{
  "category": "Compatibility",
  "display_name": "TINV",
  "entry_kind": "built_in_function",
  "eval_api": {
    "method": "POST",
    "url": "https://handbook.dnacalc.com/api/eval"
  },
  "function_id": "FUNC.TINV",
  "implementation_state": {
    "answer_bank": {
      "excel_builds": [
        "20131",
        "?"
      ],
      "larger_numeric": 4,
      "last_bit": 13,
      "matched": 15,
      "other_mismatch": 0,
      "refused": 0,
      "rows": 32,
      "unread": 0,
      "worst_ulp": 173
    },
    "detail": "Of 36 recorded answers (32 in the answer bank and 4 workbook cells), 19 do not match: 4 differ by more than 16 ULP, 15 differ by at most 16 ULP.",
    "dnacalc_commit": "9e1884369a678158dd82d3d74188daf986995e87",
    "in_catalogue": true,
    "state": "differs",
    "state_label": "Known larger differences",
    "summary": "Known larger differences on 19 of 36 recorded answers",
    "workbook_corpus": {
      "cells": 4,
      "last_bit": 2,
      "matched": 2,
      "worst_ulp": 1
    }
  },
  "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#L193-L196"
      ],
      "repository": "https://github.com/DnaCalc/DnaCalc",
      "shared_code": [
        "catalogue/distributions::nums",
        "ported/chi_f_t_family::truncate_positive_integer",
        "ported/chi_f_t_family::validate_probability_open_unit",
        "ported/chi_f_t_family::search_upper_bound",
        "ported/chi_f_t_family::t_inv_2t_kernel",
        "ported/excel_numeric::binary_with",
        "ported/excel_numeric::tan_with",
        "ported/excel_numeric::excel_tan",
        "ported/excel_numeric::excel_x87_add",
        "ported/excel_numeric::excel_x87_mul",
        "ported/excel_numeric::excel_x87_mul_add",
        "ported/excel_numeric/soft87::pack_raw",
        "ported/excel_numeric/soft87::zero",
        "ported/excel_numeric/soft87::inf",
        "ported/excel_numeric/soft87::pack",
        "ported/excel_numeric/soft87::ext_pi",
        "ported/excel_numeric/soft87::ext_one",
        "ported/excel_numeric/soft87::ext_chs",
        "ported/excel_numeric/x87::mul",
        "ported/excel_numeric/x87::add",
        "ported/special_math_common::bratio_ftoi",
        "ported/special_math_common::bratio_spmpar1",
        "ported/special_math_common::bratio_exparg",
        "ported/special_math_common::bratio_esum",
        "ported/special_math_common::bratio_esum20",
        "ported/special_math_common::bratio_alnrel",
        "ported/special_math_common::bratio_rlog1",
        "ported/special_math_common::bratio_gam1",
        "ported/special_math_common::bratio_gamln1",
        "ported/special_math_common::bratio_gamln",
        "ported/special_math_common::bratio_algdiv",
        "ported/special_math_common::bratio_bcorr",
        "ported/special_math_common::bratio_gsumln",
        "ported/special_math_common::bratio_betaln",
        "ported/special_math_common::bratio_betaln_60",
        "ported/special_math_common::bratio_erf_nswc",
        "ported/special_math_common::bratio_erfc1",
        "ported/special_math_common::bratio_rexp",
        "ported/special_math_common::bratio_psi",
        "ported/special_math_common::bratio_fpser",
        "ported/special_math_common::bratio_apser",
        "ported/special_math_common::bratio_bpser",
        "ported/special_math_common::bratio_bup",
        "ported/special_math_common::bratio_brcomp",
        "ported/special_math_common::bratio_brcmp1",
        "ported/special_math_common::bratio_bfrac",
        "ported/special_math_common::bratio_bgrat",
        "ported/special_math_common::bratio_grat1",
        "ported/special_math_common::bratio_basym",
        "ported/special_math_common::bratio",
        "ported/special_math_common::bisect_inverse",
        "ported/tan::tan_kernel"
      ],
      "source": "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/distributions.rs#L193-L196",
      "state": "differs",
      "suite": null,
      "summary": "Known larger differences on 19 of 36 recorded answers"
    }
  ],
  "json_url": "https://handbook.dnacalc.com/api/functions/FUNC.TINV.json",
  "name": "TINV",
  "notes": [],
  "schema": "efh.function-reference/v1",
  "section_order": [
    "what-it-does",
    "try-it",
    "quirks",
    "how-to-implement",
    "version-differences",
    "alternatives"
  ],
  "sections": {
    "alternatives": "\n[T.INV.2T](FUNC.T.INV.2T.md) is the explicit two-tail name; [T.INV](FUNC.T.INV.md) is a signed left-CDF quantile; [TDIST](FUNC.TDIST.md) returns a tail probability.\n\n\n",
    "how-to-implement": "\nFor degree one, the retained route is `1/TAN(PI()*p/2)`, with a separate exact `p=0.5` return of one. For higher degrees the code currently brackets and inverts the decreasing two-tail beta-ratio probability. Public-composition readings support a `sqrt(v*(1/BETA.INV(p,v/2,0.5)-1))` construction on their scope, but the current beta inverse still differs; the code therefore retains its generic inverse. Do not describe that unresolved composition as a shipped exact route.\n\n\n",
    "quirks": "\nDegrees are truncated. Invalid degrees or probabilities give `#NUM!`; nonnumeric inputs give `#VALUE!`. The public page admits probability one in its range wording, while the current shared inverse requires `0<p<1`. For a one-tail upper critical value use twice that tail probability in the two-tail inverse, within its admitted range.\n\n\n",
    "sources": "\n- [Microsoft: TINV function](https://support.microsoft.com/en-us/excel/functions/tinv-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/chi_f_t_family.rs); implementation steps and the limits identified in the text.\n\n",
    "try-it": "\n`=TINV(0.5,1)` returns `1` under the current explicit Cauchy control. Half the one-degree distribution lies beyond plus or minus one.\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 | 14 |\n| 20131 | Windows, bitness not recorded, AMD Ryzen 7 4800H with Radeon Graphics | 32 |\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.TINV.json).",
    "what-it-does": "\n`TINV(probability,deg_freedom)` returns a nonnegative Student-t critical magnitude for a **two-tailed** probability. It is the compatibility name for the two-tail inverse.\n\n\n"
  },
  "signature": {
    "display": "TINV(probability, deg_freedom)",
    "parameters": [
      {
        "description": null,
        "name": "probability",
        "optional": false,
        "repeats": false
      },
      {
        "description": null,
        "name": "deg_freedom",
        "optional": false,
        "repeats": false
      }
    ],
    "trailing_repeats": false
  },
  "sources": {
    "metadata": {
      "admission": {
        "label": "implemented",
        "reason": null
      },
      "arity": {
        "max": 2,
        "min": 2
      },
      "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": "Two-tailed inverse of Student's t distribution (older form)",
        "short_source": "dna-calc-own"
      },
      "docs": {
        "english_description": "Returns the inverse of the Student's t-distribution",
        "microsoft_url": "https://support.microsoft.com/en-us/office/tinv-function-a7c85b9d-90f5-41fe-9ca5-1cd2f3e1ed7c"
      },
      "entry_kind": "built_in_function",
      "localized_family_names": null,
      "localized_names": [
        {
          "locale": "ar-SA",
          "name": "TINV"
        },
        {
          "locale": "bg-BG",
          "name": "TINV"
        },
        {
          "locale": "cs-CZ",
          "name": "TINV"
        },
        {
          "locale": "da-DK",
          "name": "TINV"
        },
        {
          "locale": "de-DE",
          "name": "TINV"
        },
        {
          "locale": "el-GR",
          "name": "TINV"
        },
        {
          "locale": "en-AU",
          "name": "TINV"
        },
        {
          "locale": "en-GB",
          "name": "TINV"
        },
        {
          "locale": "en-US",
          "name": "TINV"
        },
        {
          "locale": "es-ES",
          "name": "DISTR.T.INV"
        },
        {
          "locale": "et-EE",
          "name": "TINV"
        },
        {
          "locale": "fi-FI",
          "name": "TJAKAUMA.KÄÄNT"
        },
        {
          "locale": "fr-FR",
          "name": "LOI.STUDENT.INVERSE*"
        },
        {
          "locale": "he-IL",
          "name": "TINV"
        },
        {
          "locale": "hr-HR",
          "name": "TINV"
        },
        {
          "locale": "hu-HU",
          "name": "INVERZ.T"
        },
        {
          "locale": "id-ID",
          "name": "TINV"
        },
        {
          "locale": "it-IT",
          "name": "TINV"
        },
        {
          "locale": "ja-JP",
          "name": "TINV"
        },
        {
          "locale": "ko-KR",
          "name": "TINV"
        },
        {
          "locale": "lt-LT",
          "name": "TINV"
        },
        {
          "locale": "lv-LV",
          "name": "TINV"
        },
        {
          "locale": "nb-NO",
          "name": "TINV"
        },
        {
          "locale": "nl-NL",
          "name": "T.INV"
        },
        {
          "locale": "pl-PL",
          "name": "ROZKŁAD.T.ODW"
        },
        {
          "locale": "pt-BR",
          "name": "TINV"
        },
        {
          "locale": "pt-PT",
          "name": "INVT"
        },
        {
          "locale": "ro-RO",
          "name": "TINV"
        },
        {
          "locale": "ru-RU",
          "name": "СТЬЮДРАСПОБР"
        },
        {
          "locale": "sk-SK",
          "name": "TINV"
        },
        {
          "locale": "sl-SI",
          "name": "TINV"
        },
        {
          "locale": "sr-Latn-RS",
          "name": "TINV"
        },
        {
          "locale": "sv-SE",
          "name": "TINV"
        },
        {
          "locale": "th-TH",
          "name": "TINV"
        },
        {
          "locale": "tr-TR",
          "name": "TTERS işlevi"
        },
        {
          "locale": "uk-UA",
          "name": "TINV"
        },
        {
          "locale": "vi-VN",
          "name": "TINV"
        },
        {
          "locale": "zh-CN",
          "name": "TINV"
        },
        {
          "locale": "zh-HK",
          "name": "TINV"
        },
        {
          "locale": "zh-TW",
          "name": "TINV"
        }
      ],
      "signature": {
        "display": "TINV(probability, deg_freedom)",
        "parameters": [
          {
            "description": null,
            "name": "probability",
            "optional": false,
            "repeats": false
          },
          {
            "description": null,
            "name": "deg_freedom",
            "optional": false,
            "repeats": false
          }
        ],
        "trailing_repeats": false
      },
      "surface_name": "TINV",
      "version_marker": null,
      "xlcall": {
        "code": "332",
        "symbol": "xlfTinv"
      }
    },
    "microsoft": "https://support.microsoft.com/en-us/office/tinv-function-a7c85b9d-90f5-41fe-9ca5-1cd2f3e1ed7c"
  },
  "try_it": {
    "formula": "=TINV(0.5,1)"
  },
  "url": "https://handbook.dnacalc.com/functions/TINV.html",
  "variants": [],
  "versions": [
    {
      "behaviour": "14 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.TINV.json"
      ]
    },
    {
      "behaviour": "32 captured inputs are indexed for this environment. Capture dates: 2026-07-17 to 2026-07-17. This is a reading count, not a comparison with another build.",
      "excel_build": "16.0 build 20131",
      "platform": "Windows, bitness not recorded, AMD Ryzen 7 4800H with Radeon Graphics",
      "sources": [
        "https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.TINV.json"
      ]
    }
  ]
}