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Math formula

How to calculate factorial

Factorials count arrangements and appear inside combination and permutation formulas.

See the formulaOpen calculator
Direct answer
Formula
n! = n * (n - 1) * ... * 2 * 1

Use the table below to match each symbol with the right input. Keep units consistent before you start.

Factorial formula
Start here when you only need the equation and variable names.
Formula
n! = n * (n - 1) * ... * 2 * 1

Factorials count arrangements and appear inside combination and permutation formulas.

Variable meanings
Check each symbol, meaning, and unit before you calculate.
SymbolNameDescriptionUnit
nNumberNon-negative whole number.Depends on inputs
!Factorial operatorInstruction to multiply down to 1.Depends on inputs
When to use this formula
Check that your situation matches the formula before you trust the result.
  • Fits counting problems where every item can be arranged or selected.
Step-by-step method
Follow these steps when you are solving it by hand.
  1. 1Start with a non-negative whole number.
  2. 2Multiply it by each smaller positive whole number.
  3. 3Use 1 for 0! by definition.
Examples
These sample numbers show the order of operations and units.
Five factorial
n
5
  1. 1.5! = 5 * 4 * 3 * 2 * 1
  2. 2.5! = 120
Result
5! equals 120.
Seven factorial
n
7
  1. 1.7! = 7 * 6 * 5 * 4 * 3 * 2 * 1
  2. 2.7! = 5040
Result
7! equals 5,040.
Mistakes to avoid
Small input or unit errors can change the answer a lot.
  • Putting the wrong value in the numerator or denominator of the factorial formula.
  • Skipping signs, order, or sorting rules that change the result.
  • Rounding before the last step.
  • Assuming a formula applies when the needed input is zero or missing.
Open the Factorial Calculator
Open the calculator for the answer without rewriting the formula.

Enter your values in the related calculator, then compare the output with the hand method above.

Open Factorial Calculator
FAQs
Short answers for common formula questions.
Can I calculate Factorial by hand?

Yes. Write the units next to each value, convert rates or measurements first, and round only the final answer.

Why does my Factorial result differ from another calculator?

Most differences come from rounding, unit conversions, rate timing, or a slightly different version of the formula.

When is the Factorial Calculator better than hand math?

Open the Factorial Calculator to check several scenarios or skip the hand arithmetic.