Powerball Odds Calculator

› Powerball

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 (Rounded) Show Working Out +
5 Main Numbers + Powerball (Jackpot) 1 in 175,223,510 Show/Hide ›

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(59,5)
C(5,5)
×
C(59-5,5-5)
×
C(35,1)
C(1,1)
×
C(35-1,1-1)
Substitute:
n for 59 (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 35 (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)
59!
5! × (59 - 5)!
5!
5! × (5 - 5)!
×
54!
0! × (54 - 0)!
×
35!
1! × (35 - 1)!
1!
1! × (1 - 1)!
×
34!
0! × (34 - 0)!
Expand:
C(59,5) = 59! ÷ (5! × (59-5)!)
C(5,5) = 5! ÷ (5! × (5-5)!)
C(59-5,5-5) = 54! ÷ (0! × (54-0)!)
C(35,1) = 35! ÷ (1! × (35-1)!)
C(1,1) = 1! ÷ (1! × (1-1)!)
C(35-1,1-1) = 34! ÷ (0! × (34-0)!)
! means 'Factorial' eg: 59! = 59 × 58 × 57 ... × 1
Note: 0! = 1
5,006,386
1 × 1
×
35
1 × 1
Simplify:
59! ÷ (5! × (59-5)!) = 5,006,386
5! ÷ (5! × (5-5)!) = 1
54! ÷ (0! × (54-0)!) = 1
35! ÷ (1! × (35-1)!) = 35
1! ÷ (1! × (1-1)!) = 1
34! ÷ (0! × (34-0)!) = 1
175,223,510 = 175,223,510
1
Calculate:
(5,006,386 ÷ 1) × (35 ÷ 1) = 175,223,510
5 Main Numbers 1 in 5,153,633 Show/Hide ›

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(59,5)
C(5,5)
×
C(59-5,5-5)
×
C(35,1)
C(1,0)
×
C(35-1,1-0)
Substitute:
n for 59 (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 35 (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)
59!
5! × (59 - 5)!
5!
5! × (5 - 5)!
×
54!
0! × (54 - 0)!
×
35!
1! × (35 - 1)!
1!
0! × (1 - 0)!
×
34!
1! × (34 - 1)!
Expand:
C(59,5) = 59! ÷ (5! × (59-5)!)
C(5,5) = 5! ÷ (5! × (5-5)!)
C(59-5,5-5) = 54! ÷ (0! × (54-0)!)
C(35,1) = 35! ÷ (1! × (35-1)!)
C(1,0) = 1! ÷ (0! × (1-0)!)
C(35-1,1-0) = 34! ÷ (1! × (34-1)!)
! means 'Factorial' eg: 59! = 59 × 58 × 57 ... × 1
Note: 0! = 1
5,006,386
1 × 1
×
35
1 × 34
Simplify:
59! ÷ (5! × (59-5)!) = 5,006,386
5! ÷ (5! × (5-5)!) = 1
54! ÷ (0! × (54-0)!) = 1
35! ÷ (1! × (35-1)!) = 35
1! ÷ (0! × (1-0)!) = 1
34! ÷ (1! × (34-1)!) = 34
175,223,510 = 5,153,633
34
Calculate:
(5,006,386 ÷ 1) × (35 ÷ 34) = 5,153,633
4 Main Numbers + Powerball 1 in 648,976 Show/Hide ›

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(59,5)
C(5,4)
×
C(59-5,5-4)
×
C(35,1)
C(1,1)
×
C(35-1,1-1)
Substitute:
n for 59 (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 35 (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)
59!
5! × (59 - 5)!
5!
4! × (5 - 4)!
×
54!
1! × (54 - 1)!
×
35!
1! × (35 - 1)!
1!
1! × (1 - 1)!
×
34!
0! × (34 - 0)!
Expand:
C(59,5) = 59! ÷ (5! × (59-5)!)
C(5,4) = 5! ÷ (4! × (5-4)!)
C(59-5,5-4) = 54! ÷ (1! × (54-1)!)
C(35,1) = 35! ÷ (1! × (35-1)!)
C(1,1) = 1! ÷ (1! × (1-1)!)
C(35-1,1-1) = 34! ÷ (0! × (34-0)!)
! means 'Factorial' eg: 59! = 59 × 58 × 57 ... × 1
Note: 0! = 1
5,006,386
5 × 54
×
35
1 × 1
Simplify:
59! ÷ (5! × (59-5)!) = 5,006,386
5! ÷ (4! × (5-4)!) = 5
54! ÷ (1! × (54-1)!) = 54
35! ÷ (1! × (35-1)!) = 35
1! ÷ (1! × (1-1)!) = 1
34! ÷ (0! × (34-0)!) = 1
175,223,510 = 648,976
270
Calculate:
(5,006,386 ÷ 270) × (35 ÷ 1) = 648,976
4 Main Numbers 1 in 19,088 Show/Hide ›

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(59,5)
C(5,4)
×
C(59-5,5-4)
×
C(35,1)
C(1,0)
×
C(35-1,1-0)
Substitute:
n for 59 (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 35 (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)
59!
5! × (59 - 5)!
5!
4! × (5 - 4)!
×
54!
1! × (54 - 1)!
×
35!
1! × (35 - 1)!
1!
0! × (1 - 0)!
×
34!
1! × (34 - 1)!
Expand:
C(59,5) = 59! ÷ (5! × (59-5)!)
C(5,4) = 5! ÷ (4! × (5-4)!)
C(59-5,5-4) = 54! ÷ (1! × (54-1)!)
C(35,1) = 35! ÷ (1! × (35-1)!)
C(1,0) = 1! ÷ (0! × (1-0)!)
C(35-1,1-0) = 34! ÷ (1! × (34-1)!)
! means 'Factorial' eg: 59! = 59 × 58 × 57 ... × 1
Note: 0! = 1
5,006,386
5 × 54
×
35
1 × 34
Simplify:
59! ÷ (5! × (59-5)!) = 5,006,386
5! ÷ (4! × (5-4)!) = 5
54! ÷ (1! × (54-1)!) = 54
35! ÷ (1! × (35-1)!) = 35
1! ÷ (0! × (1-0)!) = 1
34! ÷ (1! × (34-1)!) = 34
175,223,510 = 19,088
9,180
Calculate:
(5,006,386 ÷ 270) × (35 ÷ 34) = 19,088
3 Main Numbers + Powerball 1 in 12,245 Show/Hide ›

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(59,5)
C(5,3)
×
C(59-5,5-3)
×
C(35,1)
C(1,1)
×
C(35-1,1-1)
Substitute:
n for 59 (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 35 (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)
59!
5! × (59 - 5)!
5!
3! × (5 - 3)!
×
54!
2! × (54 - 2)!
×
35!
1! × (35 - 1)!
1!
1! × (1 - 1)!
×
34!
0! × (34 - 0)!
Expand:
C(59,5) = 59! ÷ (5! × (59-5)!)
C(5,3) = 5! ÷ (3! × (5-3)!)
C(59-5,5-3) = 54! ÷ (2! × (54-2)!)
C(35,1) = 35! ÷ (1! × (35-1)!)
C(1,1) = 1! ÷ (1! × (1-1)!)
C(35-1,1-1) = 34! ÷ (0! × (34-0)!)
! means 'Factorial' eg: 59! = 59 × 58 × 57 ... × 1
Note: 0! = 1
5,006,386
10 × 1,431
×
35
1 × 1
Simplify:
59! ÷ (5! × (59-5)!) = 5,006,386
5! ÷ (3! × (5-3)!) = 10
54! ÷ (2! × (54-2)!) = 1,431
35! ÷ (1! × (35-1)!) = 35
1! ÷ (1! × (1-1)!) = 1
34! ÷ (0! × (34-0)!) = 1
175,223,510 = 12,245
14,310
Calculate:
(5,006,386 ÷ 14,310) × (35 ÷ 1) = 12,245
3 Main Numbers 1 in 360 Show/Hide ›

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(59,5)
C(5,3)
×
C(59-5,5-3)
×
C(35,1)
C(1,0)
×
C(35-1,1-0)
Substitute:
n for 59 (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 35 (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)
59!
5! × (59 - 5)!
5!
3! × (5 - 3)!
×
54!
2! × (54 - 2)!
×
35!
1! × (35 - 1)!
1!
0! × (1 - 0)!
×
34!
1! × (34 - 1)!
Expand:
C(59,5) = 59! ÷ (5! × (59-5)!)
C(5,3) = 5! ÷ (3! × (5-3)!)
C(59-5,5-3) = 54! ÷ (2! × (54-2)!)
C(35,1) = 35! ÷ (1! × (35-1)!)
C(1,0) = 1! ÷ (0! × (1-0)!)
C(35-1,1-0) = 34! ÷ (1! × (34-1)!)
! means 'Factorial' eg: 59! = 59 × 58 × 57 ... × 1
Note: 0! = 1
5,006,386
10 × 1,431
×
35
1 × 34
Simplify:
59! ÷ (5! × (59-5)!) = 5,006,386
5! ÷ (3! × (5-3)!) = 10
54! ÷ (2! × (54-2)!) = 1,431
35! ÷ (1! × (35-1)!) = 35
1! ÷ (0! × (1-0)!) = 1
34! ÷ (1! × (34-1)!) = 34
175,223,510 = 360
486,540
Calculate:
(5,006,386 ÷ 14,310) × (35 ÷ 34) = 360
2 Main Numbers + Powerball 1 in 706 Show/Hide ›

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(59,5)
C(5,2)
×
C(59-5,5-2)
×
C(35,1)
C(1,1)
×
C(35-1,1-1)
Substitute:
n for 59 (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 35 (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)
59!
5! × (59 - 5)!
5!
2! × (5 - 2)!
×
54!
3! × (54 - 3)!
×
35!
1! × (35 - 1)!
1!
1! × (1 - 1)!
×
34!
0! × (34 - 0)!
Expand:
C(59,5) = 59! ÷ (5! × (59-5)!)
C(5,2) = 5! ÷ (2! × (5-2)!)
C(59-5,5-2) = 54! ÷ (3! × (54-3)!)
C(35,1) = 35! ÷ (1! × (35-1)!)
C(1,1) = 1! ÷ (1! × (1-1)!)
C(35-1,1-1) = 34! ÷ (0! × (34-0)!)
! means 'Factorial' eg: 59! = 59 × 58 × 57 ... × 1
Note: 0! = 1
5,006,386
10 × 24,804
×
35
1 × 1
Simplify:
59! ÷ (5! × (59-5)!) = 5,006,386
5! ÷ (2! × (5-2)!) = 10
54! ÷ (3! × (54-3)!) = 24,804
35! ÷ (1! × (35-1)!) = 35
1! ÷ (1! × (1-1)!) = 1
34! ÷ (0! × (34-0)!) = 1
175,223,510 = 706
248,040
Calculate:
(5,006,386 ÷ 248,040) × (35 ÷ 1) = 706
1 Main Numbers + Powerball 1 in 111 Show/Hide ›

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(59,5)
C(5,1)
×
C(59-5,5-1)
×
C(35,1)
C(1,1)
×
C(35-1,1-1)
Substitute:
n for 59 (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 35 (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)
59!
5! × (59 - 5)!
5!
1! × (5 - 1)!
×
54!
4! × (54 - 4)!
×
35!
1! × (35 - 1)!
1!
1! × (1 - 1)!
×
34!
0! × (34 - 0)!
Expand:
C(59,5) = 59! ÷ (5! × (59-5)!)
C(5,1) = 5! ÷ (1! × (5-1)!)
C(59-5,5-1) = 54! ÷ (4! × (54-4)!)
C(35,1) = 35! ÷ (1! × (35-1)!)
C(1,1) = 1! ÷ (1! × (1-1)!)
C(35-1,1-1) = 34! ÷ (0! × (34-0)!)
! means 'Factorial' eg: 59! = 59 × 58 × 57 ... × 1
Note: 0! = 1
5,006,386
5 × 316,251
×
35
1 × 1
Simplify:
59! ÷ (5! × (59-5)!) = 5,006,386
5! ÷ (1! × (5-1)!) = 5
54! ÷ (4! × (54-4)!) = 316,251
35! ÷ (1! × (35-1)!) = 35
1! ÷ (1! × (1-1)!) = 1
34! ÷ (0! × (34-0)!) = 1
175,223,510 = 111
1,581,255
Calculate:
(5,006,386 ÷ 1,581,255) × (35 ÷ 1) = 111
Powerball Only 1 in 55 Show/Hide ›

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.

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(59,5)
C(5,0)
×
C(59-5,5-0)
×
C(35,1)
C(1,1)
×
C(35-1,1-1)
Substitute:
n for 59 (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 35 (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)
59!
5! × (59 - 5)!
5!
0! × (5 - 0)!
×
54!
5! × (54 - 5)!
×
35!
1! × (35 - 1)!
1!
1! × (1 - 1)!
×
34!
0! × (34 - 0)!
Expand:
C(59,5) = 59! ÷ (5! × (59-5)!)
C(5,0) = 5! ÷ (0! × (5-0)!)
C(59-5,5-0) = 54! ÷ (5! × (54-5)!)
C(35,1) = 35! ÷ (1! × (35-1)!)
C(1,1) = 1! ÷ (1! × (1-1)!)
C(35-1,1-1) = 34! ÷ (0! × (34-0)!)
! means 'Factorial' eg: 59! = 59 × 58 × 57 ... × 1
Note: 0! = 1
5,006,386
1 × 3,162,510
×
35
1 × 1
Simplify:
59! ÷ (5! × (59-5)!) = 5,006,386
5! ÷ (0! × (5-0)!) = 1
54! ÷ (5! × (54-5)!) = 3,162,510
35! ÷ (1! × (35-1)!) = 35
1! ÷ (1! × (1-1)!) = 1
34! ÷ (0! × (34-0)!) = 1
175,223,510 = 55
3,162,510
Calculate:
(5,006,386 ÷ 3,162,510) × (35 ÷ 1) = 55

Approx. Overall Odds: 1 in 32

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 drop down 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 drop down 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" drop-down menu at the bottom of the form to quickly input the variables for your chosen lottery and auto-display the odds table.

Island Boat
Friday 24th October
190,000,000
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