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How to Read Math Expressions

Learn to Pronounce Math Symbols and Formulas

Basic

Expression How to Read Translate Pronounce
$$a + b$$ a plus b Translate
$$a - b$$ a minus b Translate
$$a \cdot b$$ a times b Translate
$$a / b$$ a over b Translate
$$a > b$$ a is greater than b Translate
$$a < b$$ a is less than b Translate
$$a = b$$ a is equal to b Translate
$$a \neq b$$ a is not equal to b Translate
$$a \geq b$$ a is greater than or equal to b Translate
$$a \leq b$$ a is less than or equal to b Translate
$$x^2$$ x squared Translate
$$x^3$$ x cubed Translate
$$x^n$$ x to the power of n Translate
$$\sqrt{x}$$ the square root of x Translate
$$\sqrt[n]{x}$$ the n-th root of x Translate
$$\log x$$ the logarithm of x (base 10) Translate
$$\ln x$$ the natural logarithm of x (base e) Translate
$$e^x$$ e to the power of x Translate
$$|x|$$ the modulus of x Translate
$$\overline{x}$$ x bar (the average of x) Translate
$$a \pm b$$ a plus or minus b Translate
$$\frac{a}{b}$$ a over b (fraction) Translate
$$a!$$ a factorial Translate

Numbers

Expression How to Read Translate Pronounce
$$-5$$ negative five Translate
$$0.25$$ zero point two five Translate
$$1.5$$ one point five Translate

Fractions

Expression How to Read Translate Pronounce
$$\frac{1}{2}$$ one half Translate
$$\frac{3}{4}$$ three quarters Translate
$$\frac{1}{7}$$ one seventh Translate

Powers and Roots

Expression How to Read Translate Pronounce
$$3^2$$ three squared Translate
$$5^4$$ five to the power of four Translate
$$\sqrt{4}$$ the square root of four Translate
$$\sqrt[3]{8}$$ the cube root of eight Translate

Angle Operations

Expression How to Read Translate Pronounce
$$\sin \theta$$ sine of theta Translate
$$\cos \theta$$ cosine of theta Translate
$$\tan \theta$$ tangent of theta Translate
$$\csc \theta$$ cosecant of theta Translate
$$\sec \theta$$ secant of theta Translate
$$\cot \theta$$ cotangent of theta Translate
$$\sin^{-1} x$$ arcsine of x or inverse sine of x Translate
$$\cos^{-1} x$$ arccosine of x or inverse cosine of x Translate
$$\tan^{-1} x$$ arctangent of x or inverse tangent of x Translate
$$\sin(\alpha \pm \beta)$$ sine of (alpha plus or minus beta) Translate
$$\cos(\alpha \pm \beta)$$ cosine of (alpha plus or minus beta) Translate
$$\tan(\alpha \pm \beta)$$ tangent of (alpha plus or minus beta) Translate
$$\theta \pm \phi$$ theta plus or minus phi Translate
$$\theta \cdot \phi$$ theta times phi Translate
$$\theta / \phi$$ theta over phi Translate
$$\sinh x$$ hyperbolic sine of x Translate
$$\cosh x$$ hyperbolic cosine of x Translate
$$\tanh x$$ hyperbolic tangent of x Translate

Logic and Sets

Expression How to Read Translate Pronounce
$$a := b$$ a is defined by(given as) b Translate
$$S_1 \Rightarrow S_2$$ S sub one implies S sub two Translate
$$S_1 \Leftrightarrow S_2$$ S sub one is equivalent to S sub two Translate
$$\{a, b, c\}$$ the set of a, b, and c Translate
$$a \in A$$ a is an element of set A Translate
$$\emptyset \text{ or } \{\}$$ empty set Translate
$$A \subset B$$ A is a proper subset of B Translate
$$A \subseteq B$$ A is a subset of B Translate
$$A \cup B$$ A union B Translate
$$A \cap B$$ A intersection B Translate
$$A \setminus B$$ A minus B Translate
$$\equiv$$ is equivalent to Translate
$$\exists$$ there exists Translate
$$\nexists$$ there does not exist Translate
$$\forall$$ for all Translate
$$\exists p \in \mathbb{P}, p = 2$$ there exists a prime number p such that p equals two. Translate
$$\forall x \in \mathbb{R}, x + 0 = x$$ for all x in the set of real numbers, x plus zero equals x. Translate
$$\mathbb{N}$$ the set of all natural numbers Translate
$$\mathbb{Z}$$ the set of all integers Translate
$$\mathbb{Q}$$ the set of all rational numbers Translate
$$\mathbb{R}$$ the set of all real numbers Translate
$$\mathbb{C}$$ the set of all complex numbers Translate
$$\mathbb{P}$$ the set of all prime numbers Translate
$$A \triangle B$$ symmetric difference of A and B Translate
$$A^c$$ complement of A Translate
$$\overline{A}$$ closure of A Translate

Intervals

Expression How to Read Translate Pronounce
$$[a, b]$$ closed interval from a to b Translate
$$(a, b)$$ open interval from a to b Translate
$$[a, b)$$ the interval from a to b, inclusive of a and exclusive of b. Translate
$$(a, b]$$ the interval from a to b, exclusive of a and inclusive of b. Translate
$$(a, \infty)$$ the half line starting at a and extending to infinity, exclusive of a. Translate
$$(-\infty, a)$$ the half line starting at negative infinity and extending to a, exclusive of a. Translate

Factorials and Binomial Coefficients

Expression How to Read Translate Pronounce
$$n!$$ n factorial (the product of all positive integers up to n) Translate
$$\binom{n}{k} \text{or} nC_k$$ n choose k (the number of ways to choose k elements from a set of n elements) Translate
$$P(n,k)$$ permutation of n things taken k at a time Translate

Sum and Product

Expression How to Read Translate Pronounce
$$\sum_{n=1}^{\infty} a_n$$ the sum of a sub n from n equals 1 to infinity Translate
$$\sum_{k=0}^n \binom{n}{k}$$ the sum from k equals zero to n of n choose k Translate
$$( \sum_{k=1}^n a_k b_k )^2$$ the square of the sum of the products of a sub k and b sub k from k equals 1 to n Translate
$$\prod_{k=1}^n k$$ the product from k equals one to n of k (n factorial) Translate
$$\bigcup_{i=1}^n A_i$$ union of sets A sub i from i equals 1 to n Translate
$$\bigcap_{i=1}^n A_i$$ intersection of sets A sub i from i equals 1 to n Translate

Functions

Expression How to Read Translate Pronounce
$$\varphi$$ phi (variant) Translate
$$\varphi(0) = 0$$ phi of zero equals zero Translate
$$f : A \to B$$ f is a function that maps from the set A to the set B Translate
$$x \mapsto f(x)$$ x is mapped to f(x) Translate
$$g: \mathbb{R} \to \mathbb{C}, \theta \mapsto g(\theta) := e^{i\theta}$$ g from R(real numbers) to C(complex numbers), theta maps to g of theta, defined as(given by) e to the i theta Translate
$$f: \mathbb{R} \to \mathbb{R}, x \mapsto f(x) := 1 + x^2$$ f from R(real numbers) to R, x maps to f of x, defined as(given by) one plus x squared Translate
$$h: \mathbb{C} \to [0, \infty), z \mapsto h(z) := |z|$$ function h maps complex numbers C to the set of non-negative real numbers from zero to infinity, z maps to function h of z equals the modulus of z Translate
$$\text{im}(f)$$ image or range of f Translate
$$\text{im}(f) = B$$ the image(range) of f equals B Translate
$$f: A \to \text{im}(f)$$ f from A to the image of f Translate
$$f^{-1}$$ inverse function of f Translate
$$f^{-1}(b) := a$$ f inverse of b is defined as(given by) a Translate
$$f_{i,j}$$ f sub i comma j Translate
$$f \circ g$$ f composed with g Translate
$$\ker(f)$$ kernel of f Translate
$$f(x)$$ f of x Translate
$$\lim_{x \to 0}$$ x approaches 0 Translate

Calculus Operation Notations

Expression How to Read Translate Pronounce
$$\frac{d}{dx}$$ d by dx (the derivation with respect to x) Translate
$$\frac{d}{dx} f(x)$$ the derivative of f with respect to x Translate
$$f'(x)$$ f prime of x (the derivative of f with respect to x) Translate
$$\int f(x) dx$$ the integral of f with respect to x Translate
$$\int_a^b f(x) dx$$ the definite integral of f from a to b with respect to x Translate
$$\lim_{x \to a} f(x)$$ the limit of f as x approaches a Translate
$$\oint f(x) dx$$ the line integral of f with respect to x Translate

Vector calculus and physics

Expression How to Read Translate Pronounce
$$\nabla$$ nabla or del Translate
$$\nabla f$$ gradient of(nabla) f Translate
$$\nabla \cdot \mathbf{F}$$ divergence of(nabla dot) F Translate
$$\nabla \times \mathbf{F}$$ curl of(nabla cross) F Translate
$$\partial$$ partial Translate
$$\frac{\partial}{\partial x} f(x)$$ the partial derivative of f with respect to x Translate
$$\frac{\partial f}{\partial x}$$ partial of f with respect to x Translate
$$\frac{\partial^2 f}{\partial x^2}$$ the second partial derivative of f with respect to x squared Translate
$$\frac{\partial}{\partial x_j} ( \frac{\partial f}{\partial x_i} )$$ The partial derivative with respect to x sub j of the partial derivative of f with respect to x sub i Translate
$$\frac{\partial^2 f}{\partial x_j \partial x_i}$$ The second partial derivative of f with respect to x sub j and x sub i Translate
$$\mathbf{a} \cdot \mathbf{b}$$ dot product of vectors a and b Translate
$$\mathbf{a} \times \mathbf{b}$$ cross product of vectors a and b Translate

Matrix Operations

Expression How to Read Translate Pronounce
$$A^T$$ transpose of matrix A Translate
$$A^{-1}$$ inverse of matrix A Translate

Complex Numbers

Expression How to Read Translate Pronounce
$$z = a + bi$$ z equals a plus b i (complex number) Translate
$$|z|$$ modulus of z Translate
$$\arg(z)$$ argument of z Translate
$$\overline{z}$$ complex conjugate of z Translate

Differential Equations

Expression How to Read Translate Pronounce
$$\frac{dy}{dx} = f(x,y)$$ dy by dx equals f of x and y (first-order differential equation) Translate
$$\frac{d^2y}{dx^2} + p(x)\frac{dy}{dx} + q(x)y = r(x)$$ d squared y by dx squared plus p of x times dy by dx plus q of x times y equals r of x (second-order linear differential equation) Translate

What is the Math Expression Reader?

The Math Expression Reader is a powerful yet user-friendly tool designed to help you understand and pronounce mathematical symbols and formulas. Whether you're dealing with basic arithmetic, complex algebra, or advanced calculus, our tool provides clear and professional guidance on how to read each expression correctly.

This tool is perfect for students, educators, and anyone looking to improve their mathematical literacy. With easy-to-follow instructions and examples, you can confidently navigate through various mathematical expressions and enhance your learning experience.

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