PERT / three-point estimate API

Compute the PERT three-point estimate — beta te = (O + 4M + P)/6 or triangular (O+M+P)/3 — with standard deviation (P-O)/6, variance, and an optional normal-approximation confidence interval. Answers 'what is the PERT estimate','expected duration from optimistic/likely/pessimistic','what is the 95% confidence range for this task'.

Price$0.01per request

MethodPOST

Route/v1/calc/pm-pert-estimate

StatusLive

MIME typeapplication/json

Rate limit120/minute

CacheNo cache

calcpmpertestimatethree-pointdurationscheduleuncertainty

API URLhttps://x402.hexl.dev/v1/calc/pm-pert-estimate

Integration docs

Example request

{
  "optimistic": 2,
  "mostLikely": 4,
  "pessimistic": 9,
  "confidence": 0.95
}

Example response

{
  "optimistic": 2,
  "mostLikely": 4,
  "pessimistic": 9,
  "distribution": "beta",
  "expectedDuration": 4.5,
  "standardDeviation": 1.1667,
  "variance": 1.3611,
  "formula": "te = (O + 4M + P)/6, sd = (P - O)/6",
  "confidence": 0.95,
  "intervalLow": 2.21,
  "intervalHigh": 6.79
}

Input schema

{
  "type": "object",
  "required": [
    "optimistic",
    "mostLikely",
    "pessimistic"
  ],
  "properties": {
    "optimistic": {
      "type": "number",
      "description": "O, best case (days/hours)",
      "examples": [
        2
      ]
    },
    "mostLikely": {
      "type": "number",
      "description": "M, most likely",
      "examples": [
        4
      ]
    },
    "pessimistic": {
      "type": "number",
      "description": "P, worst case",
      "examples": [
        9
      ]
    },
    "distribution": {
      "type": "string",
      "enum": [
        "beta",
        "triangular"
      ],
      "default": "beta"
    },
    "confidence": {
      "type": "number",
      "description": "Optional CI level: 0.68, 0.80, 0.90, 0.95, or 0.99",
      "examples": [
        0.95
      ]
    }
  }
}

Output schema

{
  "type": "object",
  "additionalProperties": true
}