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Proportional Symbol in LaTeX

The "proportional to" symbol ∝ is \propto in math mode: $y \propto x$. It is built into LaTeX, so no package is needed. amssymb adds a thinner variant, \varpropto.

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Proportional commands

  • \propto
    ∝

    Proportional to ∝.

  • \varpropto
    ∝

    Thinner variant (amssymb).

  • \not\propto
    ∝̸

    Not proportional to.

  • \sim
    ∼

    Similar to, scales as; often used informally for proportionality.

  • \underset{\sim}{\propto}
    ∝ ∼

    One way to build "approximately proportional to"; there is no standard command.

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Templates

Proportional to examples

Each result below is drawn from the LaTeX under it. Copy the code, edit it on this page, or open it in the full editor.

  • Direct proportion

    y ∝ x ⟺ y = k x  for some constant  k
    LaTeX
    y \propto x \iff y = kx \text{ for some constant } k
    Edit hereOpen in editor

  • Inverse square law

    I ∝ 1 r 2
    LaTeX
    I \propto \frac{1}{r^2}
    Edit hereOpen in editor

  • Gravitation

    F ∝ m 1 m 2 r 2
    LaTeX
    F \propto \frac{m_1 m_2}{r^2}
    Edit hereOpen in editor

  • Bayes’ rule up to a constant

    p ( θ ∣ x ) ∝ p ( x ∣ θ ) p ( θ )
    LaTeX
    p(\theta \mid x) \propto p(x \mid \theta)\, p(\theta)
    Edit hereOpen in editor

  • Both variants

    a ∝ b vs a ∝ b
    LaTeX
    a \propto b \quad \text{vs} \quad a \varpropto b
    Edit hereOpen in editor

\propto versus \sim

\propto says one quantity is a constant multiple of another. Physics and asymptotic analysis often use \sim for "scales like" or "is of the order of", which is a looser statement (and in probability \sim means "is distributed as"). Pick the symbol that matches what you claim and use it consistently.

Why ∝ looks like the letter alpha

In many fonts ∝ resembles a sideways-open α, which is why people sometimes type \alpha by mistake. They are different characters: \alpha is a variable letter and is spaced like one, while \propto is a relation with space on both sides. Screen readers and search also treat them differently.

If the symbol looks too small next to large fractions, that is its normal relation size, like =. Some authors prefer \varpropto, which is a little lighter.

Common mistakes

  • α is a Greek letter; it prints tight against its neighbours and means something else.

    Instead of
    y \alpha x
    Write
    y \propto x

  • The command is the short name \propto; \proportional is undefined.

    Instead of
    \proportional
    Write
    \propto

  • Like every relation symbol, \propto only works in math mode.

    Instead of
    y \propto x  % in text
    Write
    $y \propto x$

In Overleaf, MathJax and Word

  • Overleaf and pdfLaTeX

    \propto works with no packages; \varpropto needs \usepackage{amssymb}.

  • MathJax and KaTeX

    MathJax and KaTeX render \propto; MathJax also has \varpropto.

  • Microsoft Word

    In a Word equation, type \propto and press Space for ∝. Copy for Word from the editor here pastes whole proportionality statements as editable equations.

Proportional to in LaTeX: questions

What is the LaTeX command for proportional to?
\propto, in math mode: $y \propto x$.
Do I need a package for \propto?
No. Only the variant \varpropto needs amssymb.
How do I write "approximately proportional to"?
LaTeX has no single command. A common approach stacks a tilde under the symbol, \underset{\sim}{\propto} (amsmath); define it once as a macro so it is consistent.
Is ∝ the same as the Greek letter alpha?
No. They look alike in some fonts, but \propto is a relation symbol and \alpha is a letter.

Related LaTeX reference

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