{ "category": "Statistical functions", "display_name": "HARMEAN", "entry_kind": "built_in_function", "eval_api": { "method": "POST", "url": "https://handbook.dnacalc.com/api/eval" }, "function_id": "FUNC.HARMEAN", "implementation_state": { "answer_bank": { "excel_builds": [ "20430" ], "larger_numeric": 0, "last_bit": 0, "matched": 19214, "other_mismatch": 0, "refused": 0, "rows": 19214, "unread": 0, "worst_ulp": 0 }, "detail": "Recorded: 19,214 in the answer bank and 6 workbook cells.", "dnacalc_commit": "9e1884369a678158dd82d3d74188daf986995e87", "in_catalogue": true, "state": "matches", "state_label": "Matches every recorded Excel answer", "summary": "Matches all 19,220 recorded answers", "workbook_corpus": { "cells": 6, "matched": 6 } }, "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/statistics.rs#L238-L259" ], "repository": "https://github.com/DnaCalc/DnaCalc", "shared_code": [ "catalogue/statistics::all", "catalogue/statistics::direct_first", "ported/excel_numeric::binary_with", "ported/excel_numeric::excel_x87_add", "ported/excel_numeric::excel_x87_div", "ported/excel_numeric::excel_x87_recip", "ported/excel_numeric/x87::add", "ported/excel_numeric/x87::div", "ported/excel_numeric/x87::recip" ], "source": "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/statistics.rs#L238-L259", "state": "matches", "suite": null, "summary": "Matches all 19,220 recorded answers" } ], "json_url": "https://handbook.dnacalc.com/api/functions/FUNC.HARMEAN.json", "name": "HARMEAN", "notes": [], "schema": "efh.function-reference/v1", "section_order": [ "what-it-does", "try-it", "quirks", "how-to-implement", "version-differences", "alternatives" ], "sections": { "alternatives": "\n[AVERAGE](FUNC.AVERAGE.md) suits equally weighted observations; [GEOMEAN](FUNC.GEOMEAN.md) suits multiplicative factors. Use a weighted harmonic mean when the portions are unequal.\n\n\n", "how-to-implement": "\nThe mathematical identity `n/sum(1/x)` is not the current operation tree. Use `R` for the [stored 64-bit-significand operation](../model/09-staged-arithmetic.md).\n\n1. Preserve whether each value is direct, a reference cell or an array element; collect it using the rules above. Reject any admitted `x<=0`.\n2. Starting from `S=0`, visit the admitted values in order. Store `r=R(1/x)`, then store `S=R(S+r)` for each one.\n3. After the empty-set and nonfinite-sum checks, store the reciprocal mean `m=R(S/n)`.\n4. Return `R(1/m)`, subject to worksheet number publication. Replacing these last two divisions by `R(n/S)` changes the intermediate rounding history.\n\nFor `30,60`, the mathematical reciprocal sum is `1/20`; the reciprocal mean is `1/40`, whose reciprocal is 40. The current staged route also publishes 40. These worked numbers explain the route; they do not identify all Excel rounding stages on every input.\n\nSmall positive inputs can make a reciprocal overflow. Scaling the reciprocal sum can help a mathematical implementation, but its different arithmetic needs separate Excel comparisons before being offered as a compatibility route.\n\n\n", "quirks": "\nEvery admitted value must be positive. A numeric zero or negative value gives `#NUM!`; a blank cell is skipped rather than treated as zero. References and arrays also skip logical values and text, including numeric-looking text. Direct numeric text and logical constants can be converted, so direct `FALSE` becomes a rejected zero.\n\nWorksheet errors propagate, and unconvertible direct text gives `#VALUE!`. The current code checks direct scalars before reading held values, returns `#N/A` when collection finds no numbers, and gives `#NUM!` for a nonfinite reciprocal sum. Those last two choices are implementation behaviour, not claims established by Microsoft’s published error list.\n\n\n", "sources": "\n- [Microsoft: HARMEAN function](https://support.microsoft.com/en-us/excel/functions/harmean-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/catalogue/statistics.rs); implementation steps and the limits identified in the text.\n\n", "try-it": "\n`=HARMEAN(30,60)` returns `40`. Travelling 60 km at 30 km/h takes two hours; another 60 km at 60 km/h takes one hour. Total distance 120 km divided by total time three hours is 40 km/h.\n\n`=AVERAGE(30,60)` returns `45`. That is the average speed for equal amounts of time at the two speeds. The difference comes from what receives equal weight.\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| 20430 | Windows, 64-bit, CPU not recorded | 19,214 |\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.HARMEAN.json).", "what-it-does": "\n`HARMEAN(number1, [number2], ...)` returns `n / sum(1/x)` for positive observations. It is useful for rates attached to equal-sized portions. Two equal distances travelled at different speeds have equal distance weights, not equal time weights; averaging their speeds arithmetically answers a different question.\n\n\n" }, "signature": { "display": "HARMEAN(number1, [number2], ...)", "parameters": [ { "description": null, "name": "number1", "optional": false, "repeats": false }, { "description": null, "name": "number2", "optional": true, "repeats": true } ], "trailing_repeats": true }, "sources": { "metadata": { "admission": { "label": "implemented", "reason": null }, "arity": { "max": 255, "min": 1 }, "category": "Statistical functions", "classification": { "arg_preparation_profile": "ValuesOnlyPreAdapter", "coercion_lift_profile": "AggregateDirectAndRangeDualPolicy", "determinism_class": "Deterministic", "error_collapse_profile": "None", "fec_dependency_profile": "None", "host_interaction_class": "None", "kernel_signature_class": "NumsToNum", "rich_value_usage": "RichBlind", "surface_fec_dependency_profile": "RefOnly", "thread_safety_class": "SafePure", "volatility_class": "NonVolatile" }, "descriptions": { "long": null, "short": "Harmonic mean: n divided by the sum of the reciprocals", "short_source": "dna-calc-own" }, "docs": { "english_description": "Returns the harmonic mean", "microsoft_url": "https://support.microsoft.com/en-us/office/harmean-function-5efd9184-fab5-42f9-b1d3-57883a1d3bc6" }, "entry_kind": "built_in_function", "localized_family_names": null, "localized_names": [ { "locale": "ar-SA", "name": "HARMEAN" }, { "locale": "bg-BG", "name": "HARMEAN" }, { "locale": "cs-CZ", "name": "HARMEAN" }, { "locale": "da-DK", "name": "HARMIDDELVÆRDI" }, { "locale": "de-DE", "name": "HARMEAN" }, { "locale": "el-GR", "name": "HARMEAN" }, { "locale": "en-AU", "name": "HARMEAN" }, { "locale": "en-GB", "name": "HARMEAN" }, { "locale": "en-US", "name": "HARMEAN" }, { "locale": "es-ES", "name": "MEDIA.ARMO" }, { "locale": "et-EE", "name": "HARMEAN" }, { "locale": "fi-FI", "name": "KESKIARVO.HARM" }, { "locale": "fr-FR", "name": "MOYENNE.HARMONIQUE*" }, { "locale": "he-IL", "name": "HARMEAN" }, { "locale": "hr-HR", "name": "HARMEAN" }, { "locale": "hu-HU", "name": "HARM.KÖZÉP" }, { "locale": "id-ID", "name": "HARMEAN" }, { "locale": "it-IT", "name": "HARMEAN" }, { "locale": "ja-JP", "name": "HARMEAN" }, { "locale": "ko-KR", "name": "HARMEAN" }, { "locale": "lt-LT", "name": "HARMEAN" }, { "locale": "lv-LV", "name": "HARMEAN" }, { "locale": "nb-NO", "name": "GJENNOMSNITT.HARMONISK" }, { "locale": "nl-NL", "name": "HARM.GEM" }, { "locale": "pl-PL", "name": "ŚREDNIA.HARMONICZNA" }, { "locale": "pt-BR", "name": "HARMEAN" }, { "locale": "pt-PT", "name": "MÉDIA.HARMÓNICA" }, { "locale": "ro-RO", "name": "HARMEAN" }, { "locale": "ru-RU", "name": "СРГАРМ" }, { "locale": "sk-SK", "name": "HARMEAN" }, { "locale": "sl-SI", "name": "HARMEAN" }, { "locale": "sr-Latn-RS", "name": "HARMEAN" }, { "locale": "sv-SE", "name": "HARMMEDEL" }, { "locale": "th-TH", "name": "HARMEAN" }, { "locale": "tr-TR", "name": "HARORT işlevi" }, { "locale": "uk-UA", "name": "HARMEAN" }, { "locale": "vi-VN", "name": "HARMEAN" }, { "locale": "zh-CN", "name": "HARMEAN" }, { "locale": "zh-HK", "name": "HARMEAN" }, { "locale": "zh-TW", "name": "HARMEAN" } ], "signature": { "display": "HARMEAN(number1, [number2], ...)", "parameters": [ { "description": null, "name": "number1", "optional": false, "repeats": false }, { "description": null, "name": "number2", "optional": true, "repeats": true } ], "trailing_repeats": true }, "surface_name": "HARMEAN", "version_marker": null, "xlcall": { "code": "320", "symbol": "xlfHarmean" } }, "microsoft": "https://support.microsoft.com/en-us/office/harmean-function-5efd9184-fab5-42f9-b1d3-57883a1d3bc6" }, "try_it": { "formula": "=HARMEAN(30,60)" }, "url": "https://handbook.dnacalc.com/functions/HARMEAN.html", "variants": [], "versions": [ { "behaviour": "19,214 captured inputs are indexed for this environment. Capture dates: 2026-09-29 to 2026-09-29. This is a reading count, not a comparison with another build.", "excel_build": "16.0 build 20430", "platform": "Windows, 64-bit, CPU not recorded", "sources": [ "https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.HARMEAN.json" ] } ] }