Functions

The functions in gnuplot are the same as the corresponding functions in the Unix math library, except that all functions accept integer, real, and complex arguments, unless otherwise noted.

For those functions that accept or return angles that may be given in either degrees or radians (sin(x), cos(x), tan(x), asin(x), acos(x), atan(x), atan2(x) and arg(z)), the unit may be selected by set angles, which defaults to radians.

Math library functions
Function	Arguments	Returns
abs(x)	any	absolute value of 7#7, 8#8; same type
abs(x)	complex	length of 7#7, 9#9
acos(x)	any	10#10 (inverse cosine)
acosh(x)	any	11#11 (inverse hyperbolic cosine) in radians
arg(x)	complex	the phase of 7#7
asin(x)	any	12#12 (inverse sin)
asinh(x)	any	13#13 (inverse hyperbolic sin) in radians
atan(x)	any	14#14 (inverse tangent)
atan2(y,x)	int or real	15#15 (inverse tangent)
atanh(x)	any	16#16 (inverse hyperbolic tangent) in radians
besj0(x)	int or real	17#17 Bessel function of 7#7, in radians
besj1(x)	int or real	18#18 Bessel function of 7#7, in radians
besy0(x)	int or real	19#19 Bessel function of 7#7, in radians
besy1(x)	int or real	20#20 Bessel function of 7#7, in radians
ceil(x)	any	21#21, smallest integer not less than 7#7 (real part)
cos(x)	any	22#22, cosine of 7#7
cosh(x)	any	23#23, hyperbolic cosine of 7#7 in radians
erf(x)	any	24#24, error function of real(7#7)
erfc(x)	any	25#25, 1.0 - error function of real(7#7)
exp(x)	any	26#26, exponential function of 7#7
floor(x)	any	27#27, largest integer not greater than 7#7 (real part)
gamma(x)	any	28#28, gamma function of real(7#7)
ibeta(p,q,x)	any	29#29, ibeta function of real(30#30,31#31,7#7)
inverf(x)	any	inverse error function of real(7#7)
igamma(a,x)	any	32#32, igamma function of real(33#33,7#7)
imag(x)	complex	imaginary part of 7#7 as a real number
invnorm(x)	any	inverse normal distribution function of real(7#7)
int(x)	real	integer part of 7#7, truncated toward zero
lambertw(x)	real	Lambert W function
lgamma(x)	any	34#34, lgamma function of real(7#7)
log(x)	any	35#35, natural logarithm (base 36#36) of 7#7
log10(x)	any	37#37, logarithm (base 38#38) of 7#7
norm(x)	any	normal distribution (Gaussian) function of real(7#7)
rand(x)	any	39#39, pseudo random number generator
real(x)	any	real part of 7#7
sgn(x)	any	1 if 40#40, -1 if 41#41, 0 if 42#42. imag(7#7) ignored
sin(x)	any	43#43, sine of 7#7
sinh(x)	any	44#44, hyperbolic sine of 7#7 in radians
sqrt(x)	any	45#45, square root of 7#7
tan(x)	any	46#46, tangent of 7#7
tanh(x)	any	47#47, hyperbolic tangent of 7#7 in radians

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	int length of string
strstrt("string","key")	strings	int index of first character of substring "key"
substr("string",beg,end)	multiple	string "string"[beg:end]
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	column 7#7 during datafile manipulation.
defined(X)	variable name	[DEPRECATED] returns 1 if X is defined, 0 otherwise.
exists("X")	"variable name"	returns 1 if a variable named X is defined, 0 otherwise.
stringcolumn(x)	int	content of column 7#7 as a string.
timecolumn(x)	int	timecolumn 7#7 during datafile manipulation.
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
valid(x)	int	test validity of 48#48 during datafile manip.

See also

http://www.gnuplot.info/demo/airfoil.htmlairfoil.dem: use of functions and complex variables for airfoils demo.