Technical utilities · Calculation notebook

Password Generator: Secure Local Randomness: Worked Examples

Learn the inputs, formula and worked example behind the Password Generator, including password generator: calculation relationships, result interpretation, assumptions and sources.

Open calculator By Toolify · Updated

Purpose and steps

Password Generator validates length, uppercase letters, lowercase letters, digits, symbols before applying the displayed equation. Length must be at least the number of selected character types, and at most 128.

  1. Generate a password locally using the browser’s cryptographic random source. Include each selected character type at least once, then securely shuffle the generated characters.
  2. Enter Length, Uppercase letters, Lowercase letters, Digits, Symbols in the stated format. Baseline values are for reproduction.
  3. Check the output unit and convention: Read generated length with its stated unit and convention. The default example and the independent worked scenario use different inputs, so compare the assumptions before comparing the numbers.
  4. Change one input and compare the result. Length must be at least the number of selected character types, and at most 128. Use HTTPS or localhost. Store passwords in a password manager; no strength or breach-resistance guarantee is made.

Input reference and units

These values reproduce the model’s demonstration. Replace them with your own records or measurements; they are not recommended targets.

On a small screen, swipe the table horizontally to see all columns.

Parameters used by this calculator
ParameterDemonstration valueHow to enter it
Length16 Enter length without adding a unit suffix. Scope: Length must be at least the number of selected character types, and at most 128.
Uppercase letterstrue Each generated password includes at least one character of this selected type.
Lowercase letterstrue Each generated password includes at least one character of this selected type.
Digitstrue Each generated password includes at least one character of this selected type.
Symbolstrue Each generated password includes at least one character of this selected type.

Model-specific method

How this calculator produces its result

Password Generator: random index = uniform integer in [0, pool length − 1]. Input definitions: length = Length; upper = Uppercase letters; lower = Lowercase letters; digits = Digits; symbols = Symbols. Use the selected convention throughout the calculation.

Password Generator: calculation relationships

Generate a password locally using the browser’s cryptographic random source. Include each selected character type at least once, then securely shuffle the generated characters. Length must be at least the number of selected character types, and at most 128. Use HTTPS or localhost. Store passwords in a password manager; no strength or breach-resistance guarantee is made.

For a length L and an unconstrained alphabet of N characters, there are Nᴸ strings. Requiring each chosen character type changes that model, so the tool does not claim a simple entropy score. It uses cryptographic randomness and rejection sampling for character selection. Generate a 24-character example and check length and selected types; its literal characters are deliberately not published as a reusable password.

random index = uniform integer in [0, pool length − 1]
  • length: Length. Enter length without adding a unit suffix. Scope: Length must be at least the number of selected character types, and at most 128.
  • upper: Uppercase letters. Each generated password includes at least one character of this selected type.
  • lower: Lowercase letters. Each generated password includes at least one character of this selected type.
  • digits: Digits. Each generated password includes at least one character of this selected type.
  • symbols: Symbols. Each generated password includes at least one character of this selected type.
  • Result units: stated beside each output
  • Calculation relationship: random index = uniform integer in [0, pool length − 1]
  • Supported domain: see the limits below

Worked example

Password Generator baseline input: Length: 16; Uppercase letters: selected; Lowercase letters: selected; Digits: selected; Symbols: selected. Output: Generated length = 16 characters. This demonstrates length and character-type constraints, not a fixed password. Every generation changes the characters; check the length and selected character types instead.

Reproduce the default scenario

This reproduces the default inputs in the reference table above; it is not an additional independent example. Displayed rounding may differ from intermediate precision.

Generated length
16 characters

Reading results without overstating them

  • Read generated length with its stated unit and convention. The default example and the independent worked scenario use different inputs, so compare the assumptions before comparing the numbers.
  • Change one input at a time and use the equation to explain the result; do not mix unit, grade-scale, time-zone or rounding conventions across comparisons.

Assumptions and exclusions

  • Length must be at least the number of selected character types, and at most 128.
  • Use HTTPS or localhost. Store passwords in a password manager; no strength or breach-resistance guarantee is made.
Test a changed assumption in the calculator

Sources and content notes

Toolify describes the implemented algorithm and its assumptions. Sources below support the topic or applicable rules; they do not endorse this calculator. Examples are illustrative, and published rules take precedence over simplified estimates.

Report a formula, example or translation issue through our contact page. Include the tool name, inputs and expected result so it can be reproduced. Contact Toolify

From question to result

Continue with a related question

Explore all Technical utilities tools and guides