Math and trigonometry functions

This page lists the 52 functions of the math and trigonometry family. Taxonomy/source: Math and trigonometry functions. The formula function contract has every family, the engine builds, and the evaluation limits.

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Function (aliases)	Engine	Contract
`SUM`	Default + full	incumbent Signature: `optional-variadic-values` Semantics: `aggregate` Dialect: `excel-documented` Implementation: `implemented-assisted`
`ABS`	Default + full	incumbent Signature: `unary-number` Semantics: `scalar` Dialect: `excel-documented` Implementation: `implemented-assisted`
`ROUND`	Default + full	incumbent Signature: `round` Semantics: `scalar` Dialect: `excel-documented` Implementation: `implemented-assisted`
`SQRT`	Default + full	incumbent Signature: `unary-number` Semantics: `scalar` Dialect: `excel-documented` Implementation: `implemented-assisted`
`MOD`	Default + full	incumbent Signature: `binary-number` Semantics: `scalar` Dialect: `excel-documented` Implementation: `implemented-assisted`
`POW`	Default + full	incumbent Signature: `binary-number` Semantics: `scalar` Dialect: `excel-documented` Implementation: `parser-assisted-evaluator-declared`
`FLOOR`	Default + full	incumbent Signature: `binary-number` Semantics: `scalar` Dialect: `excel-documented` Implementation: `implemented-assisted`
`CEILING`	Default + full	incumbent Signature: `binary-number` Semantics: `scalar` Dialect: `excel-documented` Implementation: `implemented-assisted`
`INT`	Default + full	incumbent Signature: `unary-number` Semantics: `scalar` Dialect: `excel-documented` Implementation: `implemented-assisted`
`TRUNC`	Default + full	incumbent Signature: `trunc` Semantics: `scalar` Dialect: `excel-documented` Implementation: `implemented-assisted`
`SIGN`	Default + full	incumbent Signature: `unary-number` Semantics: `scalar` Dialect: `excel-documented` Implementation: `implemented-assisted`
`PI`	Default + full	incumbent Signature: `zero` Semantics: `scalar` Dialect: `excel-documented` Implementation: `implemented-assisted`
`RAND`	Default + full	incumbent Signature: `zero` Semantics: `volatile-random` Dialect: `excel-documented` Implementation: `implemented-random`
`RANDBETWEEN`	Default + full	incumbent Signature: `random-between` Semantics: `volatile-random` Dialect: `excel-documented` Implementation: `implemented-random`
`SUMIF`	Default + full	incumbent Signature: `sumif` Semantics: `criteria` Dialect: `excel-documented` Implementation: `implemented-assisted`
`SUMIFS`	Default + full	incumbent Signature: `sumifs` Semantics: `criteria` Dialect: `excel-documented` Implementation: `implemented-assisted`
`PRODUCT`	Default + full	required target Signature: `variadic-values` Semantics: `aggregate` Dialect: `excel-documented` Implementation: `implemented-assisted`
`SUMPRODUCT`	Default + full	required target Signature: `variadic-values` Semantics: `aggregate` Dialect: `excel-documented` Implementation: `implemented-assisted`
`POWER`	Default + full	required target Signature: `binary-number` Semantics: `scalar` Dialect: `excel-documented` Implementation: `implemented-assisted`
`EXP`	Default + full	required target Signature: `unary-number` Semantics: `scalar` Dialect: `excel-documented` Implementation: `implemented-assisted`
`LN`	Default + full	required target Signature: `unary-number` Semantics: `scalar` Dialect: `excel-documented` Implementation: `implemented-assisted`
`LOG`	Default + full	required target Signature: `log` Semantics: `scalar` Dialect: `excel-documented` Implementation: `implemented-assisted`
`LOG10`	Default + full	required target Signature: `unary-number` Semantics: `scalar` Dialect: `excel-documented` Implementation: `implemented-assisted`
`ROUNDUP`	Default + full	required target Signature: `round` Semantics: `scalar` Dialect: `excel-documented` Implementation: `implemented-assisted`
`ROUNDDOWN`	Default + full	required target Signature: `round` Semantics: `scalar` Dialect: `excel-documented` Implementation: `implemented-assisted`
`MROUND`	Default + full	required target Signature: `binary-number` Semantics: `scalar` Dialect: `excel-documented` Implementation: `implemented-assisted`
`EVEN`	Default + full	required target Signature: `unary-number` Semantics: `scalar` Dialect: `excel-documented` Implementation: `implemented-assisted`
`ODD`	Default + full	required target Signature: `unary-number` Semantics: `scalar` Dialect: `excel-documented` Implementation: `implemented-assisted`
`QUOTIENT`	Default + full	required target Signature: `binary-number` Semantics: `scalar` Dialect: `excel-documented` Implementation: `implemented-assisted`
`GCD`	Default + full	required target Signature: `variadic-values` Semantics: `aggregate` Dialect: `excel-documented` Implementation: `implemented-assisted`
`LCM`	Default + full	required target Signature: `variadic-values` Semantics: `aggregate` Dialect: `excel-documented` Implementation: `implemented-assisted`
`SUBTOTAL`	Default + full	required target Signature: `subtotal` Semantics: `aggregate` Dialect: `excel-documented` Implementation: `implemented-assisted`
`AGGREGATE`	Full only	optional analysis Signature: `aggregate` Semantics: `analysis-math` Dialect: `analysis-math` Implementation: `analysis-math`
`CEILING.MATH`	Full only	optional analysis Signature: `round-math` Semantics: `analysis-math` Dialect: `analysis-math` Implementation: `analysis-math`
`COMBIN`	Full only	optional analysis Signature: `binary-number` Semantics: `analysis-math` Dialect: `analysis-math` Implementation: `analysis-math`
`COMBINA`	Full only	optional analysis Signature: `binary-number` Semantics: `analysis-math` Dialect: `analysis-math` Implementation: `analysis-math`
`FACT`	Full only	optional analysis Signature: `unary-number` Semantics: `analysis-math` Dialect: `analysis-math` Implementation: `analysis-math`
`FACTDOUBLE`	Full only	optional analysis Signature: `unary-number` Semantics: `analysis-math` Dialect: `analysis-math` Implementation: `analysis-math`
`FLOOR.MATH`	Full only	optional analysis Signature: `round-math` Semantics: `analysis-math` Dialect: `analysis-math` Implementation: `analysis-math`
`MDETERM`	Full only	optional analysis Signature: `array-unary` Semantics: `analysis-math` Dialect: `analysis-math` Implementation: `analysis-math`
`MINVERSE`	Full only	optional analysis Signature: `matrix-unary` Semantics: `analysis-math` Dialect: `analysis-math` Implementation: `analysis-math`
`MMULT`	Full only	optional analysis Signature: `matrix-pair` Semantics: `analysis-math` Dialect: `analysis-math` Implementation: `analysis-math`
`MULTINOMIAL`	Full only	optional analysis Signature: `variadic-values` Semantics: `analysis-math` Dialect: `analysis-math` Implementation: `analysis-math`
`MUNIT`	Full only	optional analysis Signature: `matrix-unit` Semantics: `analysis-math` Dialect: `analysis-math` Implementation: `analysis-math`
`PERMUT`	Full only	optional analysis Signature: `binary-number` Semantics: `analysis-math` Dialect: `analysis-math` Implementation: `analysis-math`
`PERMUTATIONA`	Full only	optional analysis Signature: `binary-number` Semantics: `analysis-math` Dialect: `analysis-math` Implementation: `analysis-math`
`SERIESSUM`	Full only	optional analysis Signature: `series-sum` Semantics: `analysis-math` Dialect: `analysis-math` Implementation: `analysis-math`
`SQRTPI`	Full only	optional analysis Signature: `unary-number` Semantics: `analysis-math` Dialect: `analysis-math` Implementation: `analysis-math`
`SUMSQ`	Full only	optional analysis Signature: `variadic-values` Semantics: `analysis-math` Dialect: `analysis-math` Implementation: `analysis-math`
`SUMX2MY2`	Full only	optional analysis Signature: `pair-arrays` Semantics: `analysis-math` Dialect: `analysis-math` Implementation: `analysis-math`
`SUMX2PY2`	Full only	optional analysis Signature: `pair-arrays` Semantics: `analysis-math` Dialect: `analysis-math` Implementation: `analysis-math`
`SUMXMY2`	Full only	optional analysis Signature: `pair-arrays` Semantics: `analysis-math` Dialect: `analysis-math` Implementation: `analysis-math`

Signature profiles

Argument order, required/default state, accepted shapes, repetition, and return shape come directly from the inventory.

Signature: optional-variadic-values

Return shape: scalar.

Argument	Required	Default	Accepts	Repetition
`value`	no	none	`scalar`, `range`, `array`, `reference`	`zero-or-more`

Signature: unary-number

Return shape: scalar.

Argument	Required	Default	Accepts	Repetition
`number`	yes	none	`scalar`, `reference`	`once`

Signature: round

Return shape: scalar.

Argument	Required	Default	Accepts	Repetition
`number`	yes	none	`scalar`, `reference`	`once`
`digits`	yes	none	`scalar`, `reference`	`once`

Signature: binary-number

Return shape: scalar.

Argument	Required	Default	Accepts	Repetition
`number1`	yes	none	`scalar`, `reference`	`once`
`number2`	yes	none	`scalar`, `reference`	`once`

Signature: trunc

Return shape: scalar.

Argument	Required	Default	Accepts	Repetition
`number`	yes	none	`scalar`, `reference`	`once`
`digits`	no	0	`scalar`, `reference`	`once`

Signature: zero

Return shape: scalar.

Argument	Required	Default	Accepts	Repetition
none	—	—	—	—

Signature: random-between

Return shape: scalar.

Argument	Required	Default	Accepts	Repetition
`bottom`	yes	none	`scalar`, `reference`	`once`
`top`	yes	none	`scalar`, `reference`	`once`

Signature: sumif

Return shape: scalar.

Argument	Required	Default	Accepts	Repetition
`range`	yes	none	`range`, `array`, `reference`	`once`
`criteria`	yes	none	`scalar`, `reference`	`once`
`sumRange`	no	range	`range`, `array`, `reference`	`once`

Signature: sumifs

Return shape: scalar.

Argument	Required	Default	Accepts	Repetition
`sumRange`	yes	none	`range`, `array`, `reference`	`once`
`rangeAndCriteria`	yes	none	`scalar`, `range`, `array`, `reference`	`paired`

Signature: variadic-values

Return shape: scalar.

Argument	Required	Default	Accepts	Repetition
`value`	yes	none	`scalar`, `range`, `array`, `reference`	`one-or-more`

Signature: log

Return shape: scalar.

Argument	Required	Default	Accepts	Repetition
`number`	yes	none	`scalar`, `reference`	`once`
`base`	no	10	`scalar`, `reference`	`once`

Signature: subtotal

Return shape: scalar.

Argument	Required	Default	Accepts	Repetition
`functionNumber`	yes	none	`scalar`, `reference`	`once`
`reference`	yes	none	`range`, `array`, `reference`	`one-or-more`

Signature: aggregate

Return shape: scalar.

Argument	Required	Default	Accepts	Repetition
`functionNumber`	yes	none	`scalar`, `reference`	`once`
`options`	yes	none	`scalar`, `reference`	`once`
`reference`	yes	none	`range`, `array`, `reference`	`one-or-more`

Signature: round-math

Return shape: scalar.

Argument	Required	Default	Accepts	Repetition
`number`	yes	none	`scalar`, `reference`	`once`
`significance`	no	1	`scalar`, `reference`	`once`
`mode`	no	0	`scalar`, `reference`	`once`

Signature: array-unary

Return shape: array.

Argument	Required	Default	Accepts	Repetition
`array`	yes	none	`range`, `array`, `reference`	`once`

Signature: matrix-unary

Return shape: array.

Argument	Required	Default	Accepts	Repetition
`array`	yes	none	`range`, `array`, `reference`	`once`

Signature: matrix-pair

Return shape: array.

Argument	Required	Default	Accepts	Repetition
`array1`	yes	none	`range`, `array`, `reference`	`once`
`array2`	yes	none	`range`, `array`, `reference`	`once`

Signature: matrix-unit

Return shape: array.

Argument	Required	Default	Accepts	Repetition
`dimension`	yes	none	`scalar`, `reference`	`once`

Signature: series-sum

Return shape: scalar.

Argument	Required	Default	Accepts	Repetition
`x`	yes	none	`scalar`, `reference`	`once`
`n`	yes	none	`scalar`, `reference`	`once`
`m`	yes	none	`scalar`, `reference`	`once`
`coefficients`	yes	none	`range`, `array`, `reference`	`once`

Signature: pair-arrays

Return shape: scalar.

Argument	Required	Default	Accepts	Repetition
`array1`	yes	none	`range`, `array`, `reference`	`once`
`array2`	yes	none	`range`, `array`, `reference`	`once`

Semantic profiles

These values are normative for the listed Sheetwrite subset. function-defined and contextual are explicit limitations: consult the formula guides' function-specific sections rather than assuming another spreadsheet's edge behavior.

Semantics: aggregate

Dimension	Contract
shape	scalar: accepted range: accepted array: accepted broadcast: none result: scalar
coercion	blank: ignored text: ignored-in-ranges boolean: ignored-in-ranges error: propagate
text	case: not-applicable wildcard: not-applicable
environment	locale: invariant dateSystem: not-applicable
numeric	tolerance: binary64 domain: function-defined iteration: kind: none maximum: none
calculation	dependencies: tracked lazy: eager spill: scalar fill: relative-reference-rewrite copy: relative-reference-rewrite structuralRewrite: ast-reference-rewrite
persistence	snapshot: formula-source history: formula-source collaboration: formula-source xlsxSource: rewrite-on-structural-edit

Semantics: scalar

Dimension	Contract
shape	scalar: accepted range: contextual array: contextual broadcast: function-defined result: scalar
coercion	blank: zero text: number-if-parseable boolean: number error: propagate
text	case: not-applicable wildcard: not-applicable
environment	locale: invariant dateSystem: not-applicable
numeric	tolerance: binary64 domain: function-defined iteration: kind: none maximum: none
calculation	dependencies: tracked lazy: eager spill: scalar fill: relative-reference-rewrite copy: relative-reference-rewrite structuralRewrite: ast-reference-rewrite
persistence	snapshot: formula-source history: formula-source collaboration: formula-source xlsxSource: rewrite-on-structural-edit

Semantics: volatile-random

Dimension	Contract
shape	scalar: accepted range: rejected array: rejected broadcast: none result: scalar
coercion	blank: zero text: number-if-parseable boolean: number error: propagate
text	case: not-applicable wildcard: not-applicable
environment	locale: invariant dateSystem: not-applicable
numeric	tolerance: function-defined domain: bounded iteration: kind: none maximum: none
calculation	dependencies: tracked lazy: eager spill: scalar fill: relative-reference-rewrite copy: relative-reference-rewrite structuralRewrite: ast-reference-rewrite
persistence	snapshot: formula-source history: formula-source collaboration: formula-source xlsxSource: rewrite-on-structural-edit

Semantics: criteria

Dimension	Contract
shape	scalar: accepted range: accepted array: accepted broadcast: pairwise result: scalar
coercion	blank: function-defined text: function-defined boolean: function-defined error: propagate
text	case: insensitive wildcard: supported
environment	locale: invariant dateSystem: function-defined
numeric	tolerance: binary64 domain: function-defined iteration: kind: none maximum: none
calculation	dependencies: tracked lazy: eager spill: scalar fill: relative-reference-rewrite copy: relative-reference-rewrite structuralRewrite: ast-reference-rewrite
persistence	snapshot: formula-source history: formula-source collaboration: formula-source xlsxSource: rewrite-on-structural-edit

Semantics: analysis-math

Dimension	Contract
shape	scalar: accepted range: accepted array: accepted broadcast: none result: contextual
coercion	blank: function-defined text: function-defined boolean: function-defined error: function-defined
text	case: not-applicable wildcard: not-applicable
environment	locale: invariant dateSystem: not-applicable
numeric	tolerance: binary64 domain: function-defined iteration: kind: none maximum: none
calculation	dependencies: tracked lazy: eager spill: contextual fill: relative-reference-rewrite copy: relative-reference-rewrite structuralRewrite: ast-reference-rewrite
persistence	snapshot: formula-source history: formula-source collaboration: formula-source xlsxSource: rewrite-on-structural-edit

Dialect profiles

Dialect: excel-documented

Dialect	Status
Microsoft Excel	documented
Google Sheets	unverified
OpenFormula	unverified

Limitations: Google Sheets and OpenFormula results require producer evidence before compatibility is claimed.

Dialect: analysis-math

Dialect	Status
Microsoft Excel	documented
Google Sheets	unverified
OpenFormula	unverified

Limitations: Available only in the optional @sheetwrite/formulas analysis build; default @sheetwrite/wasm returns #NAME?. Hidden rows are not part of the engine model. AGGREGATE row visibility options therefore have no effect. Matrix functions use engine resource limits.

Implementation profiles

Implementation: implemented-assisted

Layer	Status and source/evidence
Parser	implemented `packages/wasm/src/calc.rs`
Evaluator	implemented `packages/wasm/src/eval/mod.rs` `packages/wasm/src/eval/functions.rs`
Formula assist	implemented `packages/core/src/formula-assist.ts`
Evidence	source-linked `packages/wasm/src/tests.rs` `packages/core/test/formula-assist.test.ts`

Implementation: parser-assisted-evaluator-declared

Layer	Status and source/evidence
Parser	implemented `packages/wasm/src/calc.rs`
Evaluator	declared
Formula assist	implemented `packages/core/src/formula-assist.ts`
Evidence	source-linked `packages/core/src/formula-assist.ts`

Implementation: implemented-random

Layer	Status and source/evidence
Parser	implemented `packages/wasm/src/calc.rs`
Evaluator	implemented `packages/wasm/src/eval/random.rs` `packages/wasm/src/eval/dependency.rs`
Formula assist	implemented `packages/core/src/formula-assist.ts`
Evidence	source-linked `packages/wasm/src/tests.rs` `packages/core/test/formula-assist.test.ts`

Implementation: analysis-math

Layer	Status and source/evidence
Parser	implemented `packages/wasm/src/calc.rs`
Evaluator	implemented `packages/wasm/src/eval/analysis/math.rs` `packages/wasm/src/eval/analysis/aggregate.rs` `packages/wasm/src/eval/analysis/matrices.rs`
Formula assist	implemented `packages/core/src/formula-assist.ts`
Evidence	source-linked `scripts/formula-contract.test.ts`

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