# Multiplication sign

×
Multiplication sign
In UnicodeU+00D7 × MULTIPLICATION SIGN (&times;)
Different from
Different fromU+0078 x LATIN SMALL LETTER X
Related
U+00F7 ÷ DIVISION SIGN

The multiplication sign, also known as the times sign or the dimension sign, is the symbol ×, used in mathematics to denote the multiplication operation and its resulting product.[1] While similar to a lowercase X (x), the form is properly a four-fold rotationally symmetric saltire.[2]

## History

The earliest known use of the × symbol to represent multiplication appears in an anonymous appendix to the 1618 edition of John Napier's Mirifici Logarithmorum Canonis Descriptio.[3] This appendix has been attributed to William Oughtred,[3] who used the same symbol in his 1631 algebra text, Clavis Mathematicae, stating:

"Multiplication of species [i.e. unknowns] connects both proposed magnitudes with the symbol 'in' or ×: or ordinarily without the symbol if the magnitudes be denoted with one letter."[4]

Two earlier uses of a notation have been identified, but do not stand critical examination.[3]

## Uses

In mathematics, the symbol × has a number of uses, including

• Multiplication of two numbers, where it is read as "times" or "multiplied by"[1]
• Cross product of two vectors, where it is usually read as "cross"
• Cartesian product of two sets, where it is usually read as "cross"[5]
• Geometric dimension of an object, such as noting that a room is 10 feet × 12 feet in area, where it is usually read as "by" (e.g., "10 feet by 12 feet")
• Screen resolution in pixels, such as 1920 pixels across × 1080 pixels down. Read as "by".
• Dimensions of a matrix, where it is usually read as "by"
• A statistical interaction between two explanatory variables, where it is usually read as "by"

In biology, the multiplication sign is used in a botanical hybrid name, for instance Ceanothus papillosus × impressus (a hybrid between C. papillosus and C. impressus) or Crocosmia × crocosmiiflora (a hybrid between two other species of Crocosmia). However, the communication of these hybrid names with a Latin letter "x" is common, when the actual "×" symbol is not readily available.

The multiplication sign is also used by historians for an event between two dates. When employed between two dates – for example 1225 and 1232 – the expression "1225×1232" means "no earlier than 1225 and no later than 1232".[6]

A monadic × symbol is used by the APL programming language to denote the sign function.

## Similar notations

The lower-case Latin letter x is sometimes used in place of the multiplication sign. This is considered incorrect in mathematical writing.

In algebraic notation, widely used in mathematics, a multiplication symbol is usually omitted wherever it would not cause confusion: "a multiplied by b" can be written as ab or a b.[1]

Other symbols can also be used to denote multiplication, often to reduce confusion between the multiplication sign × and the common variable x. In some countries, such as Germany, the primary symbol for multiplication is the "dot operator" (as in a⋅b). This symbol is also used in algebraic notation to resolve ambiguity (for instance, "b times 2" may be written as b⋅2, to avoid being confused with a value called b2). This notation is used wherever multiplication should be written explicitly, such as in "ab = a⋅2 for b = 2"; this usage is also seen in English-language texts. In some languages, the use of full stop as a multiplication symbol, such as a.b, is common when the symbol for decimal point is comma.

Historically, computer language syntax was restricted to the ASCII character set, and the asterisk * became the de facto symbol for the multiplication operator. This selection is reflected in the numeric keypad on English-language keyboards, where the arithmetic operations of addition, subtraction, multiplication and division are represented by the keys +, -, * and /, respectively.

## Typing the character

 HTML, SGML, XML × or × macOS In the Character Palette by searching for MULTIPLICATION SIGN[7] Microsoft Windows Via the Emoji and Symbol input panel, invoked with the ⊞ Win+. key combination (Windows 10 version 1803 and later) Via the Touch Keyboard component of the Taskbar (Windows 10 and later) Some non-English keyboard layouts have it as an explicit keytop, like in Arabic keyboard. Using US International keyboard layout, use Alt+= Via the Character Map utility: in the eighth row, or by searching The Alt+0215 key combination using the numeric keypad[8] OpenOffice.org times TeX \times Unix-like (Linux, ChromeOS) Ctrl+⇧ Shift+UD7 ComposeXX AltGr+⇧ Shift+, (UK extended layout)

## Unicode and HTML entities

• U+00D7 × MULTIPLICATION SIGN (&times;)

Other variants and related characters:

• U+002A * ASTERISK (&ast;, &midast;)
• U+2062 INVISIBLE TIMES (&InvisibleTimes;, &it;) (a zero-width space indicating multiplication)
• U+00B7 · MIDDLE DOT (&middot;, &CenterDot;, &centerdot;) (the interpunct, may be easier to type than the dot operator)
• U+2297 CIRCLED TIMES (&CircleTimes;, &otimes;)
• U+22C5 DOT OPERATOR (&sdot;)
• U+2715 MULTIPLICATION X
• U+2716 HEAVY MULTIPLICATION X
• U+2A09 N-ARY TIMES OPERATOR
• U+2A2F VECTOR OR CROSS PRODUCT (&Cross;) (intended to explicitly denote the cross product of two vectors)
• U+2A30 MULTIPLICATION SIGN WITH DOT ABOVE (&timesd;)
• U+2A31 MULTIPLICATION SIGN WITH UNDERBAR (&timesbar;)
• U+2A36 CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENT (&otimesas;)
• U+2AC1 SUBSET WITH MULTIPLICATION SIGN BELOW (&submult;)
• U+2AC2 SUPERSET WITH MULTIPLICATION SIGN BELOW (&supmult;)