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 10#10, 11#11; same type
abs(x)	complex	length of 10#10, 12#12
acos(x)	any	13#13 (inverse cosine)
acosh(x)	any	14#14 (inverse hyperbolic cosine) in radians
airy(x)	any	Airy function Ai(x)
arg(x)	complex	the phase of 10#10
asin(x)	any	15#15 (inverse sin)
asinh(x)	any	16#16 (inverse hyperbolic sin) in radians
atan(x)	any	17#17 (inverse tangent)
atan2(y,x)	int or real	18#18 (inverse tangent)
atanh(x)	any	19#19 (inverse hyperbolic tangent) in radians
EllipticK(k)	real k 20#20 (-1:1)	21#21 complete elliptic integral of the first kind
EllipticE(k)	real k 20#20 [-1:1]	22#22 complete elliptic integral of the second kind
EllipticPi(n,k)	real n4#41, real k 20#20 (-1:1)	23#23 complete elliptic integral of the third kind
besj0(x)	int or real	24#24 Bessel function of 10#10, in radians
besj1(x)	int or real	25#25 Bessel function of 10#10, in radians
besy0(x)	int or real	26#26 Bessel function of 10#10, in radians
besy1(x)	int or real	27#27 Bessel function of 10#10, in radians
ceil(x)	any	28#28, smallest integer not less than 10#10 (real part)
cos(x)	any	29#29, cosine of 10#10
cosh(x)	any	30#30, hyperbolic cosine of 10#10 in radians
erf(x)	any	31#31, error function of real(10#10)
erfc(x)	any	32#32, 1.0 - error function of real(10#10)
exp(x)	any	33#33, exponential function of 10#10
expint(n,x)	int 34#34, real 35#35	36#36, exponential integral of 10#10
floor(x)	any	37#37, largest integer not greater than 10#10 (real part)
gamma(x)	any	38#38, gamma function of real(10#10)
ibeta(p,q,x)	any	39#39, ibeta function of real(40#40,41#41,10#10)
inverf(x)	any	inverse error function of real(10#10)
igamma(a,x)	any	42#42, igamma function of real(43#43,10#10)
imag(x)	complex	imaginary part of 10#10 as a real number
invnorm(x)	any	inverse normal distribution function of real(10#10)
int(x)	real	integer part of 10#10, truncated toward zero
lambertw(x)	real	Lambert W function
lgamma(x)	any	44#44, lgamma function of real(10#10)
log(x)	any	45#45, natural logarithm (base 46#46) of 10#10
log10(x)	any	47#47, logarithm (base 48#48) of 10#10
norm(x)	any	normal distribution (Gaussian) function of real(10#10)
rand(x)	int	pseudo random number in the interval [0:1]
real(x)	any	real part of 10#10
sgn(x)	any	1 if 49#49, -1 if 50#50, 0 if 51#51. imag(10#10) ignored
sin(x)	any	52#52, sine of 10#10
sinh(x)	any	53#53, hyperbolic sine of 10#10 in radians
sqrt(x)	any	54#54, square root of 10#10
tan(x)	any	55#55, tangent of 10#10
tanh(x)	any	56#56, hyperbolic tangent of 10#10 in radians
voigt(x,y)	real	Voigt/Faddeeva function 57#57
		Note: voigt58#58 = 59#59faddeeva60#60

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 61#61
faddeeva(z)	complex	rescaled complex error function 62#62
erfi(x)	real	imaginary error function 63#63
VP(x,64#64,65#65)	real	Voigt profile 66#66

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
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 10#10 during datafile manipulation.
columnhead(x)	int	string containing first entry of column 10#10 in datafile.
exists("X")	string	returns 1 if a variable named X is defined, 0 otherwise.
hsv2rgb(h,s,v)	h,s,v 20#20 [0:1]	24bit RGB color value.
stringcolumn(x)	int or string	content of column 10#10 as a string.
timecolumn(N,"timeformat")	int, string	time data from column 67#67 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 68#68 during datafile manip.
value("name")	string	returns the value of the named variable.