# Factorial Calculator – Solve n!

Calculate the factorial *n!* for a number using the calculator below.

## factorial Number:

## How to Calculate a Factorial

The factorial of a number expressed as *n!* is equal to the product of all positive integers up to and including the number. This is true for all positive whole numbers, and the factorial of *0!* is equal to *1*.

### Factorial Formulas

The formula to calculate a factorial for a number is:

n! = n × (n-1) × (n-2) × … × 1

Thus, the factorial *n!* is equal to *n* times *n* minus 1, times *n* minus 2, continuing until the number 1 is reached.

This can also be expressed a little differently.

n! = 1 × 2 × 3 × … × n

Written a little differently, this states that the factorial *n!* is equal to 1 times 2 times 3 times each number, repeating until the number *n* is reached.

#### Product Notation

Using product notation this formula can be expressed like this:

#### Recurrence Relation

And the formula expressed using the recurrence relation looks like this:

n! = n × (n – 1)!

So the factorial *n!* is equal to the number *n* times the factorial of *n* minus one. This recurses until n is equal to 0.

## Factorial Table

The table below shows the factorial n! for the numbers one to one-hundred.

n | n! |
---|---|

1 | 1 |

2 | 2 |

3 | 6 |

4 | 24 |

5 | 120 |

6 | 720 |

7 | 5,040 |

8 | 40,320 |

9 | 362,880 |

10 | 3,628,800 |

11 | 39,916,800 |

12 | 479,001,600 |

13 | 6,227,020,800 |

14 | 87,178,291,200 |

15 | 1,307,674,368,000 |

16 | 20,922,789,888,000 |

17 | 355,687,428,096,000 |

18 | 6,402,373,705,728,000 |

19 | 121,645,100,408,832,000 |

20 | 2,432,902,008,176,640,000 |

21 | 5.1091E+19 |

22 | 1.1240E+21 |

23 | 2.5852E+22 |

24 | 6.2045E+23 |

25 | 1.5511E+25 |

26 | 4.0329E+26 |

27 | 1.0889E+28 |

28 | 3.0489E+29 |

29 | 8.8418E+30 |

30 | 2.6525E+32 |

31 | 8.2228E+33 |

32 | 2.6313E+35 |

33 | 8.6833E+36 |

34 | 2.9523E+38 |

35 | 1.0333E+40 |

36 | 3.7199E+41 |

37 | 1.3764E+43 |

38 | 5.2302E+44 |

39 | 2.0398E+46 |

40 | 8.1592E+47 |

41 | 3.3453E+49 |

42 | 1.4050E+51 |

43 | 6.0415E+52 |

44 | 2.6583E+54 |

45 | 1.1962E+56 |

46 | 5.5026E+57 |

47 | 2.5862E+59 |

48 | 1.2414E+61 |

49 | 6.0828E+62 |

50 | 3.0414E+64 |

51 | 1.5511E+66 |

52 | 8.0658E+67 |

53 | 4.2749E+69 |

54 | 2.3084E+71 |

55 | 1.2696E+73 |

56 | 7.1100E+74 |

57 | 4.0527E+76 |

58 | 2.3506E+78 |

59 | 1.3868E+80 |

60 | 8.3210E+81 |

61 | 5.0758E+83 |

62 | 3.1470E+85 |

63 | 1.9826E+87 |

64 | 1.2689E+89 |

65 | 8.2477E+90 |

66 | 5.4434E+92 |

67 | 3.6471E+94 |

68 | 2.4800E+96 |

69 | 1.7112E+98 |

70 | 1.1979E+100 |

71 | 8.5048E+101 |

72 | 6.1234E+103 |

73 | 4.4701E+105 |

74 | 3.3079E+107 |

75 | 2.4809E+109 |

76 | 1.8855E+111 |

77 | 1.4518E+113 |

78 | 1.1324E+115 |

79 | 8.9462E+116 |

80 | 7.1569E+118 |

81 | 5.7971E+120 |

82 | 4.7536E+122 |

83 | 3.9455E+124 |

84 | 3.3142E+126 |

85 | 2.8171E+128 |

86 | 2.4227E+130 |

87 | 2.1078E+132 |

88 | 1.8548E+134 |

89 | 1.6508E+136 |

90 | 1.4857E+138 |

91 | 1.3520E+140 |

92 | 1.2438E+142 |

93 | 1.1568E+144 |

94 | 1.0874E+146 |

95 | 1.0330E+148 |

96 | 9.9168E+149 |

97 | 9.6193E+151 |

98 | 9.4269E+153 |

99 | 9.3326E+155 |

100 | 9.3326E+157 |