Math and Science Symbols

• ∈

  Element of

  Said: is an element of, or in

  Set membership. "x ∈ A" states that x is an element of the set A. A slash through it (∉) means "is not an element of".

  • Math

  Unicode

  U+2208

  LaTeX

  \in

  HTML

  ∈

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• ∀

  For all

  Said: for all, or for every

  Universal quantifier. "∀x" means the statement that follows holds for every x in the domain under discussion.

  • Math

  Unicode

  U+2200

  LaTeX

  \forall

  HTML

  ∀

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• ∃

  There exists

  Said: there exists, or there is

  Existential quantifier. "∃x" means there is at least one x for which the statement holds. "∃!" means there exists exactly one.

  • Math

  Unicode

  U+2203

  LaTeX

  \exists

  HTML

  ∃

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• ∑

  Summation

  Said: sum, or the sum over

  Add a sequence of terms. The index and its range sit below and above the sign, as in the sum over i from 1 to n of a_i.

  This is the N-ary summation sign (U+2211), distinct from the Greek capital letter sigma Σ (U+03A3).

  • Math

  Unicode

  U+2211

  LaTeX

  \sum

  HTML

  ∑

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• ∏

  Product

  Said: product, or the product over

  Multiply a sequence of terms together, the multiplicative analogue of the summation sign.

  This is the N-ary product sign (U+220F), distinct from the Greek capital letter pi Π (U+03A0).

  • Math

  Unicode

  U+220F

  LaTeX

  \prod

  HTML

  ∏

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• ∇

  Nabla (del)

  Said: del, or nabla

  The vector differential operator. Applied to a scalar field it gives the gradient; with a dot (∇·) it gives the divergence of a vector field, and with a cross (∇×) the curl.

  • Math
  • Physics

  Unicode

  U+2207

  LaTeX

  \nabla

  HTML

  ∇

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• ∂

  Partial derivative

  Said: partial, or dee

  The partial derivative sign. ∂f/∂x is the derivative of f with respect to x while the other variables are held fixed.

  • Math
  • Physics

  Unicode

  U+2202

  LaTeX

  \partial

  HTML

  ∂

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• ∞

  Infinity

  Said: infinity

  A quantity without bound, or a limit taken as a variable grows without bound. It is a concept, not a number you can compute with directly.

  • Math

  Unicode

  U+221E

  LaTeX

  \infty

  HTML

  ∞

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• ≈

  Approximately equal to

  Said: approximately equal to

  The two sides are close in value but not necessarily exactly equal.

  • Math

  Unicode

  U+2248

  LaTeX

  \approx

  HTML

  ≈

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• ≠

  Not equal to

  Said: not equal to

  The two sides have different values.

  • Math

  Unicode

  U+2260

  LaTeX

  \neq

  HTML

  ≠

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• ≤

  Less than or equal to

  Said: less than or equal to

  The left side is smaller than or equal to the right side.

  • Math

  Unicode

  U+2264

  LaTeX

  \leq

  HTML

  ≤

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• ≥

  Greater than or equal to

  Said: greater than or equal to

  The left side is larger than or equal to the right side.

  • Math

  Unicode

  U+2265

  LaTeX

  \geq

  HTML

  ≥

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• ∝

  Proportional to

  Said: proportional to

  One quantity is a constant multiple of another. "y ∝ x" means y equals some fixed constant times x.

  • Math

  Unicode

  U+221D

  LaTeX

  \propto

  HTML

  ∝

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• ∴

  Therefore

  Said: therefore

  Introduces a conclusion that follows from the preceding statements.

  • Math

  Unicode

  U+2234

  LaTeX

  \therefore

  HTML

  ∴

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• ⊂

  Subset of

  Said: is a subset of

  Set inclusion. "A ⊂ B" means every element of A is also in B. Some authors use it only for a proper (strict) subset; use ⊆ when equality is allowed.

  • Math

  Unicode

  U+2282

  LaTeX

  \subset

  HTML

  ⊂

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• ⊆

  Subset of or equal to

  Said: is a subset of or equal to

  Set inclusion that explicitly allows the two sets to be equal. Every element of A is in B, and A may equal B.

  • Math

  Unicode

  U+2286

  LaTeX

  \subseteq

  HTML

  ⊆

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• ∪

  Union

  Said: union, or cup

  The set of all elements that are in A, in B, or in both.

  • Math

  Unicode

  U+222A

  LaTeX

  \cup

  HTML

  ∪

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• ∩

  Intersection

  Said: intersection, or cap

  The set of elements that are in both A and B.

  • Math

  Unicode

  U+2229

  LaTeX

  \cap

  HTML

  ∩

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• ∅

  Empty set

  Said: the empty set, or null set

  The set with no elements. It is a subset of every set.

  • Math

  Unicode

  U+2205

  LaTeX

  \varnothing

  HTML

  ∅

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• ∫

  Integral

  Said: integral, or the integral of

  Integration. A definite integral (with limits on the sign) gives the signed area under a curve; an indefinite integral gives a family of antiderivatives.

  • Math

  Unicode

  U+222B

  LaTeX

  \int

  HTML

  ∫

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• ⇒

  Implies

  Said: implies

  Logical implication. "P ⇒ Q" means if P is true then Q is true; it says nothing about Q when P is false.

  • Math

  Unicode

  U+21D2

  LaTeX

  \Rightarrow

  HTML

  ⇒

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• ⇔

  If and only if

  Said: if and only if, or iff

  Logical equivalence. "P ⇔ Q" means each implies the other: they are true together and false together.

  • Math

  Unicode

  U+21D4

  LaTeX

  \Leftrightarrow

  HTML

  ⇔

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• ±

  Plus or minus

  Said: plus or minus

  Either add or subtract the quantity. Used for the two roots of a quadratic, and for a value together with its uncertainty, as in 9.8 ± 0.1.

  • Math

  Unicode

  U+00B1

  LaTeX

  \pm

  HTML

  ±

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• ×

  Multiplication sign

  Said: times, or cross

  Multiplication of numbers. Between vectors it denotes the cross product, whose result is a vector perpendicular to both inputs.

  • Math

  Unicode

  U+00D7

  LaTeX

  \times

  HTML

  ×

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• ÷

  Division sign

  Said: divided by

  Division of one quantity by another.

  • Math

  Unicode

  U+00F7

  LaTeX

  \div

  HTML

  ÷

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• √

  Square root (radical)

  Said: the square root of

  The principal (non-negative) square root of the quantity under the sign. A small index on the sign gives an nth root instead.

  • Math

  Unicode

  U+221A

  LaTeX

  \sqrt{}

  HTML

  √

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• ≡

  Identical to / congruent

  Said: is identical to, or is congruent to

  Identity or definition (true for all values), or, in number theory, congruence modulo n as in "a ≡ b (mod n)".

  • Math

  Unicode

  U+2261

  LaTeX

  \equiv

  HTML

  ≡

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• μ

  Population mean

  Said: mew (rhymes with few)

  The mean of an entire population, the expected value of the distribution. It is estimated from data by the sample mean x-bar.

  In physics the same letter denotes friction, permeability, or the prefix micro.

  • Statistics

  Unicode

  U+03BC

  LaTeX

  \mu

  HTML

  μ

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• σ

  Population standard deviation

  Said: sig-muh

  The standard deviation of a population, the square root of the variance and a measure of spread in the same units as the data. Estimated from a sample by s.

  In physics the same letter denotes the Stefan-Boltzmann constant, conductivity, or stress.

  • Statistics

  Unicode

  U+03C3

  LaTeX

  \sigma

  HTML

  σ

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• σ²

  Population variance

  Said: sigma squared

  The variance of a population, the average squared deviation from the mean. Its square root is the standard deviation. The sample estimate is s-squared.

  • Statistics

  Unicode

  U+03C3 U+00B2

  LaTeX

  \sigma^2

  HTML

  σ²

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• ρ

  Population correlation coefficient

  Said: roh (rhymes with go)

  The true (population) Pearson correlation between two variables, ranging from -1 to 1 and estimated by the sample r. Also names Spearman rank correlation.

  In physics the same letter denotes density, resistivity, or charge density.

  • Statistics

  Unicode

  U+03C1

  LaTeX

  \rho

  HTML

  ρ

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• χ²

  Chi-squared

  Said: kai-squared (kai rhymes with sky)

  The chi-squared statistic and distribution, used in goodness-of-fit tests and tests of independence for categorical data. Larger values indicate greater departure from the null.

  • Statistics

  Unicode

  U+03C7 U+00B2

  LaTeX

  \chi^2

  HTML

  χ²

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• x̄

  Sample mean

  Said: x-bar

  The arithmetic mean of a sample, the sum of the observations divided by their count. It is the usual estimate of the population mean mu.

  • Statistics

  Unicode

  U+0078 U+0304

  LaTeX

  \bar{x}

  HTML

  x̄

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• p̂

  Sample proportion

  Said: p-hat

  The observed proportion of successes in a sample, the count of successes divided by the sample size. It estimates the population proportion p.

  • Statistics

  Unicode

  U+0070 U+0302

  LaTeX

  \hat{p}

  HTML

  p̂

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• H₀

  Null hypothesis

  Said: H-naught, or H-zero

  The default claim of no effect or no difference that a test is set up to reject. A test never proves H0; it either rejects it or fails to reject it.

  • Statistics

  Unicode

  U+0048 U+2080

  LaTeX

  H_0

  HTML

  H₀

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• H₁

  Alternative hypothesis

  Said: H-one

  The claim of a real effect or difference, accepted only when the data give enough evidence to reject the null hypothesis. Sometimes written H_a.

  • Statistics

  Unicode

  U+0048 U+2081

  LaTeX

  H_1

  HTML

  H₁

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• α

  Significance level

  Said: AL-fuh

  The significance level, the probability of a Type I error (rejecting a true null hypothesis). Fixed before the test, commonly at 0.05.

  In psychometrics, Cronbach alpha instead denotes a reliability coefficient.

  • Statistics

  Unicode

  U+03B1

  LaTeX

  \alpha

  HTML

  α

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• β

  Type II error rate / regression coefficient

  Said: BAY-tuh

  The probability of a Type II error (failing to reject a false null); statistical power equals 1 minus beta. In regression, beta is a coefficient (slope) on a predictor.

  • Statistics

  Unicode

  U+03B2

  LaTeX

  \beta

  HTML

  β

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• λ

  Rate parameter

  Said: LAM-duh

  The rate parameter of a Poisson distribution (mean events per interval) or of an exponential distribution (events per unit time).

  The same letter is wavelength, a decay constant, or an eigenvalue in other fields.

  • Statistics

  Unicode

  U+03BB

  LaTeX

  \lambda

  HTML

  λ

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• θ

  Generic parameter

  Said: THAY-tuh

  A stand-in for the unknown quantity being estimated, for example a distribution parameter in maximum-likelihood or Bayesian inference.

  In geometry and physics the same letter denotes an angle.

  • Statistics

  Unicode

  U+03B8

  LaTeX

  \theta

  HTML

  θ

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• r

  Sample correlation coefficient

  Said: r

  The Pearson sample correlation coefficient, measuring linear association between two variables from -1 (perfect negative) through 0 (none) to 1 (perfect positive). Its square, r-squared, is the fraction of variance explained.

  • Statistics

  Unicode

  U+0072

  LaTeX

  r

  HTML

  r

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• p

  p-value

  Said: p, or p-value

  The probability, assuming the null hypothesis is true, of a result at least as extreme as the one observed. A small p-value is evidence against the null; it is not the probability that the null is true.

  Distinct from a population proportion p, which is estimated by p-hat.

  • Statistics

  Unicode

  U+0070

  LaTeX

  p

  HTML

  p

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• s

  Sample standard deviation

  Said: s

  The standard deviation computed from a sample, using n minus 1 in the denominator (Bessel correction). It estimates the population standard deviation sigma.

  • Statistics

  Unicode

  U+0073

  LaTeX

  s

  HTML

  s

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• s²

  Sample variance

  Said: s squared

  The unbiased sample variance: the sum of squared deviations from the sample mean divided by n minus 1. It estimates the population variance.

  • Statistics

  Unicode

  U+0073 U+00B2

  LaTeX

  s^2

  HTML

  s²

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• n

  Sample size

  Said: n

  The number of observations in a sample. Capital N usually denotes the size of the whole population.

  • Statistics

  Unicode

  U+006E

  LaTeX

  n

  HTML

  n

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• Σ

  Summation / covariance matrix

  Said: SIG-muh (capital)

  As an operator, the summation sign in formulas. In multivariate statistics, capital sigma also denotes the covariance matrix of a random vector.

  The dedicated summation glyph is ∑ (U+2211); this is the Greek capital letter.

  • Statistics

  Unicode

  U+03A3

  LaTeX

  \Sigma

  HTML

  Σ

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• E

  Expectation operator

  Said: E, or expectation of

  The expected-value operator. E[X] is the long-run average (mean) of the random variable X; E is linear, so E[aX + b] equals aE[X] + b.

  In physics the same letter denotes energy or an electric field.

  • Statistics

  Unicode

  U+0045

  LaTeX

  \mathbb{E}

  HTML

  E

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• z

  z-score / z-statistic

  Said: z (zee or zed)

  The number of standard deviations an observation lies from the mean. As a test statistic it follows the standard normal distribution, used when the variance is known or the sample is large.

  • Statistics

  Unicode

  U+007A

  LaTeX

  z

  HTML

  z

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• t

  Student's t-statistic

  Said: t

  The test statistic for a mean when the population variance is unknown and estimated from the sample. It follows Student's t-distribution, which has heavier tails than the normal for small samples.

  In physics t usually denotes time.

  • Statistics

  Unicode

  U+0074

  LaTeX

  t

  HTML

  t

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• F

  F-statistic

  Said: F

  A ratio of two variances, used in ANOVA and to compare nested models. It follows the F-distribution with a pair of degrees-of-freedom parameters.

  In physics F usually denotes force.

  • Statistics

  Unicode

  U+0046

  LaTeX

  F

  HTML

  F

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• ν

  Degrees of freedom

  Said: new (nyoo)

  The number of independent values free to vary when computing a statistic. It indexes the t, chi-squared, and F distributions and is often written df or k.

  In physics the same letter denotes frequency.

  • Statistics

  Unicode

  U+03BD

  LaTeX

  \nu

  HTML

  ν

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• κ

  Cohen's kappa

  Said: KAP-uh

  A measure of agreement between two raters on categorical items that corrects for the agreement expected by chance. 1 is perfect agreement, 0 is chance-level.

  In physics the same letter denotes thermal conductivity, curvature, or the dielectric constant.

  • Statistics

  Unicode

  U+03BA

  LaTeX

  \kappa

  HTML

  κ

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• d

  Cohen's d

  Said: d

  A standardized effect size: the difference between two group means divided by their pooled standard deviation. Roughly, 0.2 is small, 0.5 medium, 0.8 large.

  In calculus a lowercase d also marks a differential, as in dx.

  • Statistics

  Unicode

  U+0064

  LaTeX

  d

  HTML

  d

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• α

  Alpha (physics and chemistry)

  Said: AL-fuh

  Several uses: an alpha particle (a helium-4 nucleus) and alpha decay in nuclear physics; angular acceleration in mechanics; the fine-structure constant in atomic physics; the alpha carbon in chemistry.

  In statistics the same letter is the significance level.

  • Physics
  • Chemistry

  Unicode

  U+03B1

  LaTeX

  \alpha

  HTML

  α

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• β

  Beta (physics)

  Said: BAY-tuh

  A beta particle (an electron or positron emitted in beta decay), and in special relativity the speed ratio v/c.

  In statistics the same letter is the Type II error rate or a regression coefficient.

  • Physics

  Unicode

  U+03B2

  LaTeX

  \beta

  HTML

  β

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• γ

  Gamma (physics and chemistry)

  Said: GAM-uh

  A gamma ray (a high-energy photon); the Lorentz factor in special relativity; the heat-capacity ratio Cp/Cv of a gas; a surface tension in physical chemistry.

  • Physics
  • Chemistry

  Unicode

  U+03B3

  LaTeX

  \gamma

  HTML

  γ

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• δ

  Delta, lowercase (small change / partial charge)

  Said: DEL-tuh

  A small or infinitesimal change; in chemistry a partial charge on an atom (δ+ or δ-) in a polar bond; in math and physics the Dirac delta function or the Kronecker delta.

  • Math
  • Physics
  • Chemistry

  Unicode

  U+03B4

  LaTeX

  \delta

  HTML

  δ

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• Δ

  Delta, capital (change / difference)

  Said: DEL-tuh (capital)

  A finite change in a quantity, final minus initial, as in ΔH for enthalpy change or Δx for displacement. In algebra it is the discriminant b² minus 4ac; in physics it can denote the Laplace operator.

  • Math
  • Physics
  • Chemistry

  Unicode

  U+0394

  LaTeX

  \Delta

  HTML

  Δ

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• ε

  Epsilon

  Said: EP-si-lon

  A small positive quantity (as in epsilon-delta limits); permittivity in electromagnetism (ε0 is the vacuum permittivity); molar absorptivity in the Beer-Lambert law; strain in mechanics.

  • Math
  • Physics
  • Chemistry

  Unicode

  U+03B5

  LaTeX

  \varepsilon

  HTML

  ε

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• η

  Eta

  Said: AY-tuh

  Efficiency of an engine or process (output over input); dynamic viscosity in fluid dynamics.

  • Physics
  • Chemistry

  Unicode

  U+03B7

  LaTeX

  \eta

  HTML

  η

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• θ

  Theta (angle)

  Said: THAY-tuh

  An angle, measured in radians or degrees; in spherical coordinates the polar angle measured from the vertical axis.

  In statistics the same letter denotes a generic unknown parameter.

  • Math
  • Physics

  Unicode

  U+03B8

  LaTeX

  \theta

  HTML

  θ

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• κ

  Kappa (physics)

  Said: KAP-uh

  Thermal conductivity; the dielectric constant of a material; the curvature of a curve in geometry.

  In statistics the same letter denotes Cohen's kappa.

  • Physics
  • Math

  Unicode

  U+03BA

  LaTeX

  \kappa

  HTML

  κ

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• λ

  Wavelength

  Said: LAM-duh

  The wavelength of a wave, the distance over which its shape repeats. For light it relates to frequency by the speed of light: c equals lambda times frequency.

  The same letter is also a decay constant, an eigenvalue, or a Poisson rate.

  • Physics

  Unicode

  U+03BB

  LaTeX

  \lambda

  HTML

  λ

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• λ

  Decay constant

  Said: LAM-duh

  The decay constant of a radioactive isotope: the probability per unit time that a given nucleus decays. It is the reciprocal of the mean lifetime, and the half-life is ln 2 divided by lambda.

  • Physics
  • Chemistry

  Unicode

  U+03BB

  LaTeX

  \lambda

  HTML

  λ

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• λ

  Eigenvalue

  Said: LAM-duh

  An eigenvalue of a matrix or linear operator A: a scalar lambda for which there is a nonzero vector v with Av equal to lambda times v.

  • Math

  Unicode

  U+03BB

  LaTeX

  \lambda

  HTML

  λ

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• μ

  Mu (physics and chemistry)

  Said: mew (rhymes with few)

  The coefficient of friction and magnetic permeability (μ0 is the vacuum permeability) in physics; the SI prefix micro (10^-6); in chemistry the chemical potential or a molecular dipole moment.

  In statistics the same letter is the population mean.

  • Physics
  • Chemistry

  Unicode

  U+03BC

  LaTeX

  \mu

  HTML

  μ

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• ν

  Nu (frequency)

  Said: new (nyoo)

  The frequency of a wave in hertz (cycles per second), as in the photon energy E equals h times nu; also the neutrino in particle physics, and kinematic viscosity in fluids.

  In statistics the same letter denotes degrees of freedom. Take care not to confuse it with v.

  • Physics

  Unicode

  U+03BD

  LaTeX

  \nu

  HTML

  ν

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• π

  Pi (the constant)

  Said: pie

  The ratio of a circle circumference to its diameter, about 3.14159. An irrational, transcendental number that appears throughout geometry, trigonometry, and analysis.

  Capital pi Π is the product operator; a chemistry use of lowercase pi is separate.

  • Math

  Unicode

  U+03C0

  LaTeX

  \pi

  HTML

  π

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• π

  Pi (chemistry)

  Said: pie

  Osmotic pressure of a solution; a pi bond, formed by sideways overlap of p orbitals, or the pi electrons of a conjugated system.

  • Chemistry

  Unicode

  U+03C0

  LaTeX

  \pi

  HTML

  π

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• ρ

  Rho (physics and chemistry)

  Said: roh (rhymes with go)

  Density (mass per unit volume); electrical resistivity of a material; and volume charge density in electromagnetism.

  In statistics the same letter is the population correlation coefficient.

  • Physics
  • Chemistry

  Unicode

  U+03C1

  LaTeX

  \rho

  HTML

  ρ

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• σ

  Sigma (physics and chemistry)

  Said: SIG-muh

  The Stefan-Boltzmann constant in blackbody radiation; electrical conductivity; mechanical stress (force per area); surface charge density; a scattering cross section; and a sigma bond in chemistry.

  In statistics the same letter is the standard deviation.

  • Physics
  • Chemistry

  Unicode

  U+03C3

  LaTeX

  \sigma

  HTML

  σ

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• τ

  Tau

  Said: taw (or rhyming with cow)

  Torque in rotational mechanics; a time constant, as the RC time constant of a circuit or a mean radioactive lifetime; shear stress; the tau lepton in particle physics.

  • Physics

  Unicode

  U+03C4

  LaTeX

  \tau

  HTML

  τ

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• φ

  Phi

  Said: fie or fee

  A phase or angle in a wave; the golden ratio (about 1.618); the electric potential; the work function in the photoelectric effect. Magnetic flux is usually capital Phi.

  • Math
  • Physics

  Unicode

  U+03C6

  LaTeX

  \varphi

  HTML

  φ

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• χ

  Chi (chemistry and physics)

  Said: kai (rhymes with sky)

  Electronegativity, the tendency of an atom to attract bonding electrons, in chemistry; magnetic or electric susceptibility in physics.

  In statistics the squared form chi-squared is a test statistic.

  • Chemistry
  • Physics

  Unicode

  U+03C7

  LaTeX

  \chi

  HTML

  χ

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• ψ

  Psi (wavefunction)

  Said: sigh (or psy)

  The wavefunction in quantum mechanics. Its squared magnitude gives the probability density of finding a particle at a point.

  • Physics

  Unicode

  U+03C8

  LaTeX

  \psi

  HTML

  ψ

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• ω

  Omega, lowercase (angular frequency)

  Said: oh-MAY-guh

  Angular frequency or angular velocity in radians per second, equal to 2 pi times the ordinary frequency.

  • Physics

  Unicode

  U+03C9

  LaTeX

  \omega

  HTML

  ω

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• Ω

  Omega, capital (ohm)

  Said: oh-MAY-guh (capital)

  The ohm, the SI unit of electrical resistance; also a solid angle in steradians, and the number of microstates in statistical mechanics.

  • Physics

  Unicode

  U+03A9

  LaTeX

  \Omega

  HTML

  Ω

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• Φ

  Phi, capital (flux)

  Said: fie or fee (capital)

  Flux through a surface: magnetic flux in Faraday law of induction, or electric flux in Gauss law.

  • Physics

  Unicode

  U+03A6

  LaTeX

  \Phi

  HTML

  Φ

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• ℏ

  Reduced Planck constant (h-bar)

  Said: h-bar

  The reduced Planck constant, the Planck constant h divided by 2 pi, about 1.055 times 10^-34 joule-seconds. It is the natural quantum of angular momentum and sets the scale of quantum effects.

  • Physics

  Unicode

  U+210F

  LaTeX

  \hbar

  HTML

  ℏ

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• °

  Degree

  Said: degree, or degrees

  Degrees of angle, one 360th of a full turn; or degrees of temperature, as in °C and °F.

  • Math
  • Physics
  • Chemistry

  Unicode

  U+00B0

  LaTeX

  ^{\circ}

  HTML

  °

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