Functions

Arguments to math functions in gnuplot can be integer, real, or complex unless otherwise noted. Functions that accept or return angles (e.g. sin(x)) treat angle values as radians, but this may be changed to degrees using the command set angles.

Math library functions
Function	Arguments	Returns
abs(x)	any	absolute value of $x$, $\vert x\vert$; same type
abs(x)	complex	length of $x$, $\sqrt{{\mbox{real}(x)^{2} + \mbox{imag}(x)^{2}}}$
acos(x)	any	$\cos^{-1} x$ (inverse cosine)
acosh(x)	any	$\cosh^{-1} x$ (inverse hyperbolic cosine) in radians
airy(x)	any	Airy function Ai(x)
arg(x)	complex	the phase of $x$
asin(x)	any	$\sin^{-1} x$ (inverse sin)
asinh(x)	any	$\sinh^{-1} x$ (inverse hyperbolic sin) in radians
atan(x)	any	$\tan^{-1} x$ (inverse tangent)
atan2(y,x)	int or real	$\tan^{-1} (y/x)$ (inverse tangent)
atanh(x)	any	$\tanh^{-1} x$ (inverse hyperbolic tangent) in radians
EllipticK(k)	real k $\in$ (-1:1)	$K(k)$ complete elliptic integral of the first kind
EllipticE(k)	real k $\in$ [-1:1]	$E(k)$ complete elliptic integral of the second kind
EllipticPi(n,k)	real n$<$1, real k $\in$ (-1:1)	$\Pi(n,k)$ complete elliptic integral of the third kind
besj0(x)	int or real	$J_{0}$ Bessel function of $x$ in radians
besj1(x)	int or real	$J_{1}$ Bessel function of $x$ in radians
besjn(n,x)	int, real	$J_{n}$ Bessel function of $x$ in radians
besy0(x)	int or real	$Y_{0}$ Bessel function of $x$ in radians
besy1(x)	int or real	$Y_{1}$ Bessel function of $x$ in radians
besyn(n,x)	int, real	$Y_{n}$ Bessel function of $x$ in radians
besi0(x)	real	Modified Bessel function of order 0, $x$ in radians
besi1(x)	real	Modified Bessel function of order 1, $x$ in radians
besin(n,x)	int, real	Modified Bessel function of order n, $x$ in radians
ceil(x)	any	$\lceil x \rceil$, smallest integer not less than $x$ (real part)
cos(x)	any	$\cos x$, cosine of $x$
cosh(x)	any	$\cosh x$, hyperbolic cosine of $x$ in radians
erf(x)	any	$\mbox{erf}(\mbox{real}(x))$, error function of real($x$)
erfc(x)	any	$\mbox{erfc}(\mbox{real}(x))$, 1.0 - error function of real($x$)
exp(x)	any	$e^{x}$, exponential function of $x$
expint(n,x)	int $n\ge0$, real $x\ge0$	$E_n(x)=\int_1^\infty t^{-n} e^{-xt}\,dt$, exponential integral of $x$
floor(x)	any	$\lfloor x \rfloor$, largest integer not greater than $x$ (real part)
gamma(x)	any	$\mbox{gamma}(\mbox{real}(x))$, gamma function of real($x$)
ibeta(p,q,x)	any	$\mbox{ibeta}(\mbox{real}(p,q,x))$, ibeta function of real($p$,$q$,$x$)
inverf(x)	any	inverse error function of real($x$)
igamma(a,x)	any	$\mbox{igamma}(\mbox{real}(a,x))$, igamma function of real($a$,$x$)
imag(x)	complex	imaginary part of $x$ as a real number
invnorm(x)	any	inverse normal distribution function of real($x$)
int(x)	real	integer part of $x$, truncated toward zero
lambertw(x)	real	Lambert W function
lgamma(x)	any	$\mbox{lgamma}(\mbox{real}(x))$, lgamma function of real($x$)
log(x)	any	$\log_{e} x$, natural logarithm (base $e$) of $x$
log10(x)	any	$\log_{10} x$, logarithm (base $10$) of $x$
norm(x)	any	normal distribution (Gaussian) function of real($x$)
rand(x)	int	pseudo random number in the open interval (0:1)
real(x)	any	real part of $x$
sgn(x)	any	1 if $x>0$, -1 if $x<0$, 0 if $x=0$. imag($x$) ignored
sin(x)	any	$\sin x$, sine of $x$
sinh(x)	any	$\sinh x$, hyperbolic sine of $x$ in radians
sqrt(x)	any	$\sqrt{x}$, square root of $x$
tan(x)	any	$\tan x$, tangent of $x$
tanh(x)	any	$\tanh x$, hyperbolic tangent of $x$ in radians
voigt(x,y)	real	Voigt/Faddeeva function $\frac{y}{\pi} \int{\frac{exp(-t^2)}{(x-t)^2+y^2}}dt$
		Note: voigt$(x,y)$ = $real($faddeeva$(x+iy))$

Special functions from libcerf (only if available)
Function	Arguments	Returns
cerf(z)	complex	complex error function
cdawson(z)	complex	complex extension of Dawson's integral $D(z)={\frac{\sqrt{\pi}}{2}e^{-z^2} erfi(z)}$
faddeeva(z)	complex	rescaled complex error function $w(z) = e^{-z^2}~ erfc(-iz)$
erfi(x)	real	imaginary error function $erf(x) = -i * erf(ix)$
VP(x,$\sigma$,$\gamma$)	real	Voigt profile $VP(x,\sigma,\gamma) = {\int^{\infty}_{-\infty}{G(x^\prime;\sigma) L(x-x^\prime;\gamma) dx^\prime }}$

String functions
Function	Arguments	Returns
gprintf("format",x,...)	any	string result from applying gnuplot's format parser
sprintf("format",x,...)	multiple	string result from C-language sprintf
strlen("string")	string	number of characters in string
strstrt("string","key")	strings	int index of first character of substring "key"
substr("string",beg,end)	multiple	string "string"[beg:end]
strftime("timeformat",t)	any	string result from applying gnuplot's time parser
strptime("timeformat",s)	string	seconds since year 1970 as given in string s
system("command")	string	string containing output stream of shell command
trim(" string ")	string	string without leading or trailing whitespace
word("string",n)	string, int	returns the nth word in "string"
words("string")	string	returns the number of words in "string"

other gnuplot functions
Function	Arguments	Returns
column(x)	int or string	column $x$ during datafile manipulation.
columnhead(x)	int	string containing first entry of column $x$ in datafile.
exists("X")	string	returns 1 if a variable named X is defined, 0 otherwise.
hsv2rgb(h,s,v)	h,s,v $\in$ [0:1]	24bit RGB color value.
palette(z)	double	RGB palette color mapped to z.
stringcolumn(x)	int or string	content of column $x$ as a string.
timecolumn(N,"timeformat")	int, string	time data from column $N$ during data input.
tm_hour(x)	int	the hour
tm_mday(x)	int	the day of the month
tm_min(x)	int	the minute
tm_mon(x)	int	the month
tm_sec(x)	int	the second
tm_wday(x)	int	the day of the week
tm_yday(x)	int	the day of the year
tm_year(x)	int	the year
time(x)	any	the current system time
valid(x)	int	test validity of $\mbox{column}(x)$ during datafile manip.
value("name")	string	returns the value of the named variable.
voxel(x,y,z)	real	value of the active grid voxel containing point (x,y,z)