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 Show Working Out +
5 Main Numbers + Powerball (Jackpot) 1 in 292,201,338.000 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:

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(69,5)
C(5,5)
×
C(69-5,5-5)
×
C(26,1)
C(1,1)
×
C(26-1,1-1)
Substitute:
n for 69 (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 26 (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)
69!
5! × (69 - 5)!
5!
5! × (5 - 5)!
×
64!
0! × (64 - 0)!
×
26!
1! × (26 - 1)!
1!
1! × (1 - 1)!
×
25!
0! × (25 - 0)!
Expand:
C(69,5) = 69! ÷ (5! × (69-5)!)
C(5,5) = 5! ÷ (5! × (5-5)!)
C(69-5,5-5) = 64! ÷ (0! × (64-0)!)
C(26,1) = 26! ÷ (1! × (26-1)!)
C(1,1) = 1! ÷ (1! × (1-1)!)
C(26-1,1-1) = 25! ÷ (0! × (25-0)!)
! means 'Factorial' eg: 69! = 69 × 68 × 67 ... × 1
Note: 0! = 1
11,238,513
1 × 1
×
26
1 × 1
Simplify:
69! ÷ (5! × (69-5)!) = 11,238,513
5! ÷ (5! × (5-5)!) = 1
64! ÷ (0! × (64-0)!) = 1
26! ÷ (1! × (26-1)!) = 26
1! ÷ (1! × (1-1)!) = 1
25! ÷ (0! × (25-0)!) = 1
292,201,338 = 292,201,338.000
1
Calculate:
(11,238,513 ÷ 1) × (26 ÷ 1) = 292,201,338.000
5 Main Numbers 1 in 11,688,053.520 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:

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(69,5)
C(5,5)
×
C(69-5,5-5)
×
C(26,1)
C(1,0)
×
C(26-1,1-0)
Substitute:
n for 69 (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 26 (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)
69!
5! × (69 - 5)!
5!
5! × (5 - 5)!
×
64!
0! × (64 - 0)!
×
26!
1! × (26 - 1)!
1!
0! × (1 - 0)!
×
25!
1! × (25 - 1)!
Expand:
C(69,5) = 69! ÷ (5! × (69-5)!)
C(5,5) = 5! ÷ (5! × (5-5)!)
C(69-5,5-5) = 64! ÷ (0! × (64-0)!)
C(26,1) = 26! ÷ (1! × (26-1)!)
C(1,0) = 1! ÷ (0! × (1-0)!)
C(26-1,1-0) = 25! ÷ (1! × (25-1)!)
! means 'Factorial' eg: 69! = 69 × 68 × 67 ... × 1
Note: 0! = 1
11,238,513
1 × 1
×
26
1 × 25
Simplify:
69! ÷ (5! × (69-5)!) = 11,238,513
5! ÷ (5! × (5-5)!) = 1
64! ÷ (0! × (64-0)!) = 1
26! ÷ (1! × (26-1)!) = 26
1! ÷ (0! × (1-0)!) = 1
25! ÷ (1! × (25-1)!) = 25
292,201,338 = 11,688,053.520
25
Calculate:
(11,238,513 ÷ 1) × (26 ÷ 25) = 11,688,053.520
4 Main Numbers + Powerball 1 in 913,129.181 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:

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(69,5)
C(5,4)
×
C(69-5,5-4)
×
C(26,1)
C(1,1)
×
C(26-1,1-1)
Substitute:
n for 69 (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 26 (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)
69!
5! × (69 - 5)!
5!
4! × (5 - 4)!
×
64!
1! × (64 - 1)!
×
26!
1! × (26 - 1)!
1!
1! × (1 - 1)!
×
25!
0! × (25 - 0)!
Expand:
C(69,5) = 69! ÷ (5! × (69-5)!)
C(5,4) = 5! ÷ (4! × (5-4)!)
C(69-5,5-4) = 64! ÷ (1! × (64-1)!)
C(26,1) = 26! ÷ (1! × (26-1)!)
C(1,1) = 1! ÷ (1! × (1-1)!)
C(26-1,1-1) = 25! ÷ (0! × (25-0)!)
! means 'Factorial' eg: 69! = 69 × 68 × 67 ... × 1
Note: 0! = 1
11,238,513
5 × 64
×
26
1 × 1
Simplify:
69! ÷ (5! × (69-5)!) = 11,238,513
5! ÷ (4! × (5-4)!) = 5
64! ÷ (1! × (64-1)!) = 64
26! ÷ (1! × (26-1)!) = 26
1! ÷ (1! × (1-1)!) = 1
25! ÷ (0! × (25-0)!) = 1
292,201,338 = 913,129.181
320
Calculate:
(11,238,513 ÷ 320) × (26 ÷ 1) = 913,129.181
4 Main Numbers 1 in 36,525.167 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:

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(69,5)
C(5,4)
×
C(69-5,5-4)
×
C(26,1)
C(1,0)
×
C(26-1,1-0)
Substitute:
n for 69 (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 26 (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)
69!
5! × (69 - 5)!
5!
4! × (5 - 4)!
×
64!
1! × (64 - 1)!
×
26!
1! × (26 - 1)!
1!
0! × (1 - 0)!
×
25!
1! × (25 - 1)!
Expand:
C(69,5) = 69! ÷ (5! × (69-5)!)
C(5,4) = 5! ÷ (4! × (5-4)!)
C(69-5,5-4) = 64! ÷ (1! × (64-1)!)
C(26,1) = 26! ÷ (1! × (26-1)!)
C(1,0) = 1! ÷ (0! × (1-0)!)
C(26-1,1-0) = 25! ÷ (1! × (25-1)!)
! means 'Factorial' eg: 69! = 69 × 68 × 67 ... × 1
Note: 0! = 1
11,238,513
5 × 64
×
26
1 × 25
Simplify:
69! ÷ (5! × (69-5)!) = 11,238,513
5! ÷ (4! × (5-4)!) = 5
64! ÷ (1! × (64-1)!) = 64
26! ÷ (1! × (26-1)!) = 26
1! ÷ (0! × (1-0)!) = 1
25! ÷ (1! × (25-1)!) = 25
292,201,338 = 36,525.167
8,000
Calculate:
(11,238,513 ÷ 320) × (26 ÷ 25) = 36,525.167
3 Main Numbers + Powerball 1 in 14,494.114 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:

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(69,5)
C(5,3)
×
C(69-5,5-3)
×
C(26,1)
C(1,1)
×
C(26-1,1-1)
Substitute:
n for 69 (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 26 (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)
69!
5! × (69 - 5)!
5!
3! × (5 - 3)!
×
64!
2! × (64 - 2)!
×
26!
1! × (26 - 1)!
1!
1! × (1 - 1)!
×
25!
0! × (25 - 0)!
Expand:
C(69,5) = 69! ÷ (5! × (69-5)!)
C(5,3) = 5! ÷ (3! × (5-3)!)
C(69-5,5-3) = 64! ÷ (2! × (64-2)!)
C(26,1) = 26! ÷ (1! × (26-1)!)
C(1,1) = 1! ÷ (1! × (1-1)!)
C(26-1,1-1) = 25! ÷ (0! × (25-0)!)
! means 'Factorial' eg: 69! = 69 × 68 × 67 ... × 1
Note: 0! = 1
11,238,513
10 × 2,016
×
26
1 × 1
Simplify:
69! ÷ (5! × (69-5)!) = 11,238,513
5! ÷ (3! × (5-3)!) = 10
64! ÷ (2! × (64-2)!) = 2,016
26! ÷ (1! × (26-1)!) = 26
1! ÷ (1! × (1-1)!) = 1
25! ÷ (0! × (25-0)!) = 1
292,201,338 = 14,494.114
20,160
Calculate:
(11,238,513 ÷ 20,160) × (26 ÷ 1) = 14,494.114
3 Main Numbers 1 in 579.765 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:

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(69,5)
C(5,3)
×
C(69-5,5-3)
×
C(26,1)
C(1,0)
×
C(26-1,1-0)
Substitute:
n for 69 (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 26 (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)
69!
5! × (69 - 5)!
5!
3! × (5 - 3)!
×
64!
2! × (64 - 2)!
×
26!
1! × (26 - 1)!
1!
0! × (1 - 0)!
×
25!
1! × (25 - 1)!
Expand:
C(69,5) = 69! ÷ (5! × (69-5)!)
C(5,3) = 5! ÷ (3! × (5-3)!)
C(69-5,5-3) = 64! ÷ (2! × (64-2)!)
C(26,1) = 26! ÷ (1! × (26-1)!)
C(1,0) = 1! ÷ (0! × (1-0)!)
C(26-1,1-0) = 25! ÷ (1! × (25-1)!)
! means 'Factorial' eg: 69! = 69 × 68 × 67 ... × 1
Note: 0! = 1
11,238,513
10 × 2,016
×
26
1 × 25
Simplify:
69! ÷ (5! × (69-5)!) = 11,238,513
5! ÷ (3! × (5-3)!) = 10
64! ÷ (2! × (64-2)!) = 2,016
26! ÷ (1! × (26-1)!) = 26
1! ÷ (0! × (1-0)!) = 1
25! ÷ (1! × (25-1)!) = 25
292,201,338 = 579.765
504,000
Calculate:
(11,238,513 ÷ 20,160) × (26 ÷ 25) = 579.765
2 Main Numbers + Powerball 1 in 701.328 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:

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(69,5)
C(5,2)
×
C(69-5,5-2)
×
C(26,1)
C(1,1)
×
C(26-1,1-1)
Substitute:
n for 69 (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 26 (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)
69!
5! × (69 - 5)!
5!
2! × (5 - 2)!
×
64!
3! × (64 - 3)!
×
26!
1! × (26 - 1)!
1!
1! × (1 - 1)!
×
25!
0! × (25 - 0)!
Expand:
C(69,5) = 69! ÷ (5! × (69-5)!)
C(5,2) = 5! ÷ (2! × (5-2)!)
C(69-5,5-2) = 64! ÷ (3! × (64-3)!)
C(26,1) = 26! ÷ (1! × (26-1)!)
C(1,1) = 1! ÷ (1! × (1-1)!)
C(26-1,1-1) = 25! ÷ (0! × (25-0)!)
! means 'Factorial' eg: 69! = 69 × 68 × 67 ... × 1
Note: 0! = 1
11,238,513
10 × 41,664
×
26
1 × 1
Simplify:
69! ÷ (5! × (69-5)!) = 11,238,513
5! ÷ (2! × (5-2)!) = 10
64! ÷ (3! × (64-3)!) = 41,664
26! ÷ (1! × (26-1)!) = 26
1! ÷ (1! × (1-1)!) = 1
25! ÷ (0! × (25-0)!) = 1
292,201,338 = 701.328
416,640
Calculate:
(11,238,513 ÷ 416,640) × (26 ÷ 1) = 701.328
1 Main Numbers + Powerball 1 in 91.977 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:

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(69,5)
C(5,1)
×
C(69-5,5-1)
×
C(26,1)
C(1,1)
×
C(26-1,1-1)
Substitute:
n for 69 (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 26 (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)
69!
5! × (69 - 5)!
5!
1! × (5 - 1)!
×
64!
4! × (64 - 4)!
×
26!
1! × (26 - 1)!
1!
1! × (1 - 1)!
×
25!
0! × (25 - 0)!
Expand:
C(69,5) = 69! ÷ (5! × (69-5)!)
C(5,1) = 5! ÷ (1! × (5-1)!)
C(69-5,5-1) = 64! ÷ (4! × (64-4)!)
C(26,1) = 26! ÷ (1! × (26-1)!)
C(1,1) = 1! ÷ (1! × (1-1)!)
C(26-1,1-1) = 25! ÷ (0! × (25-0)!)
! means 'Factorial' eg: 69! = 69 × 68 × 67 ... × 1
Note: 0! = 1
11,238,513
5 × 635,376
×
26
1 × 1
Simplify:
69! ÷ (5! × (69-5)!) = 11,238,513
5! ÷ (1! × (5-1)!) = 5
64! ÷ (4! × (64-4)!) = 635,376
26! ÷ (1! × (26-1)!) = 26
1! ÷ (1! × (1-1)!) = 1
25! ÷ (0! × (25-0)!) = 1
292,201,338 = 91.977
3,176,880
Calculate:
(11,238,513 ÷ 3,176,880) × (26 ÷ 1) = 91.977
Powerball Only 1 in 38.324 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(69,5)
C(5,0)
×
C(69-5,5-0)
×
C(26,1)
C(1,1)
×
C(26-1,1-1)
Substitute:
n for 69 (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 26 (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)
69!
5! × (69 - 5)!
5!
0! × (5 - 0)!
×
64!
5! × (64 - 5)!
×
26!
1! × (26 - 1)!
1!
1! × (1 - 1)!
×
25!
0! × (25 - 0)!
Expand:
C(69,5) = 69! ÷ (5! × (69-5)!)
C(5,0) = 5! ÷ (0! × (5-0)!)
C(69-5,5-0) = 64! ÷ (5! × (64-5)!)
C(26,1) = 26! ÷ (1! × (26-1)!)
C(1,1) = 1! ÷ (1! × (1-1)!)
C(26-1,1-1) = 25! ÷ (0! × (25-0)!)
! means 'Factorial' eg: 69! = 69 × 68 × 67 ... × 1
Note: 0! = 1
11,238,513
1 × 7,624,512
×
26
1 × 1
Simplify:
69! ÷ (5! × (69-5)!) = 11,238,513
5! ÷ (0! × (5-0)!) = 1
64! ÷ (5! × (64-5)!) = 7,624,512
26! ÷ (1! × (26-1)!) = 26
1! ÷ (1! × (1-1)!) = 1
25! ÷ (0! × (25-0)!) = 1
292,201,338 = 38.324
7,624,512
Calculate:
(11,238,513 ÷ 7,624,512) × (26 ÷ 1) = 38.324

Overall Odds: 1 in 24.867

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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