{ "category": "Statistical functions", "display_name": "MAX", "entry_kind": "built_in_function", "eval_api": { "method": "POST", "url": "https://handbook.dnacalc.com/api/eval" }, "function_id": "FUNC.MAX", "implementation_state": { "answer_bank": { "excel_builds": [ "20430" ], "larger_numeric": 0, "last_bit": 0, "matched": 1211, "other_mismatch": 0, "refused": 0, "rows": 1211, "unread": 0, "worst_ulp": 0 }, "detail": "Recorded: 1,211 in the answer bank and 25 workbook cells.", "dnacalc_commit": "9e1884369a678158dd82d3d74188daf986995e87", "in_catalogue": true, "state": "matches", "state_label": "Matches every recorded Excel answer", "summary": "Matches all 1,236 recorded answers", "workbook_corpus": { "cells": 25, "matched": 25 } }, "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/aggregate.rs#L114-L114", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/aggregate.rs#L261-L267" ], "repository": "https://github.com/DnaCalc/DnaCalc", "shared_code": [ "catalogue/aggregate::aggregate", "catalogue/aggregate::extreme", "catalogue/aggregate::holds_held_arrays", "catalogue/aggregate::read_held_references", "catalogue/aggregate::number_of", "catalogue/aggregate::each_value", "catalogue/aggregate::read_values", "catalogue/aggregate::reader", "catalogue/aggregate::read_reference", "catalogue/comparison::overflow_numbers", "catalogue/comparison::numbers", "catalogue/comparison::in_band", "catalogue/comparison::Rounded::up", "catalogue/comparison::Roundings::of", "catalogue/comparison::Roundings::disjoint", "decimal::low32", "decimal::Natural::from_u64", "decimal::Natural::pow10", "decimal::Natural::normalize", "decimal::Natural::is_zero", "decimal::Natural::mul_add_small", "decimal::Natural::times_pow10", "decimal::Natural::times_pow5", "decimal::Natural::times_pow2", "decimal::ExactDecimal::binary" ], "source": "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/aggregate.rs#L114-L114", "state": "matches", "suite": null, "summary": "Matches all 1,236 recorded answers" } ], "json_url": "https://handbook.dnacalc.com/api/functions/FUNC.MAX.json", "name": "MAX", "notes": [], "schema": "efh.function-reference/v1", "section_order": [ "what-it-does", "try-it", "quirks", "how-to-implement", "version-differences", "alternatives" ], "sections": { "alternatives": "\n### Relationships\n\n\n- **[MIN](FUNC.MIN.md)** — the exact mirror, same argument shape, same coercion table, same\n documented zero for the no-numbers case. Any behavioural difference between `MAX` and `MIN`\n beyond the comparator is a defect in one of them.\n- **[MAXA](FUNC.MAXA.md)** — the variant that counts text and logicals inside references,\n named by Microsoft's own `MAX` page as the remedy. The `A` suffix family (`MAXA`, `MINA`,\n `AVERAGEA`, `COUNTA`, `STDEVA`, `VARA`) shares that intent and does not share one uniform\n rule; each page states its own.\n- **[MAXIFS](FUNC.MAXIFS.md)** — the conditional form, which selects the population by criteria\n before taking the maximum. Note that `MAXIFS` returns `0` when no cell meets the criteria,\n which is the same convention the `MAX` documentation states for the empty case.\n- **[LARGE](FUNC.LARGE.md)** — the general order-statistic selector; `LARGE(array, 1)` is the\n maximum over the same admitted set, but `LARGE` takes exactly one array and errors on an\n empty one instead of returning zero. The pair `MAX`/`LARGE` is the cleanest illustration of\n the empty-set convention differing between two functions that compute the same thing.\n- **[DMAX](FUNC.DMAX.md)** — the database-family maximum, with criteria-range selection.\n- **[SUBTOTAL](FUNC.SUBTOTAL.md)** (function numbers 4 and 104) and\n **[AGGREGATE](FUNC.AGGREGATE.md)** (function number 4) — the filter-aware and\n error-skipping maxima. `AGGREGATE` is the only route to a maximum that ignores error values,\n which `MAX` cannot do.\n- **Confused with:** `MAX` and `LARGE` on ranges containing text (the same scan policy governs\n both, so they should agree — a disagreement is diagnostic); and with the idea that `MAX` over\n an empty range is an error, which the documentation contradicts.\n\n\n", "how-to-implement": "\n### Numerical notes\n\n\n`MAX` has no arithmetic and therefore no rounding error. The engineering questions are three,\nand each of them is about definition rather than precision.\n\n**1. The comparison predicate.** A maximum needs a total order. IEEE-754 `>` is a total order\non the doubles Excel can hold, with the single exception that `+0` and `−0` compare equal —\nExcel has no NaN in its value universe, so the usual NaN-poisoning problem does not arise at\nthis level. Whether Excel's `MAX` uses raw `>` or the tolerant, truncation-style\n15-significant-digit comparison it applies in some other families is a genuine open question;\nfor `MAX` a tolerant comparator would only affect which of two near-equal representations is\nreturned, so the consequence is smaller than it is for lookups, but it is observable.\n\n**3. The empty-set identity.** Mathematically `max ∅ = −∞`, which Excel cannot represent, so\nthe specification substitutes `0`. That substitution is not innocuous: it makes `MAX`\nnon-associative across the empty case in a way that matters for incremental computation. If a\nrange is empty, `MAX` returns a value inside the data's range rather than below it, so\n`MAX(MAX(A), MAX(B))` is not `MAX(A ∪ B)` when one of `A` or `B` is empty and the other is\nentirely negative. A workbook that computes column maxima and then takes the maximum of those\nwill report `0` for a set of all-negative data with one empty column. That is a real, silent\ncorrectness trap and it follows directly from the documented rule.\n\nFor an implementer: initialise the accumulator with a sentinel *and a found flag*, never with\n`0` or with `f64::NEG_INFINITY` alone — the first is wrong for all-negative data and the second\nproduces `−∞`, which is outside Excel's value universe. Track \"have I seen a number\" separately\nfrom \"what is the best so far\", and apply the documented zero only at the end.\n\n\n", "quirks": "\n### The two coercion policies\n\n\nThis is the section that earns the page, and it is quoted rather than paraphrased because the\ndistinction is exact. Microsoft's `MAX` page states:\n\n- \"Arguments can either be numbers or names, arrays, or references that contain numbers.\"\n- \"Logical values and text representations of numbers that you type directly into the list of\n arguments are counted.\"\n- \"If an argument is an array or reference, only numbers in that array or reference are used.\n Empty cells, logical values, or text in the array or reference are ignored.\"\n- \"If the arguments contain no numbers, MAX returns 0 (zero).\"\n- \"Arguments that are error values or text that cannot be translated into numbers cause\n errors.\"\n\nRead as a table:\n\n| Value | Typed **directly** into the argument list | Reached inside an **array or reference** |\n|---|---|---|\n| Number | counted | counted |\n| `TRUE` / `FALSE` | counted (as 1 / 0) | **ignored** |\n| Text that reads as a number | counted | **ignored** |\n| Text that does not read as a number | **error** | ignored |\n| Empty cell | — | ignored |\n| Error value | error | error |\n\nSo `MAX(TRUE, 0)` is 1 while `MAX(A1:A2)` with `TRUE` in `A1` and `0` in `A2` is 0. Same\nvalues, same function, different boundary, different rule. This is the flagship asymmetry of\n[Coercion and lifting](../model/02-coercion-and-lifting.md), and `MAX` is one of the cleanest\nplaces to see it, because both branches are documented on the same page in consecutive\nsentences.\n\nThe practical consequence is that `MAX` over a column cannot be made to see logicals or\nnumeric text. Microsoft's own page names the remedy: \"If you want to include logical values\nand text representations of numbers in a reference as part of the calculation, use the MAXA\nfunction.\" See [MAXA](FUNC.MAXA.md), and read its own coercion rules before switching, because\nthey are not simply \"the same but including text\".\n\n\n\n### Result and edge cases\n\n\nReturns `Number`.\n\n- **No numbers among the arguments.** Microsoft documents: \"If the arguments contain no\n numbers, MAX returns 0 (zero).\" So `MAX` over a wholly blank range is documented to be `0`,\n not an error and not the empty value.\n\n- **A single value.** `MAX(x)` is `x`, including for the largest finite double and the\n smallest subnormal, which is a useful check that no normalisation is applied on the way out.\n- **`+0` and `−0`.** IEEE comparison calls these equal, so which one is returned is a\n tie-breaking decision the specification does not make. `MAX(0, −0)` may legitimately return\n either representation, and the two are distinguishable through the sign bit and through\n `1/x`. Unverified.\n- **Arrays** are consumed by scanning, not lifted elementwise; `MAX` is not a lift kernel.\n- **Dates and times** are numbers wearing formats, so `MAX` over a date column returns the\n latest date — correctly, and with the format usually carried through by the cell rather than\n by the function.\n\n\n\n### Errors\n\nThere is no documented `#NUM!` or `#N/A` condition. Note the absence of an \"empty input\" error\nin the documentation — the documented answer for that case is `0`, as discussed above.\n\n\n", "sources": "- Handbook [Coercion and lifting](../model/02-coercion-and-lifting.md) — the direct-argument\n versus range-scan asymmetry, of which this function is the canonical instance.\n- Handbook [The value universe](../model/01-value-universe.md) — value kinds, the absence of\n infinities and NaN from the published gamut, and the Empty/Missing distinction.\n- Handbook projections `data/functions/FUNC.MAX.json` (arity 1–255, `xlfMax` code 7,\n `AggregateDirectAndRangeDualPolicy`, `ReductionFold`, `SequentialLeftFold`,\n `CanonicalExcelLegacy` error algebra) and `data/presence/FUNC.MAX.json` (module `max_fn.rs`,\n unshared, no defect stream named).\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 | 1,211 |\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.MAX.json).", "what-it-does": "\n`MAX(number1, [number2], …)` returns the largest of the numeric values it admits.\n\nAs mathematics this is the top order statistic, `x₍ₙ₎ = max{x₁ … xₙ}` — the supremum of a\nfinite set, which is attained and is therefore one of the inputs. `MAX` is a **selector**: its\nresult is bit-identical to one of the values it was given, it performs no arithmetic, and it\nintroduces no rounding error of its own.\n\nBecause there is no arithmetic, everything genuinely interesting about `MAX` lives in one\nquestion: **which values count?** That question has two different answers depending on how the\nvalue reached the function, and Microsoft documents both.\n\n`max` is associative, commutative and idempotent, with identity `−∞`; it is a monoid fold. The\nidentity is where the specification has to make a choice, because Excel has no `−∞` in its\nvalue universe. Microsoft's choice is documented and stated below.\n\n\n\n### Arguments\n\n\n| Argument | Meaning | Notes |\n|---|---|---|\n| `number1` | The first value | Required |\n| `number2, …` | Further values | Optional |\n\nArgument boundaries carry no meaning: `MAX(A1:A10)`, `MAX(A1:A5, A6:A10)` and\n`MAX(A1, A2, …, A10)` all reduce over one pooled set. There is no per-argument grouping and no\nshort-circuiting.\n\n\n" }, "signature": { "display": "MAX(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": "ReductionFold", "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": "Largest of the numbers", "short_source": "dna-calc-own" }, "docs": { "english_description": "Returns the maximum value in a list of arguments", "microsoft_url": "https://support.microsoft.com/en-us/office/max-function-e0012414-9ac8-4b34-9a47-73e662c08098" }, "entry_kind": "built_in_function", "localized_family_names": null, "localized_names": [ { "locale": "ar-SA", "name": "MAX" }, { "locale": "bg-BG", "name": "MAX" }, { "locale": "cs-CZ", "name": "MAX" }, { "locale": "da-DK", "name": "MAKS" }, { "locale": "de-DE", "name": "MAX" }, { "locale": "el-GR", "name": "MAX" }, { "locale": "en-AU", "name": "MAX" }, { "locale": "en-GB", "name": "MAX" }, { "locale": "en-US", "name": "MAX" }, { "locale": "es-ES", "name": "MAX" }, { "locale": "et-EE", "name": "MAX" }, { "locale": "fi-FI", "name": "MAKS" }, { "locale": "fr-FR", "name": "MAX" }, { "locale": "he-IL", "name": "MAX" }, { "locale": "hr-HR", "name": "MAX" }, { "locale": "hu-HU", "name": "MAX" }, { "locale": "id-ID", "name": "MAX" }, { "locale": "it-IT", "name": "MAX" }, { "locale": "ja-JP", "name": "MAX" }, { "locale": "ko-KR", "name": "MAX" }, { "locale": "lt-LT", "name": "MAX" }, { "locale": "lv-LV", "name": "MAX" }, { "locale": "nb-NO", "name": "MAKS" }, { "locale": "nl-NL", "name": "MAX" }, { "locale": "pl-PL", "name": "MAX" }, { "locale": "pt-BR", "name": "MÁX" }, { "locale": "pt-PT", "name": "MAX" }, { "locale": "ro-RO", "name": "MAX" }, { "locale": "ru-RU", "name": "МАКС" }, { "locale": "sk-SK", "name": "MAX" }, { "locale": "sl-SI", "name": "MAX" }, { "locale": "sr-Latn-RS", "name": "MAX" }, { "locale": "sv-SE", "name": "MAX" }, { "locale": "th-TH", "name": "MAX" }, { "locale": "tr-TR", "name": "MAK" }, { "locale": "uk-UA", "name": "MAX" }, { "locale": "vi-VN", "name": "MAX" }, { "locale": "zh-CN", "name": "MAX" }, { "locale": "zh-HK", "name": "MAX" }, { "locale": "zh-TW", "name": "MAX" } ], "signature": { "display": "MAX(number1, [number2], ...)", "parameters": [ { "description": null, "name": "number1", "optional": false, "repeats": false }, { "description": null, "name": "number2", "optional": true, "repeats": true } ], "trailing_repeats": true }, "surface_name": "MAX", "version_marker": null, "xlcall": { "code": "7", "symbol": "xlfMax" } }, "microsoft": "https://support.microsoft.com/en-us/office/max-function-e0012414-9ac8-4b34-9a47-73e662c08098" }, "try_it": { "formula": "=MAX(1,5,3)" }, "url": "https://handbook.dnacalc.com/functions/MAX.html", "variants": [], "versions": [ { "behaviour": "1,211 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.MAX.json" ] } ] }