Mega Millions Odds Calculator

› Mega Millions

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 + Mega Ball (Jackpot) 1 in 302,575,350.000 Show/Hide ›

The odds for this prize level are directly influenced by the Mega Ball. Therefore the variables associated with the main ball pool and those associated with the separate Mega Ball 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(70,5)
C(5,5)
×
C(70-5,5-5)
×
C(25,1)
C(1,1)
×
C(25-1,1-1)
Substitute:
n for 70 (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 25 (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)
70!
5! × (70 - 5)!
5!
5! × (5 - 5)!
×
65!
0! × (65 - 0)!
×
25!
1! × (25 - 1)!
1!
1! × (1 - 1)!
×
24!
0! × (24 - 0)!
Expand:
C(70,5) = 70! ÷ (5! × (70-5)!)
C(5,5) = 5! ÷ (5! × (5-5)!)
C(70-5,5-5) = 65! ÷ (0! × (65-0)!)
C(25,1) = 25! ÷ (1! × (25-1)!)
C(1,1) = 1! ÷ (1! × (1-1)!)
C(25-1,1-1) = 24! ÷ (0! × (24-0)!)
! means 'Factorial' eg: 70! = 70 × 69 × 68 ... × 1
Note: 0! = 1
12,103,014
1 × 1
×
25
1 × 1
Simplify:
70! ÷ (5! × (70-5)!) = 12,103,014
5! ÷ (5! × (5-5)!) = 1
65! ÷ (0! × (65-0)!) = 1
25! ÷ (1! × (25-1)!) = 25
1! ÷ (1! × (1-1)!) = 1
24! ÷ (0! × (24-0)!) = 1
302,575,350 = 302,575,350.000
1
Calculate:
(12,103,014 ÷ 1) × (25 ÷ 1) = 302,575,350.000
5 Main Numbers 1 in 12,607,306.250 Show/Hide ›

The odds for this prize level are indirectly influenced by the Mega Ball. Even though this prize level only involves matching 5 main numbers, the fact that you can also match 5 main numbers and a Mega Ball 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 Mega Ball 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(70,5)
C(5,5)
×
C(70-5,5-5)
×
C(25,1)
C(1,0)
×
C(25-1,1-0)
Substitute:
n for 70 (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 25 (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)
70!
5! × (70 - 5)!
5!
5! × (5 - 5)!
×
65!
0! × (65 - 0)!
×
25!
1! × (25 - 1)!
1!
0! × (1 - 0)!
×
24!
1! × (24 - 1)!
Expand:
C(70,5) = 70! ÷ (5! × (70-5)!)
C(5,5) = 5! ÷ (5! × (5-5)!)
C(70-5,5-5) = 65! ÷ (0! × (65-0)!)
C(25,1) = 25! ÷ (1! × (25-1)!)
C(1,0) = 1! ÷ (0! × (1-0)!)
C(25-1,1-0) = 24! ÷ (1! × (24-1)!)
! means 'Factorial' eg: 70! = 70 × 69 × 68 ... × 1
Note: 0! = 1
12,103,014
1 × 1
×
25
1 × 24
Simplify:
70! ÷ (5! × (70-5)!) = 12,103,014
5! ÷ (5! × (5-5)!) = 1
65! ÷ (0! × (65-0)!) = 1
25! ÷ (1! × (25-1)!) = 25
1! ÷ (0! × (1-0)!) = 1
24! ÷ (1! × (24-1)!) = 24
302,575,350 = 12,607,306.250
24
Calculate:
(12,103,014 ÷ 1) × (25 ÷ 24) = 12,607,306.250
4 Main Numbers + Mega Ball 1 in 931,001.077 Show/Hide ›

The odds for this prize level are directly influenced by the Mega Ball. Therefore the variables associated with the main ball pool and those associated with the separate Mega Ball 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(70,5)
C(5,4)
×
C(70-5,5-4)
×
C(25,1)
C(1,1)
×
C(25-1,1-1)
Substitute:
n for 70 (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 25 (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)
70!
5! × (70 - 5)!
5!
4! × (5 - 4)!
×
65!
1! × (65 - 1)!
×
25!
1! × (25 - 1)!
1!
1! × (1 - 1)!
×
24!
0! × (24 - 0)!
Expand:
C(70,5) = 70! ÷ (5! × (70-5)!)
C(5,4) = 5! ÷ (4! × (5-4)!)
C(70-5,5-4) = 65! ÷ (1! × (65-1)!)
C(25,1) = 25! ÷ (1! × (25-1)!)
C(1,1) = 1! ÷ (1! × (1-1)!)
C(25-1,1-1) = 24! ÷ (0! × (24-0)!)
! means 'Factorial' eg: 70! = 70 × 69 × 68 ... × 1
Note: 0! = 1
12,103,014
5 × 65
×
25
1 × 1
Simplify:
70! ÷ (5! × (70-5)!) = 12,103,014
5! ÷ (4! × (5-4)!) = 5
65! ÷ (1! × (65-1)!) = 65
25! ÷ (1! × (25-1)!) = 25
1! ÷ (1! × (1-1)!) = 1
24! ÷ (0! × (24-0)!) = 1
302,575,350 = 931,001.077
325
Calculate:
(12,103,014 ÷ 325) × (25 ÷ 1) = 931,001.077
4 Main Numbers 1 in 38,791.712 Show/Hide ›

The odds for this prize level are indirectly influenced by the Mega Ball. Even though this prize level only involves matching 4 main numbers, the fact that you can also match 4 main numbers and a Mega Ball 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 Mega Ball 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(70,5)
C(5,4)
×
C(70-5,5-4)
×
C(25,1)
C(1,0)
×
C(25-1,1-0)
Substitute:
n for 70 (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 25 (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)
70!
5! × (70 - 5)!
5!
4! × (5 - 4)!
×
65!
1! × (65 - 1)!
×
25!
1! × (25 - 1)!
1!
0! × (1 - 0)!
×
24!
1! × (24 - 1)!
Expand:
C(70,5) = 70! ÷ (5! × (70-5)!)
C(5,4) = 5! ÷ (4! × (5-4)!)
C(70-5,5-4) = 65! ÷ (1! × (65-1)!)
C(25,1) = 25! ÷ (1! × (25-1)!)
C(1,0) = 1! ÷ (0! × (1-0)!)
C(25-1,1-0) = 24! ÷ (1! × (24-1)!)
! means 'Factorial' eg: 70! = 70 × 69 × 68 ... × 1
Note: 0! = 1
12,103,014
5 × 65
×
25
1 × 24
Simplify:
70! ÷ (5! × (70-5)!) = 12,103,014
5! ÷ (4! × (5-4)!) = 5
65! ÷ (1! × (65-1)!) = 65
25! ÷ (1! × (25-1)!) = 25
1! ÷ (0! × (1-0)!) = 1
24! ÷ (1! × (24-1)!) = 24
302,575,350 = 38,791.712
7,800
Calculate:
(12,103,014 ÷ 325) × (25 ÷ 24) = 38,791.712
3 Main Numbers + Mega Ball 1 in 14,546.892 Show/Hide ›

The odds for this prize level are directly influenced by the Mega Ball. Therefore the variables associated with the main ball pool and those associated with the separate Mega Ball 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(70,5)
C(5,3)
×
C(70-5,5-3)
×
C(25,1)
C(1,1)
×
C(25-1,1-1)
Substitute:
n for 70 (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 25 (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)
70!
5! × (70 - 5)!
5!
3! × (5 - 3)!
×
65!
2! × (65 - 2)!
×
25!
1! × (25 - 1)!
1!
1! × (1 - 1)!
×
24!
0! × (24 - 0)!
Expand:
C(70,5) = 70! ÷ (5! × (70-5)!)
C(5,3) = 5! ÷ (3! × (5-3)!)
C(70-5,5-3) = 65! ÷ (2! × (65-2)!)
C(25,1) = 25! ÷ (1! × (25-1)!)
C(1,1) = 1! ÷ (1! × (1-1)!)
C(25-1,1-1) = 24! ÷ (0! × (24-0)!)
! means 'Factorial' eg: 70! = 70 × 69 × 68 ... × 1
Note: 0! = 1
12,103,014
10 × 2,080
×
25
1 × 1
Simplify:
70! ÷ (5! × (70-5)!) = 12,103,014
5! ÷ (3! × (5-3)!) = 10
65! ÷ (2! × (65-2)!) = 2,080
25! ÷ (1! × (25-1)!) = 25
1! ÷ (1! × (1-1)!) = 1
24! ÷ (0! × (24-0)!) = 1
302,575,350 = 14,546.892
20,800
Calculate:
(12,103,014 ÷ 20,800) × (25 ÷ 1) = 14,546.892
3 Main Numbers 1 in 606.120 Show/Hide ›

The odds for this prize level are indirectly influenced by the Mega Ball. Even though this prize level only involves matching 3 main numbers, the fact that you can also match 3 main numbers and a Mega Ball 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 Mega Ball 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(70,5)
C(5,3)
×
C(70-5,5-3)
×
C(25,1)
C(1,0)
×
C(25-1,1-0)
Substitute:
n for 70 (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 25 (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)
70!
5! × (70 - 5)!
5!
3! × (5 - 3)!
×
65!
2! × (65 - 2)!
×
25!
1! × (25 - 1)!
1!
0! × (1 - 0)!
×
24!
1! × (24 - 1)!
Expand:
C(70,5) = 70! ÷ (5! × (70-5)!)
C(5,3) = 5! ÷ (3! × (5-3)!)
C(70-5,5-3) = 65! ÷ (2! × (65-2)!)
C(25,1) = 25! ÷ (1! × (25-1)!)
C(1,0) = 1! ÷ (0! × (1-0)!)
C(25-1,1-0) = 24! ÷ (1! × (24-1)!)
! means 'Factorial' eg: 70! = 70 × 69 × 68 ... × 1
Note: 0! = 1
12,103,014
10 × 2,080
×
25
1 × 24
Simplify:
70! ÷ (5! × (70-5)!) = 12,103,014
5! ÷ (3! × (5-3)!) = 10
65! ÷ (2! × (65-2)!) = 2,080
25! ÷ (1! × (25-1)!) = 25
1! ÷ (0! × (1-0)!) = 1
24! ÷ (1! × (24-1)!) = 24
302,575,350 = 606.120
499,200
Calculate:
(12,103,014 ÷ 20,800) × (25 ÷ 24) = 606.120
2 Main Numbers + Mega Ball 1 in 692.709 Show/Hide ›

The odds for this prize level are directly influenced by the Mega Ball. Therefore the variables associated with the main ball pool and those associated with the separate Mega Ball 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(70,5)
C(5,2)
×
C(70-5,5-2)
×
C(25,1)
C(1,1)
×
C(25-1,1-1)
Substitute:
n for 70 (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 25 (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)
70!
5! × (70 - 5)!
5!
2! × (5 - 2)!
×
65!
3! × (65 - 3)!
×
25!
1! × (25 - 1)!
1!
1! × (1 - 1)!
×
24!
0! × (24 - 0)!
Expand:
C(70,5) = 70! ÷ (5! × (70-5)!)
C(5,2) = 5! ÷ (2! × (5-2)!)
C(70-5,5-2) = 65! ÷ (3! × (65-3)!)
C(25,1) = 25! ÷ (1! × (25-1)!)
C(1,1) = 1! ÷ (1! × (1-1)!)
C(25-1,1-1) = 24! ÷ (0! × (24-0)!)
! means 'Factorial' eg: 70! = 70 × 69 × 68 ... × 1
Note: 0! = 1
12,103,014
10 × 43,680
×
25
1 × 1
Simplify:
70! ÷ (5! × (70-5)!) = 12,103,014
5! ÷ (2! × (5-2)!) = 10
65! ÷ (3! × (65-3)!) = 43,680
25! ÷ (1! × (25-1)!) = 25
1! ÷ (1! × (1-1)!) = 1
24! ÷ (0! × (24-0)!) = 1
302,575,350 = 692.709
436,800
Calculate:
(12,103,014 ÷ 436,800) × (25 ÷ 1) = 692.709
1 Main Numbers + Mega Ball 1 in 89.382 Show/Hide ›

The odds for this prize level are directly influenced by the Mega Ball. Therefore the variables associated with the main ball pool and those associated with the separate Mega Ball 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(70,5)
C(5,1)
×
C(70-5,5-1)
×
C(25,1)
C(1,1)
×
C(25-1,1-1)
Substitute:
n for 70 (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 25 (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)
70!
5! × (70 - 5)!
5!
1! × (5 - 1)!
×
65!
4! × (65 - 4)!
×
25!
1! × (25 - 1)!
1!
1! × (1 - 1)!
×
24!
0! × (24 - 0)!
Expand:
C(70,5) = 70! ÷ (5! × (70-5)!)
C(5,1) = 5! ÷ (1! × (5-1)!)
C(70-5,5-1) = 65! ÷ (4! × (65-4)!)
C(25,1) = 25! ÷ (1! × (25-1)!)
C(1,1) = 1! ÷ (1! × (1-1)!)
C(25-1,1-1) = 24! ÷ (0! × (24-0)!)
! means 'Factorial' eg: 70! = 70 × 69 × 68 ... × 1
Note: 0! = 1
12,103,014
5 × 677,040
×
25
1 × 1
Simplify:
70! ÷ (5! × (70-5)!) = 12,103,014
5! ÷ (1! × (5-1)!) = 5
65! ÷ (4! × (65-4)!) = 677,040
25! ÷ (1! × (25-1)!) = 25
1! ÷ (1! × (1-1)!) = 1
24! ÷ (0! × (24-0)!) = 1
302,575,350 = 89.382
3,385,200
Calculate:
(12,103,014 ÷ 3,385,200) × (25 ÷ 1) = 89.382
Mega Ball Only 1 in 36.632 Show/Hide ›

Although this prize level involves matching the Mega Ball only (drawn from a separate ball pool), the main balls must still be taken into account since the Mega Ball can also be matched with a selection of main numbers, thereby increasing the odds of matching the Mega Ball 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(70,5)
C(5,0)
×
C(70-5,5-0)
×
C(25,1)
C(1,1)
×
C(25-1,1-1)
Substitute:
n for 70 (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 25 (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)
70!
5! × (70 - 5)!
5!
0! × (5 - 0)!
×
65!
5! × (65 - 5)!
×
25!
1! × (25 - 1)!
1!
1! × (1 - 1)!
×
24!
0! × (24 - 0)!
Expand:
C(70,5) = 70! ÷ (5! × (70-5)!)
C(5,0) = 5! ÷ (0! × (5-0)!)
C(70-5,5-0) = 65! ÷ (5! × (65-5)!)
C(25,1) = 25! ÷ (1! × (25-1)!)
C(1,1) = 1! ÷ (1! × (1-1)!)
C(25-1,1-1) = 24! ÷ (0! × (24-0)!)
! means 'Factorial' eg: 70! = 70 × 69 × 68 ... × 1
Note: 0! = 1
12,103,014
1 × 8,259,888
×
25
1 × 1
Simplify:
70! ÷ (5! × (70-5)!) = 12,103,014
5! ÷ (0! × (5-0)!) = 1
65! ÷ (5! × (65-5)!) = 8,259,888
25! ÷ (1! × (25-1)!) = 25
1! ÷ (1! × (1-1)!) = 1
24! ÷ (0! × (24-0)!) = 1
302,575,350 = 36.632
8,259,888
Calculate:
(12,103,014 ÷ 8,259,888) × (25 ÷ 1) = 36.632

Overall Odds: 1 in 23.995

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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