Factorial Calculator

Factorial is evaluated from n. The calculation reports n!, log₁₀ - for large n and Stirling Approximation.

Results

Thanks — we’ve logged this for review.

About the Factorial Calculator

Factorial is treated here as a quantitative relation between n and n!, log₁₀ - for large n, Stirling Approximation and n!!.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
n! = n x (n - 1) x (n - 2) x... x 1
0! = 1 (by convention)

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

n! = n x (n - 1) x (n - 2) x... x 1
0! = 1 (by convention)

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Card Shuffling — 52!

Inputs

n: 52
n!: 80,658,175,170,941,865,445,237,205,074,225,084,147,487,409,798,502,548,791,041,728,708,608. log₁₀ - for large n: 67.906648. Stirling Approximation: 80,529,020,351,812,133,487,650,047,975,623,865,976,152,427,841,591,557,342,877,534,126,080. n!!: 2

With n = 52 as the stated inputs, the result is n! = 80,658,175,170,941,865,445,237,205,074,225,084,147,487,409,798,502,548,791,041,728,708,608, log₁₀ - for large n = 67.906648 and Stirling Approximation = 80,529,020,351,812,133,487,650,047,975,623,865,976,152,427,841,591,557,342,877,534,126,080. Each value corresponds to the declared output fields.

Example 2: Permutations — Race Podium

Inputs

n: 8
n!: 40,320. log₁₀ - for large n: 4.605521. Stirling Approximation: 39,902.3954. n!!: 2

With n = 8 as the stated inputs, the result is n! = 40,320, log₁₀ - for large n = 4.605521 and Stirling Approximation = 39,902.3954. Each value corresponds to the declared output fields.

Example 3: Taylor Series — e^x Coefficient

Inputs

n: 5
n!: 120. log₁₀ - for large n: 2.079181. Stirling Approximation: 118.0192. n!!: 8

With n = 5 as the stated inputs, the result is n! = 120, log₁₀ - for large n = 2.079181 and Stirling Approximation = 118.0192. Each value corresponds to the declared output fields.

Example 4: Password Combinations — 6 Digits

Inputs

n: 10
n!: 3,628,800. log₁₀ - for large n: 6.559763. Stirling Approximation: 3,598,695.6168. n!!: 2

With n = 10 as the stated inputs, the result is n! = 3,628,800, log₁₀ - for large n = 6.559763 and Stirling Approximation = 3,598,695.6168. Each value corresponds to the declared output fields.

Common Use Cases

  • Calculate permutations and combinations
  • Determine number of arrangements
  • Compute probability denominators
  • Evaluate Taylor series coefficients