Approximately Equal Symbol (≈): Meaning, How to Type It, and LaTeX

The approximately equal symbol ≈ (also called the approximate symbol; Unicode U+2248, officially Almost Equal To) says that two quantities are close in value but not identical: π ≈ 3.14, √2 ≈ 1.414. This guide covers what it means, how it differs from ~ ≃ ≅ ≐ ≒, how to type it, and \approx in LaTeX. Every LaTeX example here was compiled on TeX Live 2025.

Copy it from here: ≈. For the single squiggle, see the tilde symbol ~ post.

What ≈ Means

a ≈ b is read "a is approximately (or almost) equal to b". It is used where exact equality would be false but the difference does not matter:

• Rounded values: π ≈ 3.1416, e ≈ 2.718, 1/3 ≈ 0.333.
• Measured or estimated values: g ≈ 9.81 m/s², a city population ≈ 2 million.
• Approximations in analysis: sin x ≈ x and (1 + x)ⁿ ≈ 1 + nx for small x, or a truncated Taylor series.
• Numerical results: solver or simulation output, correct to a stated number of digits.

≈ has no fixed tolerance, which is why careful writing states one: "≈ 3.14 (to two decimal places)". The symbol is usually credited to Alfred Greenhill, who used an early form of it in 1892.

≈ vs ~ vs ≃ vs ≅ vs ≐ vs ≒

Each wavy equals sign has its own meaning. The table gives the code point, the official Unicode name (not always what mathematicians call it) and the LaTeX command.

Three distinctions cover most of the confusion. ≈ vs ~: ≈ says the values are close (π ≈ 3.14); ~ says only that they share a scale (L ~ 10³ m) or that a quantity follows a distribution (X ~ N(0, 1)). ≈ vs ≅: ≅ means congruent or isomorphic, whatever its Unicode name says; see the congruent symbol ≅. ≈ vs ≃: ≃ is asymptotic equality or homotopy equivalence; some physicists use it for ≈, but ≈ is the safe choice for a rounded number.

How to Type the Approximately Equal Symbol

No standard keyboard has a ≈ key, so each platform has a shortcut or a picker. Copying is often quickest: ≈

Windows

Alt+247 works because 247 is ≈ in code page 437, the original IBM PC character set that plain Alt codes read from on US Windows. On a PC using code page 850 (common in Western Europe), 247 is a cedilla ¸ instead. Alt codes need a numeric keypad; without one, use Win+. and the Symbols tab, or in Word and Outlook type 2248 and press Alt+X to convert the hex code point into the character.

Mac

Option+X gives ≈ on the U.S. (and ABC) layout. On other layouts, the Character Viewer (Control+Command+Space) finds it under "almost equal".

iPhone and Android

On iPhone tap 123, then #+=, hold = and slide to ≈ (the same pop-up has ≠). Android keyboards vary; in Gboard check the ?123 symbol pages or hold =. Failing that, copy it from this page.

HTML and Unicode

The named entity is ≈ (HTML 4 described it as "almost equal to = asymptotic to"); the numeric forms are ≈ and ≈. HTML5 also accepts ≈ and ≈. Related entities: ∼ ∼, ≃ ≃, ≅ ≅, ≠ ≠.

Approximately Equal in LaTeX: \approx

The command is \approx. It needs no package and works only in math mode ($...$, \( ... \) or a display environment). As a relation symbol it gets the same spacing as =, whatever spaces you type.

\documentclass{article}
\begin{document}

Inline: $\pi \approx 3.1416$, $\sqrt{2} \approx 1.414$, $e \approx 2.718$, $1/3 \approx 0.333$.

Spacing is automatic: $a\approx b$ and $a \approx b$ print the same.

The relatives: $a \sim b$, $a \simeq b$, $a \cong b$, $a \doteq b$, $a \asymp b$, $a \propto b$.

Negated: $a \not\approx b$, $a \not\sim b$, $a \not\cong b$, $a \neq b$.

\end{document}

The variants below need amssymb. \napprox does not exist: amssymb has \nsim and \ncong but no negated \approx, so it stops with "Undefined control sequence". Write ≉ as \not\approx, which needs no package.

The full set of commands

All of these compiled in our test with \usepackage{amsmath,amssymb}. The full relations list, with copy-paste commands, is in the relations section of the symbol reference.

A worked example in align

Put the & before \approx, as you would before =:

\documentclass{article}
\usepackage{amsmath}
\begin{document}

\begin{align}
  \pi          &\approx 3.1416, \\
  \sqrt{2}     &\approx 1.4142, \\
  e            &\approx 2.7183, \\
  \tfrac{1}{3} &\approx 0.3333.
\end{align}

For small $x$,
\begin{align*}
  \sin x &\approx x - \frac{x^3}{6}, &
  (1 + x)^n &\approx 1 + nx, &
  e^x &\approx 1 + x + \frac{x^2}{2}.
\end{align*}

\end{document}

\sim for "distributed as" and order of magnitude

In statistics $X \sim \mathcal{N}(\mu, \sigma^2)$ reads "X is normally distributed with mean μ and variance σ²". In physics and asymptotics ∼ means "of the order of" or "asymptotically equivalent to", as in Stirling's formula. \approx is wrong in both places, and \sim is wrong for a rounded number.

\usepackage{amsmath,amssymb}

Distribution: $X \sim \mathcal{N}(\mu, \sigma^2)$, \quad $K \sim \mathrm{Poisson}(\lambda)$.

Asymptotics: $n! \sim \sqrt{2\pi n}\,(n/e)^n$, \quad $\pi(x) \sim x/\ln x$.

Order of magnitude: $L \sim 10^{3}\,\mathrm{m}$, \quad bounds: $f(n) \lesssim g(n)$.

Three errors and what they mean

The first one, from the line The value is \approx 3.14. TeX inserts a $ and carries on, so the rest of the paragraph is set as math and a second "Missing $" follows at its end:

./main.tex:3: Missing $ inserted.
<inserted text>
                $
l.3 The value is \approx
                         3.14.
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

≈ in text, and the typed character

In a sentence write $\approx$, or define a shortcut with \ensuremath that works in both modes. In text, follow it with {}: a command name swallows the next space, so \apx 3 cm prints "≈3 cm" and \apx{} 3 cm prints "≈ 3 cm". A pasted ≈ works in pdfLaTeX only after a \DeclareUnicodeCharacter line. With XeLaTeX or LuaLaTeX and unicode-math it works in math mode as is, but in text it printed nothing in our test (the default Latin Modern text font has no ≈), so keep it in $...$ there too.

\documentclass{article}
\DeclareUnicodeCharacter{2248}{\ensuremath{\approx}}  % pdfLaTeX: make a pasted ≈ work
\newcommand{\apx}{\ensuremath{\approx}}              % works in text and in math
\begin{document}

The length is \apx{} 3 cm, and in math $L \apx 3$.

Typed directly: $x ≈ y$ and in text ≈ 3 cm.

\end{document}

When to Use ≈, When to Use ~ and ±, and When ≈ Is Wrong

• Rounding: ≈ is right for a shortened number, and the digits shown are the implied precision. If a table states that all values are rounded, many journals prefer a plain = in it.
• Order of magnitude: use ~ (\sim) when only the scale is meant: N ~ 10²³ particles. ≈ 10²³ would claim the coefficient is close to 1.
• Tolerances and uncertainty: write 9.81 ± 0.02 m/s², not ≈. The plus-minus symbol gives a range; ≈ says nothing about how far off the value could be.
• Definitions and identities: never write ≈ for an exact equality. 0.999… = 1, not ≈ 1; a definition uses =, := or \triangleq.
• Congruence and isomorphism: use ≅ (\cong), and ≡ for modular arithmetic. ≈ there reads as a rounding statement.
• Values known to differ: use ≠; see the not equal sign. ≈ and ≠ are not opposites: 3.14 ≠ π and 3.14 ≈ π are both true.

Complete Example

Each relation in its proper place: ≈ for rounding, ∼ for a distribution and an asymptotic law, ± for a tolerance, ≅ for congruence, and the amssymb bounds.

\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}   % \thickapprox, \approxeq, \lesssim, \gtrsim, \nsim, \ncong
\newcommand{\apx}{\ensuremath{\approx}}   % usable in text and math

\begin{document}

\section*{Rounding}
Since $\pi = 3.14159\ldots$ we write $\pi \approx 3.14$ to two decimal places, and
\begin{align}
  \sqrt{2} &\approx 1.414, &
  e        &\approx 2.718, &
  \ln 2    &\approx 0.693.
\end{align}
The error of the first approximation is $|\sqrt{2} - 1.414| \approx 2.1 \times 10^{-4}$,
so $\sqrt{2} \not\approx 1.5$ at this precision.

\section*{Scale, distribution and tolerance}
A typical cell is $\sim 10\,\mu\mathrm{m}$ across, the sample mean satisfies
$\bar{X} \sim \mathcal{N}(\mu, \sigma^2/n)$, and Stirling's formula gives
$n! \sim \sqrt{2\pi n}\,(n/e)^n$. The measured value is $g = 9.81 \pm 0.02\ \mathrm{m/s^2}$,
and the runtime is bounded by $T(n) \lesssim n \log n$.

\section*{Not approximation}
Triangles $ABC \cong DEF$ are congruent, $7 \equiv 1 \pmod 3$, and $0.999\ldots = 1$ exactly.
In text the length is \apx{} 3 cm; the heavier $a \thickapprox b$ and $a \approxeq b$ are
amssymb variants.

\end{document}

Frequently Asked Questions

What does the ≈ symbol mean?

≈ means "approximately equal to" or "almost equal to": the two sides are close enough for the purpose but not identical, usually because one is rounded or estimated, as in π ≈ 3.14. Its Unicode name is ALMOST EQUAL TO (U+2248).

How do I type the approximately equal symbol?

On Windows hold Alt and type 247 on the numeric keypad, or in Word type 2248 then Alt+X. On a Mac (U.S. layout) press Option+X. On iPhone tap 123, then #+=, and hold the = key. In HTML write ≈ or ≈; in LaTeX, \approx in math mode. Or copy it: ≈

How do I write approximately equal in LaTeX?

Use \approx in math mode: $\pi \approx 3.1416$. It needs no package. Its relatives are \sim, \simeq, \cong and \doteq; amssymb adds \thickapprox, \approxeq, \lesssim and \gtrsim. "Not approximately equal" is \not\approx (there is no \napprox). Outside math mode \approx stops with "Missing $ inserted".

What is the difference between ≈ and ~?

The tilde (~ on the keyboard, ∼ U+223C in math) is looser: "of the same order of magnitude", "asymptotic to" or "distributed as", and in everyday writing a rough estimate (~10 minutes). ≈ says the values are close, as with a rounded number. Use ≈ when the digits matter and ~ when only the scale does.

What is the difference between ≈ and ≅?

They look alike and Unicode even names ≅ (U+2245) APPROXIMATELY EQUAL TO, but in practice ≅ means congruent (geometry) or isomorphic (algebra), and ≈ means almost equal in value. For a rounded number use ≈, never ≅.

What is the Alt code for approximately equal?

Alt+247: hold Alt, type 247 on the numeric keypad with Num Lock on, and release. That works where Windows uses the US code page 437; on code page 850 (common in Western Europe) it gives ¸ instead. Without a keypad, use Win+. and the Symbols tab, or type 2248 then Alt+X in Word.

Next Steps

The symbols that sit next to ≈ in most documents:

• The Tilde Symbol ~ – The single squiggle: its meanings, the three Unicode tildes and how to type it
• The Plus-Minus Symbol ± – Tolerances and uncertainty, where ≈ is the wrong choice
• The Not Equal Sign ≠ – Alt codes, HTML and \neq
• The Congruent Symbol ≅ – The lookalike that means something else
• Mathematical Expressions in LaTeX – Inline and display math, where \approx lives
• Greek Letters & Math Symbols – π, σ, μ and the rest of the relation symbols

Free LaTeX Tools

• Relation Symbols Reference – ≈, ∼, ≃, ≅, ≤, ≥ and every other relation with its LaTeX command
• LaTeX Symbols Reference – All categories: Greek letters, arrows, operators, set theory and more
• LaTeX Preview – Paste any example above and see the PDF without installing TeX