Chi Symbol (Χ χ): Meaning, Uses, and How to Type It

Chi is the twenty-second letter of the Greek alphabet. The lowercase χ is best known from the chi-squared test and the χ² distribution in statistics, and it also stands for electric and magnetic susceptibility in physics, the Euler characteristic in topology, and characters in number theory and group theory. The uppercase Χ looks exactly like the Latin X, which is why it is rarely used as a symbol but survives in the Chi-Rho monogram and in the abbreviation "Xmas." To type chi, use \chi in LaTeX, the HTML entity χ, or the X key on a Greek keyboard layout.

This guide covers what each form of chi means, where it appears in statistics, physics, math, and chemistry, and how to type χ and Χ on Mac, Windows, iPhone, in HTML, and in LaTeX.

The Chi Symbol Explained

Chi has two shapes, both of which you can copy from here:

• Χ — uppercase chi (Unicode U+03A7)
• χ — lowercase chi (Unicode U+03C7)

Unlike theta, phi, or rho, chi has no variant glyph, so there is no \varchi in LaTeX. The name is pronounced "kai" (rhyming with "sky") in English and "khee" in modern Greek. In the Greek numeral system chi stood for 600. The Latin letter X descends from the western Greek form of chi, which is why χ sits on the X key of Greek keyboards.

Chi should not be confused with qi (sometimes spelled chi), the concept of vital energy in Chinese philosophy. The two words sound alike in English but have nothing to do with each other.

Uppercase Chi (Χ)

Because uppercase chi is visually identical to the Latin capital X, it is almost never used as a mathematical variable. Its uses are cultural rather than scientific:

• Chi-Rho (☧) — a monogram of Χ and Ρ, the first two letters of ΧΡΙΣΤΟΣ (Christos), adopted by Emperor Constantine and one of the oldest Christian symbols
• Xmas — the X is a chi standing for "Christ," a usage that dates back centuries, not a modern abbreviation
• Fraternity and society names — Chi Omega, Alpha Chi Omega, Rho Chi, and many others

LaTeX has no \Chi command. If you need an upright capital chi in an equation, type \mathrm{X}.

Lowercase Chi (χ)

The lowercase chi carries almost all of the scientific meanings.

Uses of lowercase χ:

• Chi-squared (χ²) — the distribution and the test statistic
• Electric susceptibility — χ_e, how easily a material polarizes
• Magnetic susceptibility — χ_m, how a material responds to a magnetic field
• Euler characteristic — χ = V − E + F for a surface or polyhedron
• Characters — χ(g) in representation theory and χ(n) in number theory
• Indicator function — χ_A(x), which is 1 inside the set A and 0 outside
• Chromatic number — χ(G), the fewest colors needed to color a graph
• Electronegativity — χ on the Pauling scale in chemistry
• Flory–Huggins parameter — χ in polymer science

The Chi-Squared Distribution and Test

If Z₁, Z₂, …, Z_k are independent standard normal random variables, the sum of their squares follows a chi-squared distribution with k degrees of freedom:

Q = Z₁² + Z₂² + … + Z_k² ~ χ²(k)

The distribution has mean k and variance 2k, and it is always non-negative and right-skewed. It appears throughout statistics because sums of squared deviations are everywhere: in variance estimates, goodness-of-fit tests, and likelihood-ratio statistics.

Pearson's chi-squared test, published by Karl Pearson in 1900, compares observed counts O_i with the counts E_i expected under a hypothesis:

χ² = Σ (O_i − E_i)² / E_i

A large value means the observations are far from what the hypothesis predicts. The test is used in two common forms:

• Goodness of fit — does a die show each face equally often? Degrees of freedom: number of categories minus 1
• Test of independence — are two categorical variables related, such as smoking and lung disease in a contingency table? Degrees of freedom: (rows − 1) × (columns − 1)

The symbol is written χ² (chi-squared), never "x²," and the name is spelled "chi-squared" or "chi-square"; both are accepted. A rule of thumb is that every expected count should be at least 5 for the approximation to be reliable.

Susceptibility in Physics

Susceptibility measures how strongly a material responds to an applied field. Electric susceptibility χ_e links the polarization P of a dielectric to the electric field E:

P = ε₀ χ_e E

The relative permittivity (dielectric constant) is ε_r = 1 + χ_e, so vacuum has χ_e = 0 and water around 79 at room temperature.

Magnetic susceptibility χ_m links magnetization M to the magnetic field strength H:

M = χ_m H, with μ_r = 1 + χ_m

The sign of χ_m classifies materials: diamagnetic materials such as water and copper have small negative values, paramagnetic materials such as aluminum have small positive values, and ferromagnetic materials such as iron have large positive values that depend on the field's history. Curie's law states that for a paramagnet χ_m ∝ 1/T.

Euler Characteristic in Topology

The Euler characteristic χ is a number that describes a surface's shape regardless of how it is stretched. For a polyhedron with V vertices, E edges, and F faces:

χ = V − E + F

A cube has 8 − 12 + 6 = 2, and so does every polyhedron that can be inflated into a sphere. A torus has χ = 0, and a surface with g holes has χ = 2 − 2g. The Gauss–Bonnet theorem connects this topological number to geometry: the total Gaussian curvature of a closed surface equals 2πχ.

Characters in Algebra and Number Theory

In representation theory, the character of a representation ρ of a group is the trace of its matrices, χ(g) = tr ρ(g); character tables summarize the symmetry of molecules in chemistry. In number theory, a Dirichlet character χ(n) is a periodic, completely multiplicative function used to define Dirichlet L-functions L(s, χ), the tools behind Dirichlet's theorem on primes in arithmetic progressions.

Chi in Different Fields

Mathematics

• The χ² distribution and chi-squared test
• Euler characteristic χ of a surface or complex
• Characters χ in group theory and number theory
• Indicator function χ_A, also written 𝟙_A
• Chromatic number χ(G) of a graph

Physics

• Electric susceptibility χ_e and magnetic susceptibility χ_m
• Nonlinear optical susceptibilities χ⁽²⁾ and χ⁽³⁾, which govern frequency doubling and the Kerr effect
• Charmonium states such as χ_c in particle physics

Chemistry and Materials

• Electronegativity χ, with fluorine at 3.98 on the Pauling scale
• Flory–Huggins interaction parameter χ, which predicts whether a polymer dissolves in a solvent

Statistics

• Chi-squared tests for goodness of fit, independence, and homogeneity
• Chi-squared distribution of the scaled sample variance (n − 1)s²/σ²
• Likelihood-ratio tests, whose statistic is asymptotically χ²

How to Type Chi

Windows: Chi has no classic Alt code, so Alt + 967 works only in Microsoft Word and other apps that accept Unicode Alt codes. In Word, the most reliable method is to type 03C7 and press Alt + X. Elsewhere, open Character Map, search for "chi," and copy the character, or use the emoji panel (Win + .) and its Symbols tab.

Mac: macOS has no Option-key shortcut for chi. Add the Greek keyboard in System Settings > Keyboard > Input Sources, switch to it, and press X for χ or Shift + X for Χ. You can also open the Character Viewer with Control + Command + Space and search for "chi."

iPhone and iPad: Go to Settings > General > Keyboard > Keyboards > Add New Keyboard and choose Greek. Switch keyboards with the globe key; χ sits on the X key. Android users can add Greek in Gboard's language settings.

Word and Google Docs: In Word, use Insert > Symbol > More Symbols with the subset set to Greek and Coptic. In Google Docs, use Insert > Special characters and search for "chi." For χ², insert χ and then superscript the 2 with Ctrl + Shift + = (Windows) or Command + Shift + = (Mac).

HTML: Write χ for χ and Χ for Χ. Chi-squared is &chi;<sup>2</sup> or χ².

LaTeX: In math mode, \chi gives χ and \chi^2 gives χ². There is no \varchi and no \Chi; for an upright capital use \mathrm{X}. The following document compiles as written:

1\documentclass{article}
2\usepackage{amsmath}
3\begin{document}
4The test statistic $\chi^2$ follows a $\chi^2$ distribution with $k$ degrees of freedom.
5\[
6  \chi^2 = \sum_{i=1}^{n} \frac{(O_i - E_i)^2}{E_i},
7  \qquad
8  \mathbf{P} = \varepsilon_0 \chi_e \mathbf{E},
9  \qquad
10  \chi = V - E + F
11\]
12The Chi-Rho uses the capital letters $\mathrm{X}$ and $\mathrm{P}$.
13\end{document}
Copy

For chi in running text, the textgreek package provides \textchi, which gives an upright χ in the surrounding text font.

Related Greek Letters

The chi-squared test lives alongside σ (standard deviation) and the normal distribution; susceptibility χ sits next to the permittivity ε and permeability μ; and the Chi-Rho pairs χ with ρ.

• Sigma symbol (Σ σ) — the summation in the χ² formula and the standard deviation
• Mu symbol (Μ μ) — permeability, the partner of magnetic susceptibility
• Pi symbol (Π π) — appears in the Gauss–Bonnet theorem and the χ² density
• Theta symbol (Θ θ) — parameters tested with chi-squared statistics

The full list of letters is on our Greek alphabet reference, and Greek letters in math and science lists every letter's standard meanings. For a copy-and-paste palette, see the Greek symbol tool.

FAQ

What does the chi symbol mean in statistics?

χ² (chi-squared) names both a probability distribution and a family of hypothesis tests built on it. The test statistic Σ (O − E)²/E compares observed counts with expected counts; if it is larger than the critical value from the χ² distribution, the hypothesis is rejected.

Is chi-squared written χ² or x²?

Always χ², with the Greek letter chi. Writing x² is a common mistake that changes the meaning, because x usually denotes a data value. In LaTeX use \chi^2, and in Word insert χ followed by a superscript 2.

How do you pronounce chi?

In English the letter is pronounced "kai," rhyming with "sky," so the test is "kai-squared." Modern Greek speakers say "khee," with a throaty h sound.

Is Χ the same as the letter X?

No. Uppercase chi Χ (U+03A7) and the Latin X (U+0058) look identical in most fonts but are different characters. Software treats them as unrelated, so always use the real Greek letter when you mean chi and the Latin letter when you mean x.

Writing with Greek Symbols

Papers that report chi-squared tests, susceptibilities, and Euler characteristics need chi typeset cleanly and consistently. In LaTeX that means \chi in math mode rather than a pasted Unicode character, which keeps spacing and italics correct throughout the document.

Octree is an AI-powered LaTeX editor that handles Greek letters, equations, and bibliography formatting for you, so you can focus on the ideas instead of the markup.

Create professional documents at https://www.useoctree.com