{
  "category": "Compatibility",
  "display_name": "NORMSINV",
  "entry_kind": "built_in_function",
  "eval_api": {
    "method": "POST",
    "url": "https://handbook.dnacalc.com/api/eval"
  },
  "function_id": "FUNC.NORMSINV",
  "implementation_state": {
    "answer_bank": null,
    "detail": "Recorded: 3 workbook cells.",
    "dnacalc_commit": "9e1884369a678158dd82d3d74188daf986995e87",
    "in_catalogue": true,
    "state": "matches",
    "state_label": "Matches every recorded Excel answer",
    "summary": "Matches all 3 recorded answers",
    "workbook_corpus": {
      "cells": 3,
      "matched": 3
    }
  },
  "implementations": [
    {
      "commit": "9e1884369a678158dd82d3d74188daf986995e87",
      "flavour": "excel-compatibility-candidate",
      "language": "Rust",
      "name": "CalcFunc",
      "own_code": [
        "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/distributions.rs#L78-L80"
      ],
      "repository": "https://github.com/DnaCalc/DnaCalc",
      "shared_code": [
        "ported/excel_numeric::binary_with",
        "ported/excel_numeric::excel_x87_mul",
        "ported/excel_numeric/x87::mul",
        "ported/normal_dist_common::phi_kernel",
        "ported/normal_log_family::validate_probability_open_unit",
        "ported/normal_log_family::inverse_standard_normal_acklam_refined",
        "ported/normal_log_family::inverse_standard_normal",
        "ported/normal_log_family::norm_s_inv_kernel"
      ],
      "source": "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/distributions.rs#L78-L80",
      "state": "matches",
      "suite": null,
      "summary": "Matches all 3 recorded answers"
    }
  ],
  "json_url": "https://handbook.dnacalc.com/api/functions/FUNC.NORMSINV.json",
  "name": "NORMSINV",
  "notes": [],
  "schema": "efh.function-reference/v1",
  "section_order": [
    "what-it-does",
    "try-it",
    "quirks",
    "how-to-implement",
    "version-differences",
    "alternatives"
  ],
  "sections": {
    "alternatives": "\n[NORM.S.INV](FUNC.NORM.S.INV.md) is the modern spelling; [NORMSDIST](FUNC.NORMSDIST.md) gives the forward probability.\n\n\n",
    "how-to-implement": "\nThe current standard-normal inverse is a published-method candidate:\n\n1. Validate `0<p<1`. Choose its rational approximation branch at `p=0.02425` and `p=1-0.02425`.\n2. In the centre, set `q=p-0.5`, `r=q*q` and evaluate the coefficient polynomials in `r`, multiplying the numerator by `q`. In the lower tail use `q=sqrt(-2*crt_log(p))`; in the upper tail use `sqrt(-2*crt_log(1-p))` and reverse the sign. The cited source retains the coefficients and their Horner order.\n3. Refine the candidate `z` once. Form a small tail directly as `tail=0.5*erfc(abs(z)/sqrt(2))`, using the current library complementary error function. Set `err=tail-p` for negative `z`, or `err=(1-p)-tail` otherwise.\n4. If the normal density at `z` is nonzero, replace `z` by `z-err/density`. If it is zero, keep the rational candidate.\n\nReturn that `z`. At `p=0.5`, the central numerator has `q=0`, and the symmetric answer is zero.\n\nThis recipe can be coded from the source’s published-approximation coefficients, but it is not an identified Excel inverse. In particular, its Newton tail is a library `erfc` call; substituting the public worksheet ERFC introduces another numerical candidate. The unknown Excel approximation and stopping/rounding stages remain open.\n\n\n",
    "quirks": "\nThe probability must be strictly between zero and one; endpoints or out-of-range values give `#NUM!`. Nonnumeric arguments give `#VALUE!`. The mean and standard deviation are fixed at zero and one; there is no scale argument on this spelling.\n\nA small probability refers to the far **left** tail. For an upper-tail cutoff use the corresponding cumulative probability, while recognizing that `1-small_tail` can round to one for very small tails. Supply probability as a number, such as `0.5` or a numeric `50%` cell.\n\nMicrosoft describes an iterative inverse search over the forward normal CDF, with `#N/A` if it has not converged after 100 iterations on this legacy page. That documented method and limit do not identify the current candidate’s rational coefficients or numerical stopping stages.\n\n\n",
    "sources": "\n- [Microsoft: NORMSINV function](https://support.microsoft.com/en-us/excel/functions/normsinv-function), opened 6 November 2026; syntax, documented argument rules and errors.\n- [DnaCalc implementation](https://github.com/DnaCalc/DnaCalc/blob/da3ecc4fb19a3a5529708c311d0e8f05688ac165/crates/calc-func/src/ported/normal_log_family.rs); implementation steps and the limits identified in the text.\n\n",
    "try-it": "\n`=NORMSINV(0.5)` returns `0`, the centre of the standard normal distribution. A probability below one half has a negative quantile.\n\n\n",
    "version-differences": "The recorded environments below distinguish a reading from a same-input comparison. Counts describe captured inputs in each environment; overlapping captures and comparisons are not totals of unique worksheet calls.\n\n| Excel 16.0 build | Platform and CPU | Captured inputs |\n|---|---|---:|\n| 19929 | Windows, bitness not recorded, CPU not recorded | 2 |\n\nThe record contains no same-input comparison between these environments. Reading different inputs on different builds does not establish either a version change or cross-build agreement.\n\n[Recorded environments and comparison details](https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.NORMSINV.json).",
    "what-it-does": "\n`NORMSINV(probability)` is the compatibility quantile of the standard normal distribution: it returns z with cumulative probability p.\n\n\n"
  },
  "signature": {
    "display": "NORMSINV(probability)",
    "parameters": [
      {
        "description": null,
        "name": "probability",
        "optional": false,
        "repeats": false
      }
    ],
    "trailing_repeats": false
  },
  "sources": {
    "metadata": {
      "admission": {
        "label": "implemented",
        "reason": null
      },
      "arity": {
        "max": 1,
        "min": 1
      },
      "category": "Compatibility",
      "classification": {
        "arg_preparation_profile": "ValuesOnlyPreAdapter",
        "coercion_lift_profile": "Custom",
        "determinism_class": "Deterministic",
        "error_collapse_profile": "None",
        "fec_dependency_profile": "None",
        "host_interaction_class": "None",
        "kernel_signature_class": "Custom",
        "rich_value_usage": "RichBlind",
        "surface_fec_dependency_profile": "RefOnly",
        "thread_safety_class": "SafePure",
        "volatility_class": "NonVolatile"
      },
      "descriptions": {
        "long": null,
        "short": "Inverse of the cumulative standard normal distribution (older form)",
        "short_source": "dna-calc-own"
      },
      "docs": {
        "english_description": "Returns the inverse of the standard normal cumulative distribution",
        "microsoft_url": "https://support.microsoft.com/en-us/office/normsinv-function-8d1bce66-8e4d-4f3b-967c-30eed61f019d"
      },
      "entry_kind": "built_in_function",
      "localized_family_names": null,
      "localized_names": [
        {
          "locale": "ar-SA",
          "name": "NORMSINV"
        },
        {
          "locale": "bg-BG",
          "name": "NORMSINV"
        },
        {
          "locale": "cs-CZ",
          "name": "NORMSINV"
        },
        {
          "locale": "da-DK",
          "name": "STANDARDNORMINV"
        },
        {
          "locale": "de-DE",
          "name": "NORMSINV"
        },
        {
          "locale": "el-GR",
          "name": "NORMSINV"
        },
        {
          "locale": "en-AU",
          "name": "NORMSINV"
        },
        {
          "locale": "en-GB",
          "name": "NORMSINV"
        },
        {
          "locale": "en-US",
          "name": "NORMSINV"
        },
        {
          "locale": "es-ES",
          "name": "DISTR.NORM.ESTAND.INV"
        },
        {
          "locale": "et-EE",
          "name": "NORMSINV"
        },
        {
          "locale": "fi-FI",
          "name": "NORM.JAKAUMA.NORMIT.KÄÄNT"
        },
        {
          "locale": "fr-FR",
          "name": "LOI.NORMALE.STANDARD.INVERSE*"
        },
        {
          "locale": "he-IL",
          "name": "NORMSINV"
        },
        {
          "locale": "hr-HR",
          "name": "NORMSINV"
        },
        {
          "locale": "hu-HU",
          "name": "INVERZ.STNORM"
        },
        {
          "locale": "id-ID",
          "name": "NORMSINV"
        },
        {
          "locale": "it-IT",
          "name": "NORMSINV"
        },
        {
          "locale": "ja-JP",
          "name": "NORMSINV"
        },
        {
          "locale": "ko-KR",
          "name": "NORMSINV"
        },
        {
          "locale": "lt-LT",
          "name": "NORMSINV"
        },
        {
          "locale": "lv-LV",
          "name": "NORMSINV"
        },
        {
          "locale": "nb-NO",
          "name": "NORMSINV"
        },
        {
          "locale": "nl-NL",
          "name": "STAND.NORM.INV"
        },
        {
          "locale": "pl-PL",
          "name": "ROZKŁAD.NORMALNY.S.ODW"
        },
        {
          "locale": "pt-BR",
          "name": "NORMSINV"
        },
        {
          "locale": "pt-PT",
          "name": "INV.NORMP"
        },
        {
          "locale": "ro-RO",
          "name": "NORMSINV"
        },
        {
          "locale": "ru-RU",
          "name": "НОРМСТОБР"
        },
        {
          "locale": "sk-SK",
          "name": "NORMSINV"
        },
        {
          "locale": "sl-SI",
          "name": "NORMSINV"
        },
        {
          "locale": "sr-Latn-RS",
          "name": "NORMSINV"
        },
        {
          "locale": "sv-SE",
          "name": "NORMSINV"
        },
        {
          "locale": "th-TH",
          "name": "NORMSINV"
        },
        {
          "locale": "tr-TR",
          "name": "NORMSTERS işlevi"
        },
        {
          "locale": "uk-UA",
          "name": "NORMSINV"
        },
        {
          "locale": "vi-VN",
          "name": "NORMSINV"
        },
        {
          "locale": "zh-CN",
          "name": "NORMSINV"
        },
        {
          "locale": "zh-HK",
          "name": "NORMSINV"
        },
        {
          "locale": "zh-TW",
          "name": "NORMSINV"
        }
      ],
      "signature": {
        "display": "NORMSINV(probability)",
        "parameters": [
          {
            "description": null,
            "name": "probability",
            "optional": false,
            "repeats": false
          }
        ],
        "trailing_repeats": false
      },
      "surface_name": "NORMSINV",
      "version_marker": null,
      "xlcall": {
        "code": "296",
        "symbol": "xlfNormsinv"
      }
    },
    "microsoft": "https://support.microsoft.com/en-us/office/normsinv-function-8d1bce66-8e4d-4f3b-967c-30eed61f019d"
  },
  "try_it": {
    "formula": "=NORMSINV(0.5)"
  },
  "url": "https://handbook.dnacalc.com/functions/NORMSINV.html",
  "variants": [],
  "versions": [
    {
      "behaviour": "2 captured inputs are indexed for this environment. Capture dates are not recorded. This is a reading count, not a comparison with another build.",
      "excel_build": "16.0 build 19929",
      "platform": "Windows, bitness not recorded, CPU not recorded",
      "sources": [
        "https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.NORMSINV.json"
      ]
    }
  ]
}