Factorial Calculator

Exact n! and n!! with instant results, step-by-step breakdowns, scientific notation, digit counts, and growth visuals.

Quick examples

Integer n (0–170)

Whole numbers only. Results update as you type.

Show gamma function note (advanced)

Enter a valid integer to see n! or n!!, or tap a quick example.

What is factorial?

The factorial of a non-negative integer n, written n!, is the product of all positive integers from 1 through n. By definition, 0! = 1. Factorials count permutations: n distinct objects can be lined up in n! orders.

Why 0! = 1?

Treating 0! as 1 makes the rule n! = n × (n−1)! work for n = 1, and matches the "empty product" convention in combinatorics (one way to arrange zero objects).

How factorial works

Compute n! by multiplying 1 × 2 × … × n. Growth is extremely fast: 10! is millions, 20! is huge, 100! has 158 digits. This calculator uses BigInt for exact integers up to 170!.

Factorial examples

5! = 120
10! = 3,628,800
0! = 1
Double: 7!! = 7 × 5 × 3 × 1 = 105

Factorial table (1–50)

Exact values of n! for n from 1 to 50 (50! has 65 digits).

n	n!	Digits
1	`1`	1
2	`2`	1
3	`6`	1
4	`24`	2
5	`120`	3
6	`720`	3
7	`5040`	4
8	`40320`	5
9	`362880`	6
10	`3628800`	7
11	`39916800`	8
12	`479001600`	9
13	`6227020800`	10
14	`87178291200`	11
15	`1307674368000`	13
16	`20922789888000`	14
17	`355687428096000`	15
18	`6402373705728000`	16
19	`121645100408832000`	18
20	`2432902008176640000`	19
21	`51090942171709440000`	20
22	`1124000727777607680000`	22
23	`25852016738884976640000`	23
24	`620448401733239439360000`	24
25	`15511210043330985984000000`	26
26	`403291461126605635584000000`	27
27	`10888869450418352160768000000`	29
28	`304888344611713860501504000000`	30
29	`8841761993739701954543616000000`	31
30	`265252859812191058636308480000000`	33
31	`8222838654177922817725562880000000`	34
32	`263130836933693530167218012160000000`	36
33	`8683317618811886495518194401280000000`	37
34	`295232799039604140847618609643520000000`	39
35	`10333147966386144929666651337523200000000`	41
36	`371993326789901217467999448150835200000000`	42
37	`13763753091226345046315979581580902400000000`	44
38	`523022617466601111760007224100074291200000000`	45
39	`20397882081197443358640281739902897356800000000`	47
40	`815915283247897734345611269596115894272000000000`	48
41	`33452526613163807108170062053440751665152000000000`	50
42	`1405006117752879898543142606244511569936384000000000`	52
43	`60415263063373835637355132068513997507264512000000000`	53
44	`2658271574788448768043625811014615890319638528000000000`	55
45	`119622220865480194561963161495657715064383733760000000000`	57
46	`5502622159812088949850305428800254892961651752960000000000`	58
47	`258623241511168180642964355153611979969197632389120000000000`	60
48	`12413915592536072670862289047373375038521486354677760000000000`	62
49	`608281864034267560872252163321295376887552831379210240000000000`	63
50	`30414093201713378043612608166064768844377641568960512000000000000`	65

FAQs

Why is the maximum 170 for n!?: 170! fits in JavaScript BigInt with practical display size; larger values have thousands of digits and are rarely needed in exact form. Use scientific approximations or Stirling’s formula for asymptotics.
What is double factorial (n!!)?: n!! multiplies every other integer from n down to 1 or 2. For example 8!! = 8×6×4×2. It appears in combinatorics and some integrals.
What is the gamma function?: Γ extends factorial to complex numbers (except non-positive integers). For positive integers, Γ(n) = (n−1)!, so Γ(n+1) = n!.
Can I use decimals?: Standard factorial is defined for non-negative integers only. Decimals are not accepted in this tool so results stay exact.