# Security Math – Password Entropy Calculator

> Security Math – Password Entropy Calculator is a paid API for AI agents from security-math.x402tookit.com, paid per call via x402, $0.02/call, status unknown (last checked 2026-10-21).

Computes entropy bits for a password, PIN, or diceware passphrase given its length and character set, plus estimated crack-time ranges across attacker profiles.

## Facts

- Endpoint: GET https://security-math.x402tookit.com/password-entropy?utm_source=zero.xyz
- Price: $0.02/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-21
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/security-math-password-entropy-calculator-2d4532bc
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_y8dH99Ivr4KmUyFQB0Vot

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability security-math-password-entropy-calculator-2d4532bc
```

Example prompt: What's the entropy and estimated crack time for a 12-character random password using lowercase letters, uppercase letters, and digits — give me the ratings and attacker crack-time breakdown.

## When to prefer this

Use this endpoint when you need a rigorous, multi-attacker-profile entropy and crack-time analysis for a specific password or passphrase policy — especially when you need to compare character sets (lowercase only vs. alphanumeric vs. full ASCII), evaluate diceware passphrases, or justify security decisions with quantified crack-time estimates. Prefer it over generic password strength checkers when you need numeric entropy bits and attacker-model breakdowns rather than a simple weak/strong label.

## Known failure modes

- Missing required 'length' parameter returns an error
- Length outside 1–1000 range may return a validation error
- Conflicting flags (e.g., words=true with character flags) may produce unexpected pool sizes
- Network or payment failure returns 402 or connection error
- Very large pool sizes or extreme lengths may return degraded=true with a warning

## How this service works

Entropy bits for a random password policy, PIN or diceware passphrase from length and alphabet, with crack-time ranges.

## Output

Returns entropy bits total and per character/word, a strength rating and verdict, a summary explanation, a list of contributing reasons, and an array of crack-time entries for different attacker profiles (each with attacker name, assumption, guesses-per-second, average time, and worst-case time). Also includes a disclaimer, any factors not checked, and a timestamp.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "$schema": "https://json-schema.org/draft/2020-12/schema",
 "required": [
  "input"
 ],
 "properties": {
  "input": {
   "type": "object",
   "required": [
    "type",
    "method"
   ],
   "properties": {
    "type": {
     "type": "string",
     "const": "http"
    },
    "method": {
     "enum": [
      "GET"
     ],
     "type": "string"
    },
    "queryParams": {
     "type": "object",
     "required": [
      "length"
     ],
     "properties": {
      "lower": {
       "type": "string",
       "description": "true if a-z are used (default true)"
      },
      "upper": {
       "type": "string",
       "description": "true if A-Z are used (default false)"
      },
      "words": {
       "type": "string",
       "description": "true for a passphrase of random words drawn from poolSize words"
      },
      "digits": {
       "type": "string",
       "description": "true if 0-9 are used (default false)"
      },
      "length": {
       "type": "integer",
       "description": "Number of random characters (or words when words=true), 1 to 1000"
      },
      "symbols": {
       "type": "string",
       "description": "true if the 32 ASCII punctuation symbols are used (default false)"
      },
      "poolSize": {
       "type": "integer",
       "description": "Override: exact alphabet size, or word-list size when words=true (diceware = 7776)"
      }
     }
    }
   },
   "additionalProperties": false
  },
  "output": {
   "type": "object",
   "required": [
    "type"
   ],
   "properties": {
    "type": {
     "type": "string"
    },
    "example": {
     "type": "object",
     "properties": {
      "asOf": {
       "type": [
        "null",
        "string"
       ]
      },
      "unit": {
       "type": [
        "null",
        "string"
       ]
      },
      "length": {
       "type": [
        "null",
        "number"
       ]
      },
      "rating": {
       "type": [
        "null",
        "string"
       ]
      },
      "source": {
       "type": [
        "null",
        "string"
       ]
      },
      "reasons": {
       "type": [
        "array",
        "null"
       ],
       "items": {
        "type": "string"
       }
      },
      "summary": {
       "type": [
        "null",
        "string"
       ]
      },
      "verdict": {
       "type": [
        "null",
        "string"
       ]
      },
      "degraded": {
       "type": [
        "boolean",
        "null"
       ]
      },
      "crackTimes": {
… (truncated)
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/security-math-password-entropy-calculator-2d4532bc/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from security-math.x402tookit.com](https://www.zero.xyz/host/security-math.x402tookit.com/llms.txt)