The squiggly line in math is called a tilde (~), and it has several different meanings depending on the context. Most commonly, it means “approximately equal to,” “similar to,” or “is distributed as.” You might see it as a single wave (~), a double wave (≈), or paired with other symbols like an equals sign (≅). Each version carries a distinct meaning.
Approximately Equal To (≈)
The most familiar use of the squiggly line is the double tilde (≈), which means “approximately equal to.” You’ll see this when a number has been rounded or estimated rather than calculated exactly. For example, π ≈ 3.14 tells you that pi is close to 3.14 but not exactly 3.14. The single tilde (~) is sometimes used the same way in casual notation, especially when typing on a keyboard where the ≈ symbol isn’t easy to access.
This symbol shows up constantly in everyday math, science, and engineering whenever exact values are impractical. If you’re estimating a square root, rounding a long decimal, or reporting a measurement with limited precision, the squiggly line signals that the number is close enough for the purpose at hand but not perfectly precise.
Similar To (~) in Geometry
In geometry, a single tilde (~) between two shapes means they are “similar.” Two geometric figures are similar when their corresponding angles are equal and their corresponding sides are in the same proportion. Think of it as the shapes being identical in form but different in size, like a photograph and an enlarged print of the same image.
For example, writing △ABC ~ △DEF means triangle ABC has the same angle measurements as triangle DEF, but the triangles may be different sizes. Every side of one triangle is scaled by the same factor relative to the other. This is different from congruence, which uses the symbol ≅ (a tilde sitting on top of an equals sign). Congruent figures are the same shape AND the same size. Similar figures only need to be the same shape.
Negation (~) in Logic
In formal logic, the tilde placed before a statement means “not.” Writing ~p translates to “not p,” flipping a true statement to false or a false statement to true. This use dates back to the Italian mathematician Giuseppe Peano, who introduced it in 1897.
Placement matters here. Writing ~p in the expression ~p ∧ q negates only the first part (p), while writing ~(p ∧ q) with parentheses negates the entire compound statement. If you’re working through a logic course, the tilde is one of the first symbols you’ll encounter, and it works much like the word “not” in plain English.
Distribution Notation (~) in Statistics
In statistics and probability, the tilde means “is distributed as” or “follows the distribution.” It connects a random variable to its probability distribution. For instance, X ~ N(μ, σ²) is shorthand for “X follows a normal distribution with mean μ and variance σ².” Penn State’s statistics program describes this as one of the most common shorthand notations in the field.
You’ll run into this in any statistics class once you start working with distributions. Rather than writing out “the variable X follows a normal distribution with a mean of 0 and a variance of 1,” statisticians simply write X ~ N(0, 1). The tilde is doing all the heavy lifting in that sentence, replacing several words with a single symbol.
Equivalence Relations (~) in Advanced Math
In higher-level mathematics, the tilde defines something called an equivalence relation. This is a formal way of saying two things are “equivalent” under a specific rule. For the tilde to qualify as an equivalence relation, it must satisfy three properties:
- Reflexive: every element is equivalent to itself (x ~ x)
- Symmetric: if x is equivalent to y, then y is equivalent to x (if x ~ y, then y ~ x)
- Transitive: if x is equivalent to y and y is equivalent to z, then x is equivalent to z
This concept is sometimes called the “twiddle” definition in textbooks. It shows up in abstract algebra and set theory, where you need precise rules for grouping things that share a property.
Other Squiggly Line Variants
Beyond the common uses above, a few rarer squiggly line symbols appear in specialized math:
- ≃ (tilde over a dash): means “asymptotically equal to,” used in calculus and analysis when two functions grow at the same rate as their input gets very large
- ≋ (triple tilde): a less common symbol occasionally used for strict equivalence in certain notations
- ≅ (tilde over equals): means “congruent to” in geometry, or “isomorphic to” in algebra
How to Type the Tilde
On most keyboards, the basic tilde (~) sits in the upper-left corner, sharing a key with the backtick (`). Press Shift and that key together. On Windows, you can also use the Alt code: hold Alt and type 126 on the number pad. The double tilde (≈) is harder to access. On a Mac, press Option + X. On Windows, you’ll typically need to insert it as a special character or copy it from a character map.
In many contexts, especially quick calculations, emails, or online discussions, people simply use the single tilde (~) as a stand-in for “approximately,” even though ≈ is technically the correct symbol for that meaning.