Absolute value and norm in LaTeX
The absolute value of a number is its distance from zero, written with vertical bars; in LaTeX \lvert x \rvert gives correctly spaced bars and \lVert x \rVert gives a norm.
LaTeX command
\lvert x \rvertNot the symbol you meant? Draw it to find the command →
The recommended commands are \lvert for the left bar and \rvert for the right, as in \lvert x \rvert. They are true delimiters, so LaTeX gives them the right spacing and treats the enclosed expression correctly. A plain | x | also works but is an ordinary symbol, so its spacing around neighbouring operators can be slightly off.
A norm uses double bars: \lVert x \rVert. This is the standard notation for vector length or the size of a function in a function space. The single-bar and double-bar delimiter commands are supported by KaTeX and give consistent, professional-looking output.
When the content is tall, such as a fraction inside bars, pair the bars with \left and \right so they grow to fit: \left\lvert \frac{a}{b} \right\rvert, or the shorter \left| ... \right|. For heavy reuse, the mathtools package lets you declare a paired delimiter once and call it by name.
Other forms
\lVert x \rVerta norm|x|quick bars (spacing is worse)Examples
$\lvert -3 \rvert = 3$a basic absolute value
$\lVert \mathbf{v} \rVert = \sqrt{v_1^2 + v_2^2}$a vector norm with double bars
$\left| \frac{a}{b} \right|$auto-sized bars around a fraction
$\lvert x - a \rvert < \delta$an epsilon-delta style inequality
Tips and common mistakes
- Prefer
\lvert...\rvertover plain | ... | so the spacing around the bars is correct. - For a norm use the double-bar pair
\lVert...\rVert(note the capital V). - For tall content, wrap in
\left| ...\right| or\left\lvert...\right\rvertso the bars stretch. - Avoid plain | | around large expressions; the bars will not grow and the spacing suffers.
- For consistency across a document, define a paired delimiter with mathtools rather than typing bars by hand.
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Convert your maths to LaTeX →FAQ
How do I write absolute value in LaTeX?
Use \lvert x \rvert for correctly spaced bars, or the quick |x| if spacing is not critical. Both render vertical bars around the expression.
How do I write a norm?
Use the double-bar delimiters \lVert x \rVert. This gives the two vertical lines used for vector and function norms.
How do I make the bars stretch around a fraction?
Pair them with \left and \right: \left| \frac{a}{b} \right|, or \left\lvert \frac{a}{b} \right\rvert. The bars then grow to match the height of the content.