Factorial Digit Count Calculator

Count exact radix digits of n! using bounded BigInt factorial, avoiding logarithm rounding at powers of base; 0!=1 has one digit.

Description

Factorial digit counts depend on radix.

Factorial digit counts depend on radix. Exact factorial conversion avoids logarithmic estimates rounding incorrectly near a radix power.^[1]

Count exact radix digits of n! using bounded BigInt factorial, avoiding logarithm rounding at powers of base; 0!=1 has one digit.

When to use Factorial Digit Count Calculator

Use this tool to count exact radix digits of n! using bounded BigInt factorial, avoiding logarithm rounding at powers of base; 0!=1 has one digit.

Choose the integer, sequence, coefficients or function parameters for your calculation. Follow the stated ordering, domain and size limits.

How to use Factorial Digit Count Calculator and understand its results

Choose the integer, sequence, coefficients or function parameters for your calculation. Follow the stated ordering, domain and size limits.
Enter factorialIndex, radix using the field table and calculation rules, then run the tool.
Read exactFactorialDigitCount. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
factorialIndex	Factorial index	number	Required
radix	Radix	number	Required

Use integer factorial index 0–2000 and radix 2–36. Form n! with BigInt, convert directly in that radix and count digits; 0!=1 has one digit.

digit count = length of radix representation of n!

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
exactFactorialDigitCount	Exact factorial digit count	number

json

{
  "input": {
    "factorialIndex": 10,
    "radix": 10
  },
  "output": {
    "exactFactorialDigitCount": 7
  }
}

Limitations and assumptions

This bounded exact count does not return the factorial itself or its leading digits.

Numeric inputs and returned numeric values must be finite; an unrepresentable returned value produces an error. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Ménage Number Calculator: Count reduced circular ménage arrangements with one sex fixed in circular order and opposite-sex placements avoiding adjacent spouses; n≥2, no extra rotation/sex arrangement multiplier. For a complementary task, use Bell Transform Calculator: Compute complete exponential Bell-polynomial transform with b0=1 and b_n=Σ C(n−1,k−1)a_k b_(n−k); caller sequence differs materially from a single Bell number.

References

Factorial Digit Count Calculator — tool.io

Similar or alternative tools

Ménage Number Calculator
Count reduced circular ménage arrangements with one sex fixed in circular order and opposite-sex placements avoiding adjacent spouses; n≥2, no extra rotation/sex arrangement multiplier.
Bell Transform Calculator
Compute complete exponential Bell-polynomial transform with b0=1 and b_n=Σ C(n−1,k−1)a_k b_(n−k); caller sequence differs materially from a single Bell number.