Factorial Calculator
This factorial calculator works out n! the moment you type a whole number, where n! is the product of every whole number from n down to 1. You'll see the full value at once, plus the answer in scientific notation, the digit count, and a quick note such as 0! = 1. It handles every value from 0 to 170, it'll show you the whole multiplication chain so you can follow the math, and the live chart next to it makes it obvious just how fast the factorial grows.
- Any whole number 0 to 170
- Full multiplication chain
- Scientific notation
- Digit count
- Live growth chart
Last updated June 18, 2026 Method: n! = n × (n - 1) × … × 1 Reviewed by the Calcowa math team
Show the multiplication chain
Enter a whole number from 0 to 170 to see the factorial.
10! = 10 × 9 × … × 1 = 3,628,800
What is a factorial?
A factorial is the product of every positive whole number from 1 up to n, written as n!. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. It's one of the most useful tools in combinatorics because it counts how many ways you can arrange n distinct items in a row.
The factorial formula is n! = n × (n - 1) × (n - 2) × … × 2 × 1. You can also write it recursively as n! = n × (n - 1)!, which is exactly how the loop inside this factorial calculator builds the answer, one factor at a time.
Why does 0! equal 1?
0! = 1 is one of those rules that throws people at first, but it's logical once you see why. The recursive definition says n! = n × (n - 1)!. Plug in n = 1 and you get 1! = 1 × 0!. Since 1! = 1, that forces 0! to equal 1. No other value keeps the formula consistent.
Here's another angle: 0! counts the ways to arrange zero objects, and there's exactly one way to do that, which is to do nothing. The empty product rule formalizes it, since a product with no factors equals the multiplicative identity, 1. That's why this factorial calculator returns 1 for both 0! and 1!.
How do you calculate n! by hand?
To calculate a factorial by hand, start at n and multiply by each smaller whole number until you reach 1. Here's the full sequence:
- 1
Start at nWrite down your number n. If n is 0 or 1, the answer is just 1, so you can stop.
- 2
Multiply by the next number downMultiply n by (n - 1). For 6! that first step is 6 × 5 = 30.
- 3
Keep stepping downCarry on multiplying by each smaller number: × 4, × 3, × 2.
- 4
Stop at 1Multiply by 1 last. Anything × 1 is unchanged, so 6! lands on 720.
- 5
Check against the calculatorType the same n above and you'll see the value, the scientific form, and the chain.
What is 10! and what is 20!?
10! is the product 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1, and it comes to 3,628,800. That's already over three million, and it shows how quickly the factorial climbs. Bump n up to 20 and the answer leaps to twenty-digit territory.
10! = 10 × 9 × … × 1 = 3,628,800
and 20! = 2,432,902,008,176,640,000, about 2.43 × 10¹&sup8;
Type 10 or 20 into the calculator above and you'll get the matching full value, the scientific notation, and the digit count without working it out by hand.
Where do factorials show up?
Factorials show up constantly in combinatorics. The number of ways to arrange n distinct items in a row is n!. If you only want to order r of those n items, that's a permutation: P(n, r) = n! / (n - r)!. If the order doesn't matter, it's a combination: C(n, r) = n! / (r! × (n - r)!). You can work both out with our permutation calculator.
They also appear in probability and in Taylor series. The series for e uses 1/0! + 1/1! + 1/2! + …, and the expansions for sin and cos both carry factorials in their denominators. Since factorials are really repeated multiplication, our exponent calculator is handy when you're comparing how a power grows against a factorial, and the full math calculators hub covers the rest.
What is the largest factorial you can calculate?
In standard floating-point math, 170! is the largest factorial you can hold, and it's about 7.26 × 10³&sup0;&sup6;. Once you reach 171!, the result tops the maximum number and reads as Infinity, so this calculator flags any n above 170. For very large factorials you'd need an arbitrary-precision library, but for textbook and probability problems you're well inside the 0 to 170 range.
Factorial growth table
A factorial grows faster than any fixed-base power, and this table makes that obvious at a glance. Here are the values from 0! through 20!, with the full integer and the scientific form side by side. The 10! row is highlighted since it's the most common one you'll meet.
| n | n! | Scientific notation |
|---|---|---|
| 0 | 1 | 1 |
| 1 | 1 | 1 |
| 2 | 2 | 2 |
| 3 | 6 | 6 |
| 4 | 24 | 24 |
| 5 | 120 | 120 |
| 6 | 720 | 720 |
| 7 | 5,040 | 5,040 |
| 8 | 40,320 | 40,320 |
| 9 | 362,880 | 362,880 |
| 10 | 3,628,800 | 3.63 × 10&sup6; |
| 12 | 479,001,600 | 4.79 × 10&sup8; |
| 15 | 1,307,674,368,000 | 1.31 × 10¹² |
| 20 | 2,432,902,008,176,640,000 | 2.43 × 10¹&sup8; |
Frequently asked questions
Is a factorial the same as a power?
No. A power multiplies the same base by itself, like 5 to the 3 = 5 × 5 × 5. A factorial multiplies a run of different numbers, like 5! = 5 × 4 × 3 × 2 × 1. Factorials grow far faster than powers, which is why n! overtakes any fixed-base power as n climbs.
A factorial is the product of every whole number from 1 up to n. Written as n!, it means n × (n - 1) × (n - 2) × … × 2 × 1. So 5! = 5 × 4 × 3 × 2 × 1 = 120. You'll meet it any time you count how many ways you might order a set of distinct items.
0! = 1 by definition. The empty product rule says a product with no factors equals 1, and that's the value that keeps the recursive formula n! = n × (n - 1)! consistent: 1! = 1 × 0! only works when 0! = 1. There's also just one way to arrange nothing, so the count is 1.
10! = 3,628,800. That's the product 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1. You'll run into 10! in permutation and combination problems whenever you're arranging 10 distinct items in a row.
20! = 2,432,902,008,176,640,000, or about 2.43 × 10¹&sup8;. It's big enough that many calculators can't show it as a full integer, so it's often written in scientific notation. This factorial calculator shows both the full value and the scientific form.
They turn up in combinatorics (permutations and combinations), probability, Taylor series, and number theory. The permutation formula P(n, r) = n! / (n - r)! and the combination formula C(n, r) = n! / (r! × (n - r)!) both lean on factorials directly.
170! is the largest exact factorial standard floating-point math can hold, and it's about 7.26 × 10³&sup0;&sup6;. Push to 171! and the value overflows past the maximum number, so it reads as Infinity. Every result from 0! through 170! shows as an integer and in scientific notation.
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