the Powerball. Therefore the variables associated with the main ball pool and those associated with the separate Powerball 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)
C(r,m) × C(n-r, r-m)
×
C(t,b)
C(b,d) × C(t-b,b-d)
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
t = Number of balls in the bonus pool
b = Balls drawn from the bonus pool
d = Balls to be matched from the bonus pool
C(50,5)
C(5,2) × C(50-5, 5-2)
×
C(20,1)
C(1,1) × C(20-1, 1-1)
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)
t for 20 (number of balls in the bonus pool)
b for 1 (balls drawn from the bonus pool)
d for 1 (balls to be matched from the bonus pool)
50!
5! × (50-5)!

5!
2! × (5-2)!
×
45!
3! x (45-3)!
×
20!
1! × (20-1)!

1!
1! × (1-1)!
×
19!
0! × (19-0)!
Expand: C(50,5) = 50! ÷ (5! × (50-5)!)
C(5,2) = 5! ÷ (2! × (5-2)!)
C(50-5, 5-2) = 45! ÷ (3! × (45-3)!)
C(20,1) = 20! ÷ (1! × (20-1)!)
C(1,1) = 1! ÷ (1! × (1-1)!)
C(20-1, 1-1) = 19! ÷ (0! × (19-0)!)
! means 'Factorial' eg: 50! = 50 × 49 × 48 ... × 1
Note: 0! = 1
2,118,760
10 × 14,190
×
20
1 × 1
Simplify: 50! ÷ (5! × (50-5)!) = 2,118,760
5! ÷ (2! × (5-2)!) = 10
45! ÷ (3! × (45-3)!) = 14,190
20! ÷ (1! × (20-1)!) = 20
1! ÷ (1! × (1-1)!) = 1
19! ÷ (0! × (19-0)!) = 1
42,375,200
141,900
=
299
Calculate: (2,118,760 ÷ (10 × 14,190)) × (20 ÷ (1 × 1)) = 299
1 Main Numbers + Powerball
1 in 57

The odds for this prize level are directly influenced by the Powerball. Therefore the variables associated with the main ball pool and those associated with the separate Powerball 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)
C(r,m) × C(n-r, r-m)
×
C(t,b)
C(b,d) × C(t-b,b-d)
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
t = Number of balls in the bonus pool
b = Balls drawn from the bonus pool
d = Balls to be matched from the bonus pool
C(50,5)
C(5,1) × C(50-5, 5-1)
×
C(20,1)
C(1,1) × C(20-1, 1-1)
Substitute: n for 50 (number of balls in the main pool)
r for 5 (balls drawn from the main pool)
m for 1 (balls to be matched from the main pool)
t for 20 (number of balls in the bonus pool)
b for 1 (balls drawn from the bonus pool)
d for 1 (balls to be matched from the bonus pool)
50!
5! × (50-5)!

5!
1! × (5-1)!
×
45!
4! x (45-4)!
×
20!
1! × (20-1)!

1!
1! × (1-1)!
×
19!
0! × (19-0)!
Expand: C(50,5) = 50! ÷ (5! × (50-5)!)
C(5,1) = 5! ÷ (1! × (5-1)!)
C(50-5, 5-1) = 45! ÷ (4! × (45-4)!)
C(20,1) = 20! ÷ (1! × (20-1)!)
C(1,1) = 1! ÷ (1! × (1-1)!)
C(20-1, 1-1) = 19! ÷ (0! × (19-0)!)
! means 'Factorial' eg: 50! = 50 × 49 × 48 ... × 1
Note: 0! = 1
2,118,760
5 × 148,995
×
20
1 × 1
Simplify: 50! ÷ (5! × (50-5)!) = 2,118,760
5! ÷ (1! × (5-1)!) = 5
45! ÷ (4! × (45-4)!) = 148,995
20! ÷ (1! × (20-1)!) = 20
1! ÷ (1! × (1-1)!) = 1
19! ÷ (0! × (19-0)!) = 1
42,375,200
744,975
=
57
Calculate: (2,118,760 ÷ (5 × 148,995)) × (20 ÷ (1 × 1)) = 57
Powerball Only
1 in 35

Although this prize level involves matching the Powerball only (drawn from a separate ball pool), the main balls must still be taken into account since the Powerball can also be matched with a selection of main numbers, thereby increasing the odds of matching the Powerball alone (Please note: calculations have been rounded):

C(n,r)
C(r,m) × C(n-r, r-m)
×
C(t,b)
C(b,d) × C(t-b,b-d)
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
t = Number of balls in the bonus pool
b = Balls drawn from the bonus pool
d = Balls to be matched from the bonus pool
C(50,5)
C(5,0) × C(50-5, 5-0)
×
C(20,1)
C(1,1) × C(20-1, 1-1)
Substitute: n for 50 (number of balls in the main pool)
r for 5 (balls drawn from the main pool)
m for 0 (balls to be matched from the main pool)
t for 20 (number of balls in the bonus pool)
b for 1 (balls drawn from the bonus pool)
d for 1 (balls to be matched from the bonus pool)
50!
5! × (50-5)!

5!
0! × (5-0)!
×
45!
5! x (45-5)!
×
20!
1! × (20-1)!

1!
1! × (1-1)!
×
19!
0! × (19-0)!
Expand: C(50,5) = 50! ÷ (5! × (50-5)!)
C(5,0) = 5! ÷ (0! × (5-0)!)
C(50-5, 5-0) = 45! ÷ (5! × (45-5)!)
C(20,1) = 20! ÷ (1! × (20-1)!)
C(1,1) = 1! ÷ (1! × (1-1)!)
C(20-1, 1-1) = 19! ÷ (0! × (19-0)!)
! means 'Factorial' eg: 50! = 50 × 49 × 48 ... × 1
Note: 0! = 1
2,118,760
1 × 1,221,759
×
20
1 × 1
Simplify: 50! ÷ (5! × (50-5)!) = 2,118,760
5! ÷ (0! × (5-0)!) = 1
45! ÷ (5! × (45-5)!) = 1,221,759
20! ÷ (1! × (20-1)!) = 20
1! ÷ (1! × (1-1)!) = 1
19! ÷ (0! × (19-0)!) = 1
42,375,200
1,221,759
=
35
Calculate: (2,118,760 ÷ (1 × 1,221,759)) × (20 ÷ (1 × 1)) = 35

Approx. Overall Odds*: 1 in 18

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.