Factorial Calculator

1. Enter a whole number from 0 upward.
2. Read the factorial, the product of every whole number down to 1.
3. See how many digits the result has.
4. See the number of trailing zeros at the end.

Here is what each result means:

A factorial is the product of a whole number and every whole number below it down to 1, written with an exclamation mark. So 5! = 5 x 4 x 3 x 2 x 1 = 120. By definition 0! = 1, which keeps the counting rules consistent.

Factorials count the number of ways to arrange things. There are n! orders for n distinct items, which is why factorials sit at the heart of permutations, combinations and probability. They grow astonishingly fast: 10 factorial already passes three million, and 100 factorial has 158 digits.

It multiplies from 2 up to n, keeping every digit exact with big-integer arithmetic.

1. Start from 1 and multiply by each whole number up to n.
2. Keep full precision so even huge results stay exact.
3. Count the digits, and the trailing zeros from factors of 5.

Factorials appear in counting problems; for breaking numbers into primes instead, use the prime factorization calculator.

Work out 5! and 6!.

Calculation: 5! = 120, and since 6! = 6 x 5!, it is 6 x 120 = 720. Each step just multiplies the previous factorial by the next number, which is why factorials climb so quickly.

Factorials rise faster than powers, which is why large ones need big-integer maths.

By 20 factorial the result already exceeds what a standard number type can hold exactly, so this tool uses big integers.

Factorials are the building block of counting formulas.

Each of these divides one factorial by others, so a factorial tool is the first step in many probability problems.

The Value of N

Each step up multiplies by a larger number, so the result grows faster and faster as n rises.

Trailing Zeros

Every factor of 5 paired with a 2 adds a trailing zero, so the count of zeros grows with n in steps.

Digit Length

The number of digits climbs steadily, reaching 158 digits at 100 factorial and far more beyond.

Probability and Counting

Find arrangements, or the pieces of a permutation or combination formula.

Algebra and Series

Evaluate factorials that appear in binomial expansions and power series.

Checking Huge Results

Get the exact value, digit count and trailing zeros for a large factorial.

1. Thinking 0 Factorial Is 0

By definition, 0 factorial is 1, not 0. This keeps counting formulas working.

2. Taking a Factorial of a Decimal

The plain factorial is defined only for whole numbers. Decimals need the gamma function instead.

3. Expecting a Negative Factorial

Factorials are not defined for negative numbers in ordinary maths.

4. Underestimating the Growth

Factorials explode. Even 20 factorial is over two quintillion, so results get long fast.

5. Losing Precision

A standard number type rounds large factorials. Exact answers need big-integer arithmetic, which this tool uses.

The result is exact for whole numbers in range; only display length is trimmed for very long values.

A factorial is the product of a whole number and every whole number below it down to 1. It is written with an exclamation mark, so 5 factorial is 5 times 4 times 3 times 2 times 1, which is 120.

Zero factorial is defined as 1. It may seem odd, but it keeps counting formulas consistent, since there is exactly one way to arrange nothing.

Multiply the number by every whole number below it down to 1. For 6 factorial, that is 6 times 5 times 4 times 3 times 2 times 1, which is 720. This tool does it exactly for any whole number.

Not the ordinary factorial, which is defined only for whole numbers. The gamma function extends the idea to decimals and negatives, but that is a separate calculation.

Each trailing zero comes from a factor of 10, which is a 2 times a 5. Fives are rarer than twos, so the number of trailing zeros equals the count of factors of 5 in the product.

100 factorial has 158 digits. Factorials grow extremely fast, so even modest inputs produce very long numbers, which is why this tool uses exact big-integer arithmetic.

They count arrangements and underpin permutations, combinations and probability. They also appear in algebra, in binomial expansions and in the power series of many functions.

It computes exact factorials for whole numbers up to 5000. The full result can have thousands of digits, so above a length the display is shortened while the digit count stays exact.

No. The calculation runs in your browser and nothing you enter is stored or sent anywhere, unless you choose Save, which keeps the result only on this device.

• Factorial (Wikipedia).
• Factorials explained (Maths Is Fun).
• Combinations and permutations (Maths Is Fun).