A filter operator is a predefined keyword attached to an individual step of a filter. It defines the particular action of that step.
Important: In general, each first filter step of a filter run not given any input titles receives the output of [all[tiddlers]] as its input.
Table legend:
✓  ...  Used to mark the most common ones 
!  ...  The column indicates whether an operator allows negation using the ! prefix.For specifics as to each operator's negated output please refer to its documentation 
C  ...  Most steps process the selection of titles that are supplied as their input, but a few construct an entirely new selection instead, as indicated by the last column. A C? indicates it might construct a new selection, depending on usage. For specifics as to each operator's selection creation please refer to its documentation 
The following table lists all core operators:
Operator  Purpose  ✓  ! 
C 

all  find all titles of a fundamental category  ✓  C? 

backlinks  find the titles that link to each input title  
backtranscludes  find the titles that transclude each input title  
charcode  generates string characters from their numeric character codes  
contains  filter the input by searching list fields for a value  ! 

count  count the number of entries in a list  
days  filter the input by date  ! 

duplicateslugs  find titles that yield duplicate slugs  
each  select one of each group of input titles by field  
eachday  select one of each group of input titles by date  
else  if the list of input titles is empty then return a list consisting of a single constant string, otherwise return the original titles  
enlist  select titles from the parameter interpreted as a title list  ! 
C 

field  filter the input by field  ✓  ! 

fields  select all field names of the input titles  
filter  apply a subfilter to each input title and return the titles that return a nonempty result from the subfilter  ! 

function  apply a function to the input list, and return the result  
get  select all values of a field in the input titles  
getindex  select all values of a data property in the input titles  
has  filter the input by field existence  ✓  ! 

haschanged  filter the input by tiddler modification status  ! 

indexes  select all data properties of the input titles  
is  filter the input by fundamental category  ✓  ! 

join  join a list of strings together with the separator S 

jsonextract  retrieve the JSON string of a property from JSON strings  
jsonget  retrieve the value of a property from JSON strings  
jsonindexes  retrieve the value of a property from JSON strings  
jsonset  set the value of a property in JSON objects  
jsontype  retrieve the type of a property from JSON strings  
length  returns the number of characters of each item in the list  
links  find the titles linked to by each input title  ✓  
list  select titles via a list field  ! 
C 

listed  find the titles that list the input titles  
lookup  applies a prefix to each input title to yield the title of a tiddler from which the final value is retrieved. With a single parameter, the default field is "text" and the default index is "0". If a second parameter is provided, that becomes the target field or index.  
lowercase  returns each item in the list as lowercase  
match  returns each item in the list that matches the parameter string  
minlength  filter items whose length is greater than the specified minimum length  
range  generate a range of numbers  ! 
C 

reduce  apply a subfilter to each input title in turn, accumulating a single value  
regexp  filter the input by patternmatched field  ! 

sameday  filter the input by date  
search  filter the input by searching tiddler content  ✓  ! 

sentencecase  returns each item in the list with the first letter capitalised  
slugify  returns each item in the list in a humanreadable form for use in URLs or filenames  
split  returns each item in the list split into separate strings according to the specified separator S ; duplicates are not removed 

splitregexp  returns each item in the list split into separate strings according to the specified regular expression R 

subfilter  select titles from the parameter interpreted as a filter expression  ! 
C? 

then  replace input titles by a constant string  
title  select a single title  ✓  ! 
C 
titlecase  returns each item in the list with each word capitalised  
transcludes  find the titles transcluded by each input title  ✓  
uppercase  returns each item in the list as uppercase  
Order Operators  
after  find which input title follows a specified one  
before  find which input title precedes a specified one  
bf  same as rest 

butfirst  same as rest 

butlast  discard the last N input titles 

first  select the first N input titles 

last  select the last N input titles 

limit  select the first or last N input titles 
✓  ! 

next  find which titles in a list field follow the input ones 

nsort  sort the input by number field  ! 

nsortcs  sort the input titles by number field, treating upper and lower case as different  ! 

nth  select the N th input title 

order  selectively reverse the input list  ✓  
previous  find which titles in a list field precede the input ones 

rest  discard the first N input titles 

reverse  reverse the order of the input titles  
sort  sort the input by text field  ✓  ! 

sortan  sort the input by text field considering them as alphanumerics  ✓  ! 

sortcs  sort the input by text field, treating upper and lower case as different  ! 

sortsub  sort the input by the result of evaluating a subfilter for each item  ! 

zth  select the Z th input title 

Listops Operators  
allafter  discard all items except those after the marker  
allbefore  discard all items except those before the marker  
append  append a range of items from an array to the list  
cycle  toggle the titles specified in the first parameter in a cyclical manner  
insertafter  insert an item T into a list immediately after an item A 

insertbefore  insert an item T into a list immediately before an item B 

move  move marker N places in the list  
prepend  prepend a range of items from an array to the list  
putafter  move N trailing items after the marker  
putbefore  move N trailing items before the marker  
putfirst  move N trailing items to the head of the list  
putlast  move N leading items to the tail of the list  
remove  remove a list of titles specified in the parameter from the input  
replace  replace marker with N trailing items  
sortby  sort the current list in the order of the list referenced in the parameter  
toggle  toggle the title specified in the parameter in the input  
unique  remove all duplicate items from the current list  
String Operators  
addprefix  extend each input title with a prefix  
addsuffix  extend each input title with a suffix  
applypatches  applies a set of patches to transform the input  
compare  filter the input by comparing each item against the parameter  ! 

decodebase64  apply base 64 decoding to a string  
decodehtml  apply HTML decoding to a string  
decodeuri  apply URI decoding to a string  
decodeuricomponent  apply URI component decoding to a string  
encodebase64  apply base 64 encoding to a string  
encodehtml  apply HTML encoding to a string  
encodeuri  apply URI encoding to a string  
encodeuricomponent  apply URI component encoding to a string  
enlistinput  select titles by interpreting each input title as a title list  
escapecss  apply CSS escaping to a selection of titles through the CSS.escape() method / operation  
escaperegexp  escape special characters used in regular expressions  
format  format the input string according to one of supported formats  
jsonstringify  apply JSON string encoding to a string, see also the similar stringify 

levenshtein  determine the Levenshtein distance of the input title(s) and a given string  
makepatches  returns a set of patches that transform the input to a given string  
pad  returns each item in the list padded to the specified length  
prefix  filter the input titles by how they start  ! 

removeprefix  filter the input titles by how they start, deleting that prefix  
removesuffix  filter the input titles by how they end, deleting that suffix  
searchreplace  returns each item in the list, replacing within each title the string specified by the first parameter with the second parameter  
sha256  apply sha256 hash to a string  
splitbefore  select a delimited prefix from each input title  
stringify  apply JavaScript string encoding to a string, see also the similar jsonstringify 

substitute  returns each item in the list, replacing within each title placeholders for filters, parameters and variables with their corresponding values  
suffix  filter the input titles by how they end  ! 

trim  returns each item in the list with whitespace, or a given character string, trimmed from the start and/or end  
Mathematics Operators  
abs  calculate the absolute value of a list of numbers  
acos  calculate the arccosine value (in radians) of a list of numbers  
add  treating each input title as a number, add to each the numeric value of the parameter  
asin  calculate the arcsine value (in radians) of a list of numbers  
atan  calculate the arctangent value (in radians) of a list of numbers  
atan2  returns the angle in the plane (in radians) between the positive xaxis and the ray from (0,0) to the point (x,y), for [Y ]atan2[X ] 

average  treating each input title as a number, compute their arithmetic mean  
ceil  rounds a list of numbers up to the next largest integer  
compare  filter the input by comparing each item against the parameter  ! 

cos  calculate the cosine value of a list of angles (given in radians)  
divide  treating each input title as a number, divide it by the numeric value of the parameter  
exponential  convert each number to exponential notation with N digits 

fixed  convert each number to fixed point notation with N digits after the decimal point 

floor  rounds a list of numbers to the largest integer less than or equal to each number  
log  treating each input title as a number, return its logarithm with base equal to the numeric value of the parameter if specified, otherwise base e 

max  treating each input title as a number, take the maximum of its value and the numeric value of the parameter  
maxall  find the largest of a list of numbers  
median  treating each input title as a number, compute their median value  
min  treating each input title as a number, take the minimum of its value and the numeric value of the parameter  
minall  find the smallest of a list of numbers  
multiply  treating each input title as a number, multiply it by the numeric value of the parameter  
negate  calculate the negation of a list of numbers  
power  treating each input title as a number, raise it to the power of the numeric value of the parameter  
precision  convert each number to a string with N significant digits 

product  produce the product of the input numbers  
remainder  treating each input title as a number, return the remainder when divided by the numeric value of the parameter  
round  rounds a list of numbers to the nearest integer  
sign  return 1, 0 or 1 for a list of numbers according to whether each number is negative, zero, or positive  
sin  calculate the sine value of a list of angles (given in radians)  
standarddeviation  treating each input title as a number, compute their standarddeviation  
subtract  treating each input title as a number, subtract from each the numeric value of the parameter  
sum  produce the sum of the input numbers  
tan  calculate the tangent value of a list of angles (given in radians)  
trunc  truncates a list of numbers to their integer part, removing any fractional part  
untrunc  rounds a list of numbers to the next integer with largest absolute value, that is, away from zero  
variance  treating each input title as a number, compute their variance  
Tag Operators  
tag  filter the input by tag  ✓  ! 

tagging  find the tiddlers that have the input tags  
tags  select all tags of the input tiddlers  
untagged  discard any input titles that have tags  ! 

Special Operators  
commands  select the titles of all the Node.js commands  C 

deserialize  extract JSON representation of tiddlers from the input strings  
deserializers  C 

editiondescription  select the descriptions of the input editions  
editions  select the names of all the TiddlyWiki editions  C 

getvariable  select all values of variables named in the input titles  
modulesproperty  retrieve a module property  
modules  select the names of all modules of the input module types  
moduletypes  select the names of all TiddlyWiki module types  C 

plugintiddlers  select all shadow titles in the input plugins  
shadowsource  select the plugin titles that contain the input shadows  
storyviews  select the names of all the story views  C 

subtiddlerfields  select all fields present in the selected tiddlers within a plugin  
variables  select the names of all the actively defined variables  C 
A typical step is written as [operator[parameter]]
, although not all of the operators need a parameter.
For the exact rules, see Filter Syntax.