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 11#11, 12#12; same type
abs(x)	complex	length of 11#11, 13#13
acos(x)	any	14#14 (inverse cosine)
acosh(x)	any	15#15 (inverse hyperbolic cosine)
airy(x)	any	Airy function Ai(x)
arg(x)	complex	the phase of 11#11
asin(x)	any	16#16 (inverse sin)
asinh(x)	any	17#17 (inverse hyperbolic sin)
atan(x)	any	18#18 (inverse tangent)
atan2(y,x)	int or real	19#19 (inverse tangent)
atanh(x)	any	20#20 (inverse hyperbolic tangent)
EllipticK(k)	real k 21#21 (-1:1)	22#22 complete elliptic integral of the first kind
EllipticE(k)	real k 21#21 [-1:1]	23#23 complete elliptic integral of the second kind
EllipticPi(n,k)	real n4#41, real k 21#21 (-1:1)	24#24 complete elliptic integral of the third kind
besj0(x)	int or real	25#25 Bessel function of 11#11 in radians
besj1(x)	int or real	26#26 Bessel function of 11#11 in radians
besjn(n,x)	int, real	27#27 Bessel function of 11#11 in radians
besy0(x)	int or real	28#28 Bessel function of 11#11 in radians
besy1(x)	int or real	29#29 Bessel function of 11#11 in radians
besyn(n,x)	int, real	30#30 Bessel function of 11#11 in radians
besi0(x)	real	Modified Bessel function of order 0, 11#11 in radians
besi1(x)	real	Modified Bessel function of order 1, 11#11 in radians
besin(n,x)	int, real	Modified Bessel function of order n, 11#11 in radians
ceil(x)	any	31#31, smallest integer not less than 11#11 (real part)
cos(x)	any	32#32, cosine of 11#11
cosh(x)	any	33#33, hyperbolic cosine of 11#11 in radians
erf(x)	any	34#34, error function of real(11#11)
erfc(x)	any	35#35, 1.0 - error function of real(11#11)
exp(x)	any	36#36, exponential function of 11#11
expint(n,x)	int 37#37, real 38#38	39#39, exponential integral of 11#11
floor(x)	any	40#40, largest integer not greater than 11#11 (real part)
gamma(x)	any	41#41, gamma function of real(11#11)
ibeta(p,q,x)	any	42#42, ibeta function of real(43#43,44#44,11#11)
inverf(x)	any	inverse error function of real(11#11)
igamma(a,x)	any	45#45, igamma function of real(46#46,11#11)
imag(x)	complex	imaginary part of 11#11 as a real number
invnorm(x)	any	inverse normal distribution function of real(11#11)
int(x)	real	integer part of 11#11, truncated toward zero
lambertw(x)	real	Lambert W function
lgamma(x)	any	47#47, lgamma function of real(11#11)
log(x)	any	48#48, natural logarithm (base 49#49) of 11#11
log10(x)	any	50#50, logarithm (base 51#51) of 11#11
norm(x)	any	normal distribution (Gaussian) function of real(11#11)
rand(x)	int	pseudo random number in the open interval (0:1)
real(x)	any	real part of 11#11
sgn(x)	any	1 if 52#52, -1 if 53#53, 0 if 54#54. imag(11#11) ignored
sin(x)	any	55#55, sine of 11#11
sinh(x)	any	56#56, hyperbolic sine of 11#11 in radians
sqrt(x)	any	57#57, square root of 11#11
tan(x)	any	58#58, tangent of 11#11
tanh(x)	any	59#59, hyperbolic tangent of 11#11 in radians
voigt(x,y)	real	Voigt/Faddeeva function 60#60
		Note: voigt61#61 = 62#62faddeeva63#63

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 64#64
faddeeva(z)	complex	rescaled complex error function 65#65
erfi(x)	real	imaginary error function 66#66
VP(x,67#67,68#68)	real	Voigt profile 69#69

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 11#11 during datafile input
columnhead(x)	int	string containing first entry of column 11#11 in datafile.
exists("X")	string	returns 1 if a variable named X is defined, 0 otherwise.
hsv2rgb(h,s,v)	h,s,v 21#21 [0:1]	24bit RGB color value.
palette(z)	double	RGB palette color mapped to z.
stringcolumn(x)	int or string	content of column 11#11 as a string.
timecolumn(N,"timeformat")	int, string	time data from column 70#70 during data input.
tm_hour(t)	time in sec	the hour (0..23)
tm_mday(t)	time in sec	the day of the month (1..31)
tm_min(t)	time in sec	the minute (0..59)
tm_mon(t)	time in sec	the month (0..11)
tm_sec(t)	time in sec	the second (0..59)
tm_wday(t)	time in sec	the day of the week (Sun..Sat) as (0..6)
tm_week(t)	time in sec	week of year in ISO8601 "week date" system (1..53)
tm_yday(t)	time in sec	the day of the year (0..365)
tm_year(t)	time in sec	the year
time(x)	any	the current system time in seconds
valid(x)	int	test validity of 71#71 during datafile input
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)