About this character
The plus-minus sign was introduced by the English mathematician William Oughtred in his Clavis Mathematicae of 1631 to indicate either of two values, one positive and one negative. Oughtred's notation was a typographic novelty — combining the existing plus and minus signs into a single mark — and was adopted rapidly across continental Europe in the second half of the 17th century. Today the symbol is universal in mathematics and the sciences.
U+00B1 is most often seen in three places. First, in error bars and tolerance specifications: a measurement of 9.81 ± 0.02 m/s² means a central value with a quantified uncertainty, conventionally one standard deviation in scientific writing and a manufacturing tolerance in engineering writing. Second, in the quadratic formula and other contexts where polynomial roots come in pairs: x = (−b ± √(b² − 4ac)) / 2a. Third, in trigonometric and signal identities where the sign alternates with the case: sin(α ± β) = sin α cos β ± cos α sin β. In the trigonometric identity case, the two ± signs are typographically distinct from each other if you want to distinguish the corresponding-sign reading from the opposite-sign reading: Unicode provides U+2213 ∓ MINUS-OR-PLUS SIGN for exactly this purpose, where the second sign is read as the opposite of the first.
The Unicode general category for U+00B1 is Sm (Symbol, Math), reflecting its primary mathematical role. The Bidi class is ET (European Terminator), so it attaches to a preceding number in bidirectional text — see the bidirectional text guide for the algorithm. Some house styles use a non-breaking space (U+00A0) between the central value and the ± sign; SI typography uses a thin space (U+2009) around the symbol. The plus-minus sign is also occasionally used non-mathematically as a "more or less" qualifier in writing about quantities ("the building is ±100 metres tall"), though this is informal.
From the Unicode data
Its East Asian Width is Ambiguous: it takes one column in Western contexts and two in East Asian legacy contexts, a common cause of misaligned tables in terminals.