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Using Desmos: List of Supported Functions

Created: 2025/3/25

Last Update: 2025/3/27

Graph Calculator

Trigonometric Functions

Function	Input Example	Meaning
$\sin$	sin(x)	Sine
$\cos$	cos(x)	Cosine
$\tan$	tan(x)	Tangent
$\csc$	csc(x)	Cosecant $(=1/\sin x)$
$\sec$	sec(x)	Secant $(=1/\cos x)$
$\cot$	cot(x)	Cotangent $(=1/\tan x)$

Inverse Trigonometric Functions

Function	Input Example	Meaning
$\arcsin$	arcsin(x)	Arcsine
$\arccos$	arccos(x)	Arccosine
$\arctan$	arctan(x)	Arctangent
$\mathrm{arccsc}$	arccsc(x)	Arccosecant
$\mathrm{arcsec}$	arcsec(x)	Arcsecant
$\mathrm{arccot}$	arccot(x)	Arccotangent

Statistics

Function	Input Example	Meaning
$\mathrm{mean}$	mean([1,3,4])	Mean
$\mathrm{median}$	median([1,3,4])	Median
$\mathrm{min}$	min([1,3,4])	Minimum
$\mathrm{max}$	max([1,3,4])	Maximum
$\mathrm{quartile}$	quartile([1,3,4],2)	Quartile
$\mathrm{quantile}$	quantile([1,3,4],0.2)	Quantile
$\mathrm{stdev}$	stdev([1,3,4])	Sample Standard Deviation
$\mathrm{stdevp}$	stdevp([1,3,4])	Population Standard Deviation
$\mathrm{var}$	var([1,3,4])	Sample Variance
$\mathrm{varp}$	varp([1,3,4])	Population Variance
$\mathrm{mad}$	mad([1,3,4])	Mean Absolute Deviation
$\mathrm{cov}$	cov([2,4,5],[1,3,2])	Sample Covariance
$\mathrm{covp}$	covp([2,4,5],[1,3,2])	Population Covariance
$\mathrm{corr}$	corr([2,4,5],[1,3,2])	Pearson Correlation Coefficient
$\mathrm{spearman}$	spearman([2,4,5],[1,3,2])	Spearman's Rank Correlation Coefficient
$\mathrm{stats}$	stats([1,3,3,4,5])	Five-Number Summary
$\mathrm{count}$	count([1,3,3,4,5])	Element Count
$\mathrm{total}$	total([1,3,4])	Total Value

List Operations

Function	Input Example	Meaning
$\mathrm{join}$	join([1,2],[3,4])	List Concatenation
$\mathrm{sort}$	sort([1,5,4])	List Sorting
$\mathrm{shuffle}$	shuffle([1,5,4])	List Shuffling
$\mathrm{unique}$	unique([1,5,5,6])	Create a List with Unique Values
$\mathrm{for}$	(a,0)for1<a<3	Parameter Display, etc.

Visualization

Function	Input Example	Meaning
$\mathrm{histogram}$	histogram([1,5,5,10])	Histogram The second argument can specify the width
$\mathrm{dotplot}$	dotplot([1,5,5,10])	Dot Plot The second argument can specify the width
$\mathrm{boxplot}$	boxplot([1,5,5,10])	Box Plot

Probability Distributions

Function	Input Example	Meaning
$\mathrm{normaldist}$	normaldist(0,1)	Normal Distribution with a Given Mean and Standard Deviation
$\mathrm{tdist}$	tdist(10)	t-Distribution with a Given Degree of Freedom
$\mathrm{chisqdist}$	chisqdist(5)	Chi-Square Distribution with a Given Degree of Freedom
$\mathrm{poissondist}$	poissondist(5.5)	Poisson Distribution with a Given Mean
$\mathrm{binomialdist}$	binomialdist(10,0.3)	Binomial Distribution with a Given Number of Trials and Success Probability
$\mathrm{uniformdist}$	uniformdist(0,1)	Uniform Distribution over a Given Interval
$\mathrm{pdf}$	pdf(D,x)	Probability Density Function of a Given Distribution
$\mathrm{cdf}$	cdf(D,x)	Cumulative Distribution Function of a Given Distribution
$\mathrm{inversecdf}$	inversecdf(C,x)	Quantile Function (Inverse Cumulative Distribution Function) of a Given Distribution
$\mathrm{random}$	random()	Random Number between 0 and 1 Returns a Random Element for a List

Statistical Tests

Function	Input Example	Meaning
$\mathrm{ttest}$	ttest([20,31,51],40)	t-Test for a Sample and a Value
$\mathrm{tscore}$	tscore([20,31,51],40)	T-Score for a Sample and a Value
$\mathrm{ittest}$	ittest([10,13],[21,23])	t-Test for Two Samples

Calculus

Function	Input Example	Meaning
$\mathrm{exp}$	exp(x)	Exponential Function with Base $e$
$\mathrm{ln}$	ln(x)	Natural Logarithm
$\mathrm{log}$	log(x)	Common Logarithm
$\mathrm{log_a}$	log_a(x)	Logarithm with an Arbitrary Base
$\dfrac d{dx}$	d/dx	Differentiate with Respect to $x$
$f'(x)$	f'(x)	Derivative
$\displaystyle\int$	int	Integral
$\displaystyle\sum$	sum	Sum of a Sequence
$\displaystyle\prod$	prod	Product of a Sequence

Hyperbolic Functions

Function	Input Example	Meaning
$\mathrm{sinh}$	sinh(x)	Hyperbolic Sine
$\mathrm{cosh}$	cosh(x)	Hyperbolic Cosine
$\mathrm{tanh}$	tanh(x)	Hyperbolic Tangent
$\mathrm{csch}$	csch(x)	Hyperbolic Cosecant
$\mathrm{sech}$	sech(x)	Hyperbolic Secant
$\mathrm{coth}$	coth(x)	Hyperbolic Cotangent

Color Customization

Function	Input Example	Meaning
$\mathrm{rgb}$	c=rgb(255,165,0)	Create a Color by Specifying Red, Green, and Blue Amounts Each Ranges from 0 to 255
$\mathrm{hsv}$	c=hsv(25,0.8,1)	Create a Color by Specifying Hue, Saturation, and Brightness Each Ranges from 0~360, 0~1, 0~1

Sound

Function	Input Example	Meaning
$\mathrm{tone}$	tone(440)	Play a Sound of a Given Frequency The Second Argument Can Specify Gain

Number Theory

Function	Input Example	Meaning
$\mathrm{lcm}$	lcm(2,3,4)	Least Common Multiple
$\mathrm{gcd}$	gcd(6,12,18)	Greatest Common Divisor
$\mathrm{mod}$	mod(17,5)	Remainder
$\mathrm{ceil}$	ceil(13.5)	Smallest Integer Not Less Than the Number
$\mathrm{floor}$	floor(13.5)	Largest Integer Not Greater Than the Number
$\mathrm{round}$	round(1.32,2)	Round to a Given Place
$\mathrm{sign}$	sign(-20)	Sign
$\mathrm{nthroot}$	nthroot	nth Root
${}_n \mathrm{P}_k$	nPr(6,2)	Permutation
${}_n \mathrm{C}_k$	nCr(6,2)	Binomial Coefficient

Advanced

Function	Input Example	Meaning
$\mathrm{\to}$	a->a+1	Variable Update
$\mathrm{with}$	y=x+awitha=2	Variable Substitution

Complex Numbers

Function	Input Example	Meaning
$\mathrm{real}$	real(2+4i)	Real Part
$\mathrm{imag}$	imag(2+4i)	Imaginary Part
$\mathrm{conj}$	conj(2+4i)	Complex Conjugate
$\mathrm{arg}$	arg(2+4i)	Argument
$\mathrm{\|\|}$	\|2+4i\|	Absolute Value

Geometry

Function	Input Example	Meaning
$\mathrm{midpoint}$	midpoint((1,0),(2,1))	Midpoint of Two Points
$\mathrm{distance}$	distance((1,0),(2,1))	Distance between Two Points
$\mathrm{polygon}$	polygon((0,0),(1,0),(0,1))	Polygon
$\mathrm{\cdot}$	(1,0)*(0,1)	Dot Product
$\mathrm{\times}$	(1,0,0)cross(0,1,0)	Cross Product (3D)
$\mathrm{\|\|}$	\|(1,2)\|	Magnitude

Polar Coordinates

Function	Input Example	Meaning
$\theta$	theta	Angle
$r$	r	Distance from Origin

Constants, etc.

Function	Input Example	Meaning
$\pi$	pi	Pi
$\tau$	tau	Twice Pi
$e$	e	Euler's Number
$\sim$	~	Regression Model
$\infty$	infinity	Infinity
$\mathrm{width}$	width	Display Area Width
$\mathrm{height}$	height	Display Area Height

3D Calculator

Most of the functions above can be used as is. Additionally, the following functions are available.

Polar Coordinates (Spherical Coordinates)

Function	Input Example	Meaning
$\rho$	rho	Distance from Origin in Spherical Coordinates
$\theta$	theta	Azimuth Angle
$\phi$	phi	Zenith Angle
$r$	r	Distance from z-Axis in Cylindrical Coordinates

Geometry

Function	Input Example	Meaning
$\mathrm{segment}$	segment((0,0,0),(2,2,2))	Line Segment
$\mathrm{triangle}$	triangle((0,0,0),(2,2,2),(1,3,2))	Triangle
$\mathrm{sphere}$	sphere((0,0,0),1)	Sphere with a Given Center and Radius
$\mathrm{vector}$	vector((0,0,0),(1,1,1))	Vector with a Given Start and End Point
$\mathrm{length}$	length(v1)	Magnitude of a Vector or Line Segment
$\mathrm{.start}$	v1.start	Start Point of a Vector
$\mathrm{.end}$	v1.end	End Point of a Vector

Reference

Supported Functions - Desmos Help Center

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Getting Started with Desmos: Basic Operations

Using Desmos: Working with Lists

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