# Aggregation Pipeline Operators¶

Note

For details on specific operator, including syntax and examples, click on the specific operator to go to its reference page.

## Expression Operators¶

In this section

- Arithmetic Expression Operators
- Array Expression Operators
- Boolean Expression Operators
- Comparison Expression Operators
- Conditional Expression Operators
- Date Expression Operators
- Literal Expression Operator
- Object Expression Operators
- Set Expression Operators
- String Expression Operators
- Text Expression Operator
- Trigonometry Expression Operators
- Type Expression Operators
- Accumulators (
`$group`

) - Accumulators (in Other Stages)
- Variable Expression Operators

These expression operators are available to construct expressions for use in the aggregation pipeline stages.

Operator expressions are similar to functions that take arguments. In general, these expressions take an array of arguments and have the following form:

If operator accepts a single argument, you can omit the outer array designating the argument list:

To avoid parsing ambiguity if the argument is a literal array, you must
wrap the literal array in a `$literal`

expression or keep
the outer array that designates the argument list.

### Arithmetic Expression Operators¶

Arithmetic expressions perform mathematic operations on numbers. Some arithmetic expressions can also support date arithmetic.

Name | Description |
---|---|

`$abs` |
Returns the absolute value of a number. |

`$add` |
Adds numbers to return the sum, or adds numbers and a date to return a new date. If adding numbers and a date, treats the numbers as milliseconds. Accepts any number of argument expressions, but at most, one expression can resolve to a date. |

`$ceil` |
Returns the smallest integer greater than or equal to the specified number. |

`$divide` |
Returns the result of dividing the first number by the second. Accepts two argument expressions. |

`$exp` |
Raises e to the specified exponent. |

`$floor` |
Returns the largest integer less than or equal to the specified number. |

`$ln` |
Calculates the natural log of a number. |

`$log` |
Calculates the log of a number in the specified base. |

`$log10` |
Calculates the log base 10 of a number. |

`$mod` |
Returns the remainder of the first number divided by the second. Accepts two argument expressions. |

`$multiply` |
Multiplies numbers to return the product. Accepts any number of argument expressions. |

`$pow` |
Raises a number to the specified exponent. |

`$round` |
Rounds a number to to a whole integer or to a specified
decimal place. |

`$sqrt` |
Calculates the square root. |

`$subtract` |
Returns the result of subtracting the second value from the first. If the two values are numbers, return the difference. If the two values are dates, return the difference in milliseconds. If the two values are a date and a number in milliseconds, return the resulting date. Accepts two argument expressions. If the two values are a date and a number, specify the date argument first as it is not meaningful to subtract a date from a number. |

`$trunc` |
Truncates a number to a whole integer or to a specified
decimal place. |

### Array Expression Operators¶

`$arrayElemAt` |
Returns the element at the specified array index. |
---|---|

`$arrayToObject` |
Converts an array of key value pairs to a document. |

`$concatArrays` |
Concatenates arrays to return the concatenated array. |

`$filter` |
Selects a subset of the array to return an array with only the elements that match the filter condition. |

`$in` |
Returns a boolean indicating whether a specified value is in an array. |

`$indexOfArray` |
Searches an array for an occurence of a specified value and
returns the array index of the first occurence. If the
substring is not found, returns `-1` . |

`$isArray` |
Determines if the operand is an array. Returns a boolean. |

`$map` |
Applies a subexpression to each element of an array and returns the array of resulting values in order. Accepts named parameters. |

`$objectToArray` |
Converts a document to an array of documents representing key-value pairs. |

`$range` |
Outputs an array containing a sequence of integers according to user-defined inputs. |

`$reduce` |
Applies an expression to each element in an array and combines them into a single value. |

`$reverseArray` |
Returns an array with the elements in reverse order. |

`$size` |
Returns the number of elements in the array. Accepts a single expression as argument. |

`$slice` |
Returns a subset of an array. |

`$zip` |
Merge two arrays together. |

### Boolean Expression Operators¶

Boolean expressions evaluate their argument expressions as booleans and return a boolean as the result.

In addition to the `false`

boolean value, Boolean expression evaluates
as `false`

the following: `null`

, `0`

, and `undefined`

values. The Boolean expression evaluates all other values as `true`

,
including non-zero numeric values and arrays.

Name | Description |
---|---|

`$and` |
Returns `true` only when all its expressions evaluate to
`true` . Accepts any number of argument expressions. |

`$not` |
Returns the boolean value that is the opposite of its argument expression. Accepts a single argument expression. |

`$or` |
Returns `true` when any of its expressions evaluates to
`true` . Accepts any number of argument expressions. |

### Comparison Expression Operators¶

Comparison expressions return a boolean except for `$cmp`

which returns a number.

The comparison expressions take two argument expressions and compare both value and type, using the specified BSON comparison order for values of different types.

`$cmp` |
Returns `0` if the two values are equivalent, `1` if the
first value is greater than the second, and `-1` if the
first value is less than the second. |
---|---|

`$eq` |
Returns `true` if the values are equivalent. |

`$gt` |
Returns `true` if the first value is greater than the
second. |

`$gte` |
Returns `true` if the first value is greater than or equal
to the second. |

`$lt` |
Returns `true` if the first value is less than the second. |

`$lte` |
Returns `true` if the first value is less than or equal to
the second. |

`$ne` |
Returns `true` if the values are not equivalent. |

### Conditional Expression Operators¶

Name | Description |
---|---|

`$cond` |
A ternary operator that evaluates one expression, and depending on the result, returns the value of one of the other two expressions. Accepts either three expressions in an ordered list or three named parameters. |

`$ifNull` |
Returns either the non-null result of the first expression or the result of the second expression if the first expression results in a null result. Null result encompasses instances of undefined values or missing fields. Accepts two expressions as arguments. The result of the second expression can be null. |

`$switch` |
Evaluates a series of case expressions. When it finds an
expression which evaluates to `true` , `$switch` executes
a specified expression and breaks out of the control flow. |

### Date Expression Operators¶

The following operators returns date objects or components of a date object:

Name | Description |
---|---|

`$dateFromParts` |
Constructs a BSON Date object given the date’s constituent parts. |

`$dateFromString` |
Converts a date/time string to a date object. |

`$dateToParts` |
Returns a document containing the constituent parts of a date. |

`$dateToString` |
Returns the date as a formatted string. |

`$dayOfMonth` |
Returns the day of the month for a date as a number between 1 and 31. |

`$dayOfWeek` |
Returns the day of the week for a date as a number between 1 (Sunday) and 7 (Saturday). |

`$dayOfYear` |
Returns the day of the year for a date as a number between 1 and 366 (leap year). |

`$hour` |
Returns the hour for a date as a number between 0 and 23. |

`$isoDayOfWeek` |
Returns the weekday number in ISO 8601 format, ranging from
`1` (for Monday) to `7` (for Sunday). |

`$isoWeek` |
Returns the week number in ISO 8601 format, ranging from
`1` to `53` . Week numbers start at `1` with the week
(Monday through Sunday) that contains the year’s first
Thursday. |

`$isoWeekYear` |
Returns the year number in ISO 8601 format. The year starts with the Monday of week 1 (ISO 8601) and ends with the Sunday of the last week (ISO 8601). |

`$millisecond` |
Returns the milliseconds of a date as a number between 0 and 999. |

`$minute` |
Returns the minute for a date as a number between 0 and 59. |

`$month` |
Returns the month for a date as a number between 1 (January) and 12 (December). |

`$second` |
Returns the seconds for a date as a number between 0 and 60 (leap seconds). |

`$toDate` |
Converts value to a Date. New in version 4.0. |

`$week` |
Returns the week number for a date as a number between 0 (the partial week that precedes the first Sunday of the year) and 53 (leap year). |

`$year` |
Returns the year for a date as a number (e.g. 2014). |

The following arithmetic operators can take date operands:

Name | Description |
---|---|

`$add` |
Adds numbers and a date to return a new date. If adding numbers and a date, treats the numbers as milliseconds. Accepts any number of argument expressions, but at most, one expression can resolve to a date. |

`$subtract` |
Returns the result of subtracting the second value from the first. If the two values are dates, return the difference in milliseconds. If the two values are a date and a number in milliseconds, return the resulting date. Accepts two argument expressions. If the two values are a date and a number, specify the date argument first as it is not meaningful to subtract a date from a number. |

### Literal Expression Operator¶

Name | Description |
---|---|

`$literal` |
Return a value without parsing. Use for values that the
aggregation pipeline may interpret as an expression. For
example, use a `$literal` expression to a string
that starts with a `$` to avoid parsing as a field path. |

### Object Expression Operators¶

Name | Description |
---|---|

`$mergeObjects` |
Combines multiple documents into a single document. New in version 3.6. |

`$objectToArray` |
Converts a document to an array of documents representing key-value pairs. New in version 3.6. |

### Set Expression Operators¶

Set expressions performs set operation on arrays, treating arrays as sets. Set expressions ignores the duplicate entries in each input array and the order of the elements.

If the set operation returns a set, the operation filters out duplicates in the result to output an array that contains only unique entries. The order of the elements in the output array is unspecified.

If a set contains a nested array element, the set expression does *not* descend
into the nested array but evaluates the array at top-level.

Name | Description |
---|---|

`$allElementsTrue` |
Returns `true` if no element of a set evaluates to
`false` , otherwise, returns `false` . Accepts a single
argument expression. |

`$anyElementTrue` |
Returns `true` if any elements of a set evaluate to
`true` ; otherwise, returns `false` . Accepts a single
argument expression. |

`$setDifference` |
Returns a set with elements that appear in the first set but not in the second set; i.e. performs a relative complement of the second set relative to the first. Accepts exactly two argument expressions. |

`$setEquals` |
Returns `true` if the input sets have the same distinct
elements. Accepts two or more argument expressions. |

`$setIntersection` |
Returns a set with elements that appear in all of the
input sets. Accepts any number of argument expressions. |

`$setIsSubset` |
Returns `true` if all elements of the first set appear
in the second set, including when the first set equals the
second set; i.e. not a strict subset. Accepts exactly
two argument expressions. |

`$setUnion` |
Returns a set with elements that appear in any of the
input sets. |

### String Expression Operators¶

String expressions, with the exception of
`$concat`

, only have a well-defined behavior for strings of ASCII characters.

`$concat`

behavior is well-defined regardless of
the characters used.

Name | Description |
---|---|

`$concat` |
Concatenates any number of strings. |

`$dateFromString` |
Converts a date/time string to a date object. |

`$dateToString` |
Returns the date as a formatted string. |

`$indexOfBytes` |
Searches a string for an occurence of a substring and returns
the UTF-8 byte index of the first occurence. If the substring
is not found, returns `-1` . |

`$indexOfCP` |
Searches a string for an occurence of a substring and returns
the UTF-8 code point index of the first occurence. If the
substring is not found, returns `-1` |

`$ltrim` |
Removes whitespace or the specified characters from the beginning of a string. New in version 4.0. |

`$regexFind` |
Applies a regular expression (regex) to a string and returns
information on the New in version 4.2. |

`$regexFindAll` |
Applies a regular expression (regex) to a string and returns information on the all matched substrings. New in version 4.2. |

`$regexMatch` |
Applies a regular expression (regex) to a string and returns a boolean that indicates if a match is found or not. New in version 4.2. |

`$rtrim` |
Removes whitespace or the specified characters from the end of a string. New in version 4.0. |

`$split` |
Splits a string into substrings based on a delimiter. Returns an array of substrings. If the delimiter is not found within the string, returns an array containing the original string. |

`$strLenBytes` |
Returns the number of UTF-8 encoded bytes in a string. |

`$strLenCP` |
Returns the number of UTF-8 code points in a string. |

`$strcasecmp` |
Performs case-insensitive string comparison and returns:
`0` if two strings are equivalent, `1` if the first
string is greater than the second, and `-1` if the first
string is less than the second. |

`$substr` |
Deprecated. Use `$substrBytes` or
`$substrCP` . |

`$substrBytes` |
Returns the substring of a string. Starts with the character at the specified UTF-8 byte index (zero-based) in the string and continues for the specified number of bytes. |

`$substrCP` |
Returns the substring of a string. Starts with the character at the specified UTF-8 code point (CP) index (zero-based) in the string and continues for the number of code points specified. |

`$toLower` |
Converts a string to lowercase. Accepts a single argument expression. |

`$toString` |
Converts value to a string. New in version 4.0. |

`$trim` |
Removes whitespace or the specified characters from the beginning and end of a string. New in version 4.0. |

`$toUpper` |
Converts a string to uppercase. Accepts a single argument expression. |

### Trigonometry Expression Operators¶

Trigonometry expressions perform trigonometric operations on numbers.
Values that represent angles are always input or output in radians. Use
`$degreesToRadians`

and `$radiansToDegrees`

to
convert between degree and radian measurements.

Name | Description |
---|---|

`$sin` |
Returns the sine of a value that is measured in radians. |

`$cos` |
Returns the cosine of a value that is measured in radians. |

`$tan` |
Returns the tangent of a value that is measured in radians. |

`$asin` |
Returns the inverse sin (arc sine) of a value in radians. |

`$acos` |
Returns the inverse cosine (arc cosine) of a value in radians. |

`$atan` |
Returns the inverse tangent (arc tangent) of a value in radians. |

`$atan2` |
Returns the inverse tangent (arc tangent) of `y / x` in
radians, where `y` and `x` are the first and second
values passed to the expression respectively. |

`$asinh` |
Returns the inverse hyperbolic sine (hyperbolic arc sine) of a value in radians. |

`$acosh` |
Returns the inverse hyperbolic cosine (hyperbolic arc cosine) of a value in radians. |

`$atanh` |
Returns the inverse hyperbolic tangent (hyperbolic arc tangent) of a value in radians. |

`$degreesToRadians` |
Converts a value from degrees to radians. |

`$radiansToDegrees` |
Converts a value from radians to degrees. |

### Type Expression Operators¶

Name | Description |
---|---|

`$convert` |
Converts a value to a specified type. New in version 4.0. |

`$toBool` |
Converts value to a boolean. New in version 4.0. |

`$toDate` |
Converts value to a Date. New in version 4.0. |

`$toDecimal` |
Converts value to a Decimal128. New in version 4.0. |

`$toDouble` |
Converts value to a double. New in version 4.0. |

`$toInt` |
Converts value to an integer. New in version 4.0. |

`$toLong` |
Converts value to a long. New in version 4.0. |

`$toObjectId` |
Converts value to an ObjectId. New in version 4.0. |

`$toString` |
Converts value to a string. New in version 4.0. |

`$type` |
Return the BSON data type of the field. |

### Accumulators (`$group`

)¶

Available for use in the `$group`

stage, accumulators are
operators that maintain their state (e.g. totals, maximums, minimums,
and related data) as documents progress through the pipeline.

When used as accumulators in the `$group`

stage, these
operators take as input a single expression, evaluating the expression
once for each input document, and maintain their stage for the group of
documents that share the same group key.

Name | Description |
---|---|

`$addToSet` |
Returns an array of unique expression values for each
group. Order of the array elements is undefined. |

`$avg` |
Returns an average of numerical values. Ignores non-numeric values. |

`$first` |
Returns a value from the first document for each group. Order is only defined if the documents are in a defined order. |

`$last` |
Returns a value from the last document for each group. Order is only defined if the documents are in a defined order. |

`$max` |
Returns the highest expression value for each group. |

`$mergeObjects` |
Returns a document created by combining the input documents for each group. |

`$min` |
Returns the lowest expression value for each group. |

`$push` |
Returns an array of expression values for each group. |

`$stdDevPop` |
Returns the population standard deviation of the input values. |

`$stdDevSamp` |
Returns the sample standard deviation of the input values. |

`$sum` |
Returns a sum of numerical values. Ignores non-numeric values. |

### Accumulators (in Other Stages)¶

Some operators that are available as accumulators for the
`$group`

stage are also available for use in other stages but
not as accumulators. When used in these other stages, these operators
do not maintain their state and can take as input either a single
argument or multiple arguments. For details, refer to the specific
operator page.

Changed in version 3.2.

The following accumulator operators are also available in the
`$project`

, `$addFields`

, and `$set`

stages.

Name | Description |
---|---|

`$avg` |
Returns an average of the specified expression or list of expressions for each document. Ignores non-numeric values. |

`$max` |
Returns the maximum of the specified expression or list of expressions for each document |

`$min` |
Returns the minimum of the specified expression or list of expressions for each document |

`$stdDevPop` |
Returns the population standard deviation of the input values. |

`$stdDevSamp` |
Returns the sample standard deviation of the input values. |

`$sum` |
Returns a sum of numerical values. Ignores non-numeric values. |

## Alphabetical Listing of Expression Operators¶

Name | Description |
---|---|

`$abs` |
Returns the absolute value of a number. |

`$acos` |
Returns the inverse cosine (arc cosine) of a value in radians. |

`$acosh` |
Returns the inverse hyperbolic cosine (hyperbolic arc cosine) of a value in radians. |

`$add` |
Adds numbers to return the sum, or adds numbers and a date to return a new date. If adding numbers and a date, treats the numbers as milliseconds. Accepts any number of argument expressions, but at most, one expression can resolve to a date. |

`$addToSet` |
Returns an array of Available in |

`$allElementsTrue` |
Returns `true` if no element of a set evaluates to `false` ,
otherwise, returns `false` . Accepts a single argument expression. |

`$and` |
Returns `true` only when all its expressions evaluate to
`true` . Accepts any number of argument expressions. |

`$anyElementTrue` |
Returns `true` if any elements of a set evaluate to `true` ;
otherwise, returns `false` . Accepts a single argument expression. |

`$arrayElemAt` |
Returns the element at the specified array index. |

`$arrayToObject` |
Converts an array of key value pairs to a document. |

`$asin` |
Returns the inverse sine (arc sine) of a value in radians. |

`$asinh` |
Returns the inverse hyperbolic sin (hyperbolic arc sine) of a value in radians. |

`$atan` |
Returns the inverse tangent (arc tangent) of a value in radians. |

`$atan2` |
Returns the inverse tangent (arc tangent) of `y / x` in radians,
where `y` and `x` are the first and second values passed to the
expression respectively. |

`$atanh` |
Returns the inverse hyperbolic tangent (hyperbolic arc tangent) of a value in radians. |

`$avg` |
Returns an average of numerical values. Ignores non-numeric values. |

`$ceil` |
Returns the smallest integer greater than or equal to the specified number. |

`$cmp` |
Returns: `0` if the two values are
equivalent, `1` if the first value is greater than the
second, and `-1` if the first value is less than the
second. |

`$concat` |
Concatenates any number of strings. |

`$concatArrays` |
Concatenates arrays to return the concatenated array. |

`$cond` |
A ternary operator that evaluates one expression, and depending on the result, returns the value of one of the other two expressions. Accepts either three expressions in an ordered list or three named parameters. |

`$convert` |
Converts a value to a specified type. |

`$cos` |
Returns the cosine of a value that is measured in radians. |

`$dateFromParts` |
Constructs a BSON Date object given the date’s constituent parts. |

`$dateToParts` |
Returns a document containing the constituent parts of a date. |

`$dateFromString` |
Returns a date/time as a date object. |

`$dateToString` |
Returns the date as a formatted string. |

`$dayOfMonth` |
Returns the day of the month for a date as a number between 1 and 31. |

`$dayOfWeek` |
Returns the day of the week for a date as a number between 1 (Sunday) and 7 (Saturday). |

`$dayOfYear` |
Returns the day of the year for a date as a number between 1 and 366 (leap year). |

`$degreesToRadians` |
Converts a value from degrees to radians. |

`$divide` |
Returns the result of dividing the first number by the second. Accepts two argument expressions. |

`$eq` |
Returns `true` if the values are
equivalent. |

`$exp` |
Raises e to the specified exponent. |

`$filter` |
Selects a subset of the array to return an array with only the elements that match the filter condition. |

`$first` |
Returns a value from the first document for each group. Order is only defined if the documents are in a defined order. Available in |

`$floor` |
Returns the largest integer less than or equal to the specified number. |

`$gt` |
Returns `true` if the first value is
greater than the second. |

`$gte` |
Returns `true` if the first value is
greater than or equal to the second. |

`$hour` |
Returns the hour for a date as a number between 0 and 23. |

`$ifNull` |
Returns either the non-null result of the first expression or the result of the second expression if the first expression results in a null result. Null result encompasses instances of undefined values or missing fields. Accepts two expressions as arguments. The result of the second expression can be null. |

`$in` |
Returns a boolean indicating whether a specified value is in an array. |

`$indexOfArray` |
Searches an array for an occurence of a specified value and returns
the array index of the first occurence. If the substring is not found,
returns `-1` . |

`$indexOfBytes` |
Searches a string for an occurence of a substring and returns the
UTF-8 byte index of the first occurence. If the substring is not
found, returns `-1` . |

`$indexOfCP` |
Searches a string for an occurence of a substring and returns the
UTF-8 code point index of the first occurence. If the
substring is not found, returns `-1` . |

`$isArray` |
Determines if the operand is an array. Returns a boolean. |

`$isoDayOfWeek` |
Returns the weekday number in ISO 8601 format, ranging from
`1` (for Monday) to `7` (for Sunday). |

`$isoWeek` |
Returns the week number in ISO 8601 format, ranging
from `1` to `53` . Week
numbers start at `1` with the week (Monday through Sunday)
that contains the year’s first Thursday. |

`$isoWeekYear` |
Returns the year number in ISO 8601 format. The year starts with the Monday of week 1 (ISO 8601) and ends with the Sunday of the last week (ISO 8601). |

`$last` |
Returns a value from the last document for each group. Order is only defined if the documents are in a defined order. Available in |

`$let` |
Defines variables for use within the scope of a subexpression and returns the result of the subexpression. Accepts named parameters. Accepts any number of argument expressions. |

`$literal` |
Return a value without parsing. Use for values that the aggregation
pipeline may interpret as an expression. For example, use a
`$literal` expression to a string that starts with a
`$` to avoid parsing as a field path. |

`$ln` |
Calculates the natural log of a number. |

`$log` |
Calculates the log of a number in the specified base. |

`$log10` |
Calculates the log base 10 of a number. |

`$lt` |
Returns `true` if the first value is less
than the second. |

`$lte` |
Returns `true` if the first value is less
than or equal to the second. |

`$ltrim` |
Removes whitespace or the specified characters from the beginning of a string. |

`$map` |
Applies a subexpression to each element of an array and returns the array of resulting values in order. Accepts named parameters. |

`$max` |
Returns the highest expression value for each group. |

`$mergeObjects` |
Combines multiple documents into a single document. |

`$meta` |
Access text search metadata. |

`$min` |
Returns the lowest expression value for each group. |

`$millisecond` |
Returns the milliseconds of a date as a number between 0 and 999. |

`$minute` |
Returns the minute for a date as a number between 0 and 59. |

`$mod` |
Returns the remainder of the first number divided by the second. Accepts two argument expressions. |

`$month` |
Returns the month for a date as a number between 1 (January) and 12 (December). |

`$multiply` |
Multiplies numbers to return the product. Accepts any number of argument expressions. |

`$ne` |
Returns `true` if the values are not
equivalent. |

`$not` |
Returns the boolean value that is the opposite of its argument expression. Accepts a single argument expression. |

`$objectToArray` |
Converts a document to an array of documents representing key-value pairs. |

`$or` |
Returns `true` when any of its expressions evaluates to `true` .
Accepts any number of argument expressions. |

`$pow` |
Raises a number to the specified exponent. |

`$push` |
Returns an array of expression values for each group. Available in |

`$radiansToDegrees` |
Converts a value from radians to degrees. |

`$range` |
Outputs an array containing a sequence of integers according to user-defined inputs. |

`$reduce` |
Applies an expression to each element in an array and combines them into a single value. |

`$regexFind` |
Applies a regular expression (regex) to a string and returns
information on the first matched substring. |

`$regexFindAll` |
Applies a regular expression (regex) to a string and returns information on the all matched substrings. |

`$regexMatch` |
Applies a regular expression (regex) to a string and returns a boolean that indicates if a match is found or not. |

`$reverseArray` |
Returns an array with the elements in reverse order. |

`$round` |
Rounds a number to a whole integer or to a specified decimal place. |

`$rtrim` |
Removes whitespace or the specified characters from the end of a string. |

`$second` |
Returns the seconds for a date as a number between 0 and 60 (leap seconds). |

`$setDifference` |
Returns a set with elements that appear in the first set but not in the second set; i.e. performs a relative complement of the second set relative to the first. Accepts exactly two argument expressions. |

`$setEquals` |
Returns `true` if the input sets have the same distinct elements.
Accepts two or more argument expressions. |

`$setIntersection` |
Returns a set with elements that appear in all of the input sets.
Accepts any number of argument expressions. |

`$setIsSubset` |
Returns `true` if all elements of the first set appear in the
second set, including when the first set equals the second set; i.e.
not a strict subset.
Accepts exactly two argument expressions. |

`$setUnion` |
Returns a set with elements that appear in any of the input sets. |

`$size` |
Returns the number of elements in the array. Accepts a single expression as argument. |

`$sin` |
Returns the sine of a value that is measured in radians. |

`$slice` |
Returns a subset of an array. |

`$split` |
Splits a string into substrings based on a delimiter. Returns an array of substrings. If the delimiter is not found within the string, returns an array containing the original string. |

`$sqrt` |
Calculates the square root. |

`$stdDevPop` |
Returns the population standard deviation of the input values. |

`$stdDevSamp` |
Returns the sample standard deviation of the input values. |

`$strcasecmp` |
Performs case-insensitive string comparison and returns: `0` if two
strings are equivalent, `1` if the first string is greater than the
second, and `-1` if the first string is less than the second. |

`$strLenBytes` |
Returns the number of UTF-8 encoded bytes in a string. |

`$strLenCP` |
Returns the number of UTF-8 code points in a string. |

`$substr` |
Deprecated. Use `$substrBytes` or `$substrCP` . |

`$substrBytes` |
Returns the substring of a string. Starts with the character at the specified UTF-8 byte index (zero-based) in the string and continues for the specified number of bytes. |

`$substrCP` |
Returns the substring of a string. Starts with the character at the specified UTF-8 code point (CP) index (zero-based) in the string and continues for the number of code points specified. |

`$subtract` |
Returns the result of subtracting the second value from the first. If the two values are numbers, return the difference. If the two values are dates, return the difference in milliseconds. If the two values are a date and a number in milliseconds, return the resulting date. Accepts two argument expressions. If the two values are a date and a number, specify the date argument first as it is not meaningful to subtract a date from a number. |

`$sum` |
Returns a sum of numerical values. Ignores non-numeric values. |

`$switch` |
Evaluates a series of case expressions. When it finds an expression
which evaluates to `true` , `$switch` executes a specified
expression and breaks out of the control flow. |

`$tan` |
Returns the tangent of a value that is measured in radians. |

`$toBool` |
Converts value to a boolean. |

`$toDate` |
Converts value to a Date. |

`$toDecimal` |
Converts value to a Decimal128. |

`$toDouble` |
Converts value to a double. |

`$toInt` |
Converts value to an integer. |

`$toLong` |
Converts value to a long. |

`$toObjectId` |
Converts value to an ObjectId. |

`$toString` |
Converts value to a string. |

`$toLower` |
Converts a string to lowercase. Accepts a single argument expression. |

`$toUpper` |
Converts a string to uppercase. Accepts a single argument expression. |

`$trim` |
Removes whitespace or the specified characters from the beginning and end of a string. |

`$trunc` |
Truncates a number to a whole integer or to a specified decimal place. |

`$type` |
Return the BSON data type of the field. |

`$week` |
Returns the week number for a date as a number between 0 (the partial week that precedes the first Sunday of the year) and 53 (leap year). |

`$year` |
Returns the year for a date as a number (e.g. 2014). |

`$zip` |
Merge two arrays together. |

For the pipeline stages, see Aggregation Pipeline Stages.