Home: go to the homepage U+2200 to U+22FF Mathematical Operators

# U+221DProportional To

U+221D was added in Unicode version 1.1 in 1993. It belongs to the block U+2200 to U+22FF Mathematical Operators in the U+0000 to U+FFFF Basic Multilingual Plane.

This character is a Math Symbol and is commonly used, that is, in no specific script.

The glyph is not a composition. Its width in East Asian texts is determined by its context. It can be displayed wide or narrow. In bidirectional text it acts as Other Neutral. When changing direction it is mirrored. If its East Asian Width is “narrow”, U+221D forms a word with similar characters, which prevents a line break inside it. Otherwise it allows line breaks around it, except in some numeric contexts.

The CLDR project calls this character “proportional” for use in screen reading software. It assigns these additional labels, e.g. for search in emoji pickers: proportionality.

In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio. The ratio is called coefficient of proportionality (or proportionality constant) and its reciprocal is known as constant of normalization (or normalizing constant). Two sequences are inversely proportional if corresponding elements have a constant product, also called the coefficient of proportionality.

This definition is commonly extended to related varying quantities, which are often called variables. This meaning of variable is not the common meaning of the term in mathematics (see variable (mathematics)); these two different concepts share the same name for historical reasons.

Two functions $f\left(x\right)$ and $g\left(x\right)$ are proportional if their ratio $\frac{f\left(x\right)}{g\left(x\right)}$ is a constant function.

If several pairs of variables share the same direct proportionality constant, the equation expressing the equality of these ratios is called a proportion, e.g., a/b = x/y = ⋯ = k (for details see Ratio). Proportionality is closely related to linearity.

## Representations

System Representation
8733
UTF-8 E2 88 9D
UTF-16 22 1D
UTF-32 00 00 22 1D
URL-Quoted %E2%88%9D
HTML hex reference &#x221D;
Wrong windows-1252 Mojibake âˆ
HTML named entity &Proportional;
HTML named entity &prop;
HTML named entity &propto;
HTML named entity &varpropto;
HTML named entity &vprop;
Encoding: EUC-KR (hex bytes) A1 F0
Encoding: JIS0208 (hex bytes) A2 E7
LATEX \propto
digraph 0(

## Complete Record

Property Value
Age (age) 1.1 (1993)
Unicode Name (na) PROPORTIONAL TO
Unicode 1 Name (na1)
Block (blk) Mathematical Operators
General Category (gc) Math Symbol
Script (sc) Common
Bidirectional Category (bc) Other Neutral
Combining Class (ccc) Not Reordered
Decomposition Type (dt) none
Decomposition Mapping (dm) Proportional To
Lowercase (Lower)
Simple Lowercase Mapping (slc) Proportional To
Lowercase Mapping (lc) Proportional To
Uppercase (Upper)
Simple Uppercase Mapping (suc) Proportional To
Uppercase Mapping (uc) Proportional To
Simple Titlecase Mapping (stc) Proportional To
Titlecase Mapping (tc) Proportional To
Case Folding (cf) Proportional To
ASCII Hex Digit (AHex)
Alphabetic (Alpha)
Bidi Control (Bidi_C)
Bidi Mirrored (Bidi_M)
Composition Exclusion (CE)
Case Ignorable (CI)
Changes When Casefolded (CWCF)
Changes When Casemapped (CWCM)
Changes When NFKC Casefolded (CWKCF)
Changes When Lowercased (CWL)
Changes When Titlecased (CWT)
Changes When Uppercased (CWU)
Cased (Cased)
Full Composition Exclusion (Comp_Ex)
Default Ignorable Code Point (DI)
Dash (Dash)
Deprecated (Dep)
Diacritic (Dia)
Emoji Modifier Base (EBase)
Emoji Component (EComp)
Emoji Modifier (EMod)
Emoji Presentation (EPres)
Emoji (Emoji)
Extender (Ext)
Extended Pictographic (ExtPict)
FC NFKC Closure (FC_NFKC) Proportional To
Grapheme Cluster Break (GCB) Any
Grapheme Base (Gr_Base)
Grapheme Extend (Gr_Ext)
Hex Digit (Hex)
Hyphen (Hyphen)
ID Continue (IDC)
ID Start (IDS)
IDS Binary Operator (IDSB)
IDS Trinary Operator and (IDST)
IDSU (IDSU) 0
ID_Compat_Math_Continue (ID_Compat_Math_Continue) 0
ID_Compat_Math_Start (ID_Compat_Math_Start) 0
Ideographic (Ideo)
InCB (InCB) None
Indic Mantra Category (InMC)
Indic Positional Category (InPC) NA
Indic Syllabic Category (InSC) Other
Jamo Short Name (JSN)
Join Control (Join_C)
Logical Order Exception (LOE)
Math (Math)
Noncharacter Code Point (NChar)
NFC Quick Check (NFC_QC) Yes
NFD Quick Check (NFD_QC) Yes
NFKC Casefold (NFKC_CF) Proportional To
NFKC Quick Check (NFKC_QC) Yes
NFKC_SCF (NFKC_SCF) Proportional To
NFKD Quick Check (NFKD_QC) Yes
Other Alphabetic (OAlpha)
Other Default Ignorable Code Point (ODI)
Other Grapheme Extend (OGr_Ext)
Other ID Continue (OIDC)
Other ID Start (OIDS)
Other Lowercase (OLower)
Other Math (OMath)
Other Uppercase (OUpper)
Prepended Concatenation Mark (PCM)
Pattern Syntax (Pat_Syn)
Pattern White Space (Pat_WS)
Quotation Mark (QMark)
Regional Indicator (RI)
Sentence Break (SB) Other
Soft Dotted (SD)
Sentence Terminal (STerm)
Terminal Punctuation (Term)
Unified Ideograph (UIdeo)
Variation Selector (VS)
Word Break (WB) Other
White Space (WSpace)
XID Continue (XIDC)
XID Start (XIDS)
Expands On NFC (XO_NFC)
Expands On NFD (XO_NFD)
Expands On NFKC (XO_NFKC)
Expands On NFKD (XO_NFKD)
Bidi Paired Bracket (bpb) Proportional To
Bidi Paired Bracket Type (bpt) None
East Asian Width (ea) ambiguous
Hangul Syllable Type (hst) Not Applicable
ISO 10646 Comment (isc)
Joining Group (jg) No_Joining_Group
Joining Type (jt) Non Joining
Line Break (lb) Ambiguous (Alphabetic or Ideographic)
Numeric Type (nt) none
Numeric Value (nv) not a number
Simple Case Folding (scf) Proportional To
Script Extension (scx)
Vertical Orientation (vo) R