This cheat sheet lists 15 Calculus symbols from nyuyo. It includes contour-integral, coproduct, double-integral and more. Each entry shows the symbol, its meaning, LaTeX command, Unicode code point and HTML entity. Every entry also shows how to read an example aloud.
contour-integral
Character
∮
Name
Contour Integral
Meaning
Integrates along a closed curve, returning to the starting point.
LaTeX
\oint
Unicode
U+222E
HTML entity
∮
Example expression
∮ F ⋅ dr
Read aloud
the contour integral of F dot d r
Related symbols
Integral, Double Integral
coproduct
Character
∐
Name
Coproduct
Meaning
An upside-down product sign. For sets it means the disjoint union, and in category theory it names the coproduct, which is dual to the product.
LaTeX
\coprod
Unicode
U+2210
HTML entity
∐
Example expression
∐ᵢ Aᵢ
Read aloud
the coproduct of A i over i
Related symbols
Product, Union, Summation, Direct Sum
double-integral
Character
∬
Name
Double Integral
Meaning
Integrates a function of two variables over a region of the plane. In LaTeX, \iint needs the amsmath package.
LaTeX
\iint
Unicode
U+222C
HTML entity
∬
Example expression
∬ f dA
Read aloud
the double integral of f d A
Related symbols
Integral, Contour Integral, Partial Derivative
double-prime
Character
″
Name
Double Prime
Meaning
Written after a function name to mean its second derivative. It is also used for seconds of arc and for inches.
LaTeX
''
Unicode
U+2033
HTML entity
″
Example expression
f″(x)
Read aloud
f double prime of x
Related symbols
Prime, Triple Prime, Partial Derivative, Degree
integral
Character
∫
Name
Integral
Meaning
Denotes integration. With limits, it gives the signed area under a curve between them; without limits, it gives an antiderivative.
LaTeX
\int
Unicode
U+222B
HTML entity
∫
Example expression
∫₀¹ x dx = 1/2
Read aloud
the integral from zero to one of x d x equals one half
Related symbols
Double Integral, Contour Integral
laplacian
Character
∇²
Name
Laplacian
Meaning
The sum of a function's second partial derivatives, one for each variable. It is the divergence of the gradient, and is also written Δ.
LaTeX
\nabla^2
Unicode
U+2207 U+00B2
HTML entity
∇²
Example expression
∇²f = ∂²f/∂x² + ∂²f/∂y²
Read aloud
the Laplacian of f equals the second partial of f with respect to x plus the second partial of f with respect to y
Related symbols
Nabla, Partial Derivative
nabla
Character
∇
Name
Nabla
Meaning
The vector differential operator. Applied to a scalar function it gives the gradient; with a dot or cross product it gives the divergence or curl.
LaTeX
\nabla
Unicode
U+2207
HTML entity
∇
Example expression
∇f
Read aloud
del f, or the gradient of f
Related symbols
Partial Derivative, Capital Delta
partial-derivative
Character
∂
Name
Partial Derivative
Meaning
Denotes a derivative with respect to one variable while the other variables are held fixed.
LaTeX
\partial
Unicode
U+2202
HTML entity
∂
Example expression
∂f/∂x
Read aloud
the partial derivative of f with respect to x
Related symbols
Nabla, Integral, Delta, Capital Delta
prime
Character
′
Name
Prime
Meaning
Written after a function name to mean its derivative. It is also used to name a related object, such as A′ for a second point near A, and for minutes of arc.
LaTeX
'
Unicode
U+2032
HTML entity
′
Example expression
f′(x)
Read aloud
f prime of x
Related symbols
Partial Derivative, Integral, Degree
product
Character
∏
Name
Product
Meaning
Multiplies a sequence of terms. The index and its range are written below and above the sign.
LaTeX
\prod
Unicode
U+220F
HTML entity
∏
Example expression
∏ₖ₌₁ⁿ k = n!
Read aloud
the product of k for k from one to n equals n factorial
Related symbols
Summation, Factorial
summation
Character
∑
Name
Summation
Meaning
Adds up a sequence of terms. The index and its range are written below and above the sign.
LaTeX
\sum
Unicode
U+2211
HTML entity
∑
Example expression
∑ₖ₌₁ⁿ k
Read aloud
the sum of k for k from one to n
Related symbols
Product, Capital Sigma, Integral, Plus
surface-integral
Character
∯
Name
Surface Integral
Meaning
Integrates over a closed surface, such as the boundary of a solid. It is used for the flux of a field out of a region, as in the divergence theorem. In LaTeX, \oiint needs a package such as esint.
Integrates a function of three variables over a solid region of space. In LaTeX, \iiint needs the amsmath package.
LaTeX
\iiint
Unicode
U+222D
HTML entity
∭
Example expression
∭ f dV
Read aloud
the triple integral of f d V
Related symbols
Double Integral, Integral
triple-prime
Character
‴
Name
Triple Prime
Meaning
Written after a function name to mean its third derivative. For higher derivatives, a number in parentheses is used instead, as in f⁽⁴⁾.
LaTeX
'''
Unicode
U+2034
HTML entity
‴
Example expression
f‴(x)
Read aloud
f triple prime of x
Related symbols
Prime, Double Prime
volume-integral
Character
∰
Name
Volume Integral
Meaning
A triple integral with a circle through it, marking integration over a closed volume. It is rare; most authors write an ordinary triple integral instead. In LaTeX, \oiiint needs a package such as esint.
LaTeX
\oiiint
Unicode
U+2230
HTML entity
∰
Example expression
∰ f dV
Read aloud
the closed volume integral of f d V
Related symbols
Triple Integral, Surface Integral
FAQ
How many Calculus symbols are on this page?
This page lists 15 Calculus symbols, including contour-integral, coproduct, double-integral.
How do I type Calculus symbols in LaTeX?
Each symbol on this page has its LaTeX command shown next to it, for example ', '', '''. Copy the command into your maths mode.
What are the Unicode code points for Calculus symbols?
Every symbol lists its Unicode code point, such as U+2032, U+2033, U+2034, so you can insert it in documents and web pages.
How do I write Calculus symbols in HTML?
Each entry shows its HTML entity where one exists, for example ∰, ∯, ∐. You can paste it directly into your page.
How do I read Calculus symbols aloud?
Each symbol has an example expression and a spoken version, such as ∂f/∂x, ∇²f = ∂²f/∂x² + ∂²f/∂y², ∇f read as del f, or the gradient of f, f double prime of x, f prime of x.