FORTRAN (or Fortran) has three major favors currently, Fortran 77, Fortran 90 and Fortran 95. Fortran 77 is the most popular one and de-facto. Fortran 90 relaxes some constrains of Fortran 77, most notably is the allowance of free-format programming in Fortran 90. Fortran 95 is just a revision of Fortran 90. Knowing that it was developed in 1950s in IBM, Fortran is the most enduring computer programming language in history.

ANSI Fortran 77 fundamentals

Note: Fortran 77 ignores all kinds of space!


Sample code:

      program myname
  • Fortran 77 is not free-format, every line is constrained by the following use:
    • Col 1: It is blank; or it is a c or * for comment line
    • Col 2-5: Statement label (optional), numbered for use with loop or goto statements
    • Col 6: Leave blank; or put any character (usually +) here to mean continuation of previous line
    • Col 7-72 : Statements
    • Col 73-80: Sequence number (optional, rarely used today)
  • Similar to Pascal,
    • Every Fortran program has to be named
    • Variables being used have to be declared first
  • Fortran commands are line-delimited, no semi-colon is needed at the end-of-line
  • Fortran is case-insensitive

Variables and types

Fortran has the following types of variables: integer, real, double precision, complex, logical, character.

  • integer: 32-bit signed integer
  • real: 32-bit floating point, can be expressed as 1.0, -0.5, or 1.23E-4
  • double precision: 64-bit floating point, expression is same as real and additionally 1.23D-4 to mean \(1.23\times 10^{-4}\) in double precision
  • complex: Complex numbers, using an ordered pair of real number such as (1.2,3.4) to mean \(1.2+j3.4\). There is no double precision complex number.
  • logical: Either .TRUE. or .FALSE., the two dots are required
  • character: Trival. Strings are expressed as array of characters, e.g. 'asdfgh'


  • Variable names consists of 1 to 6 characters chosen from [a-z0-9]
  • Numbers can be manipulated by the following in precedence order: ** (exponentiation), * and /, + and -. Parenthesis is allowed to denote precedence.
  • Integer divisions are truncated
  • Constants are declared as variables first, then use the parameter statement to assign values, for example:
      integer i, j, n
      real radius, area, pi
      parameter(pi=3.14159, n=10)
  • Usually, type conversions are done automatically. But the following function are provided for explicit type conversion:
    • int(), real(), and dble(): Convert to integer, real, and double precision respectively
    • ichar() and char(): Convert character to integer and vice versa.

Arrays are declared by suffixing a pair of parenthesis to denote the dimension, for example:

      integer i(10), j(-3:3)
      real matrix(1:5, 3:10)

Then, we can have i(1) to i(10) and j(-3) to j(3), as well as matrix(1,3) to matrix(5,10). Fortran allows multidimensional arrays to be declared up to 7 dimensions.

Boolean expressions:

  • Comparing numbers can be done by:
    • .LT. / .LE. / .GT. / .GE. / .EQ. / .NE.
  • Boolean operations can be done by:
    • .AND. / .OR. / .NOT.
  • .EQV. is logical equivalence and .NEQV. is logical nonequivalence (i.e. XOR)
  • All Boolean things are surrounded by a pair of dots

In case variables have initial values, they can be initialized by the data statements:

      data list-of-variables /list-of-values/, ...

For example, the following three pieces are equivalent:

      integer m, n
      real x, y
      data m/10/, n/20/, x/2.5/, y/2.5/

      integer m, n
      real x, y
      data m,n/10,20/, x,y/2*2.5/

      integer m, n
      real x, y
      m = 10
      n = 20
      x = 2.5
      y = 2.5

Initializing array can be done similarly:

      real A(10,20)
      data A/200*0.5/, A(1,1)/0.0/

Flow control

Basic if-statements are in two forms:

      if (logical_expression) statement
      if (logical_expression) then

They are for one-line of executable statement or multiple lines respectively.

The general form of if-statement is as follows:

      if (logical_expression) then
      elseif (logical_expression) then

In Fortran, there is no for-loop, but use do-continue to mean exactly the same thing:

      do label var =  begin, end, step
label continue

The step is optional (use 1 if omitted). For example:

      do 10 i = 1, n
          fctl = fctl * i
 10   continue
      do 20 i = 9, 1, -2
 20   continue

In ANSI standard, there is no while-loop either, we use if-goto to simulate the same thing:

label if (logical expr) then
         goto label

Similarly, do-while loop is done by the following:

label continue
      if (logical expr) goto label

Note that: Because Fortran 77 ignores spaces, and do20i is a perfect variable name, and there are implicit variable declaration rules in Fortran 77, hence the following line is not flagged as error in compiler:

do 20 i = 1.100

Hence great care is expected in coding.

String operations

A string is declared as character array, such as

      character metal*10
      parameter (metal='cadmium')

declares metal as a 10-character long array to hold a string.

String is assigned by = and the text string is quoted. Extra spaces in the character array is padded by space. We can obtain substring, for example, cad by metal(1:3) or metal(:3) and obtain mium by metal(4:).

Strings can be concatenated by // in Fortran, for example:

metal = 'cad' // 'mium'

String length is measured by len(s) and index(n,h) returns the position of needle n in the haystack h. If n is at the very beginning of h, index returns 1. It returns zero if not found.

Common built-in functions

Fortran’s built-in functions are generic, i.e. they accepts any sensible type as input:

abs() absolute value, or modulus of a complex number
min(,,...) minimum value of all arguments
max(,,...) maximum value of all arguments
sqrt() square root
sin() sine
cos() cosine
tan() tangent
sinh() hyperbolic sine
cosh() hyperbolic cosine
tanh() hyperbolic tangent
asin() arcsine
acos() arc-cosine
atan() arctangent
atan2(,) arctangent of arg1/arg2
exp() natural exponential
log() natural logarithm
log10() common logarithm
aint() truncates a real number but preserves the data type
anint() round to the nearest integer but preserves the data type
nint() convert to integer by rounding off to the nearest integer
mod(,) the remainder of dividing integers arg1 by arg 2
sign(,) setting arg1 the same sign as arg2
dim(,) if arg1 \(>\) arg2, return arg1 \(-\) arg2, or zero otherwise
dprod(,) return the double precision produce of two reals
real() converts a number into real, of return the real part of a complex number
aimag() returns the imaginary part of a complex number
conjg() returns the complex conjugate of a complex number

Functions and subroutines

Syntax of a Fortran function:

      type function name (parameter1, parameter2, ...)

Note that:

  • Functions bear a return type
  • Parameters have to be declared in the declaration statements
  • The return value is stored in an implicitly-defined variable with the same name as the function
  • Functions are terminated by return instead of stop
  • Functions can be called with corresponding parameters supplied
  • All parameters are passed-by-reference in Fortran 77!

If functions are simple enough, we can use statement functions:

      real g, m1, m2, r
      newton(m1, m2, r) = g * m1 * m2 / r**2
      force = newton(x, y, distnce)

Statement functions are one-liners and defined inside the program block, before any executable statements. It can also reference to other variables defined in the same program block.

Subroutine is almost identical to function, but it does not return anything:

      subroutine name (list-of-arguments)

Subroutines are called by the syntax call name(param1,param2,...)

In case array is passed to function or subroutine, we may avoid to declare the dimension of array explicitly, but use an asterisk or other scalar parameters instead:

      subroutine matvec (m, n, A, lda, x, y)
      integer m, n, lda
      real x(*), y(*), A(lda,*)
      integer i, j

Moreover, Fortran does not support global variables. In case global variables are needed, we use common block instead. For example:

      program myprog
      integer a, b, c
      common /myname/ a, b

      subroutine mysub (param1, param2)
      real param1, param2
      integer a, b
      common /myname/ a, b

The common statements declare variables a and b are members of common block named myname and than the common blocks of the same name will be mapped to each other, hence the variables a and b behaves like global variables. Notes that the variable names are insignificant. Whenever common blocks are declared, the variables are mapped sequentially according to the order of specification.

I/O and formating

The simplex form of Fortran I/O is called the list directed I/O, syntax are:

      read(*,*) list-of-variables
      write(*,*) list-of-variables

The read statement reads a whole line from stdin, then assign each space-delimited or comma-delimited value to the list of variables accordingly. Unmatched values are ignored and unmatched variables are unassigned.

The write statement concatenates all the variables in the list and output to stdout. A newline is automatically added at the end. There are actually simplier form of the two read/write statements in case of input and output to stdin and stdout:

      read *, list-of-variables
      print *, list-of-variables

The input or output can actually be formatted. Take write statements as example, the syntax is:

      write(*, label) list-of-variables
 label format format-code

where the label in write statement refer to the format line, which in turn illustrates how should the output be formatted. For example:

      write(*, 900) i, x
  900 format (I4,F8.3)

The format string can be composed of:

A*w* text string of width *w*
D*w*.*d* double precision numbers, exponent notation with width *w* and *d* decimal places
E*w*.*d* real numbers, exponent notation with width *w* and *d* decimal places
F*w*.*d* real numbers, fixed point format with width *w* and *d* decimal places
I*w* integer with width *w*
*n*X *n* horizontal skip (space), *n*=1 if omitted
/ vertical skip (newline)

In case there are un-exhausted width, numbers will be adjusted to the right. Note that the following two format lines are equivalent (i.e. repetitions can be short-handed):

 950  format (2X, I3, 2X, I3, 2X, I3, 2X, I3)
 950  format (4(2X, I3))

Format lines can also be specified inside the write statement, such as:

      write (*,'(A, F8.3)') 'The answer is x = ', x

In case an array is going to be printed, implicit loop can be used inside the write statement:

      do 10 i = 1, 5
         write(*,1000) (a(i,j), j=1,10)
   10 continue
 1000 format (I6)

which will print the array a in 5x10 matrix form. Furthermore,

      write(*,1010) (x(i), i=1,50)
 1010 format (10I6)

will print x(1) to x(10) in the first line, and x(11) to x(20) in the second line, etc.

Besides I/O to stdin and stdout, we can do I/O to files. In the read and write statements, the first asterisk can be replaced by a unit number (from 1 to 99, but usually numbers 1-8 are reserved), to identify which file to I/O from or to. To use a file, you have to open it first:

    open ([UNIT=]u [, IOSTAT=ios] [, ERR=err], FILE=fname, STATUS=sta [, ACCESS=acc] [, FORM=frm] [, RECL=rl])


u the unique unit number in the range 9-99 that denotes this file
ios an integer variable, it is set to zero if successful upon return, non-zero otherwise
err a label, the program will goto this label if there is an error
fname a character string denoting the filename
sta any of NEW, OLD or SCRATCH to denote whether to create a new file, open an existing file, or create a new file and delete when the file is closed
acc either SEQUENTIAL (default) or DIRECT
frm either FORMATTED or UNFORMATTED (default)
rl specified the length of each record in a direct-access file

When we finished using a file, we have to close it:

      close ([UNIT=]u[,IOSTAT=ios,ERR=err,STATUS=sta])

To do I/O with a file, the read and write statement is in the following syntax:

      read ([UNIT=]u, [FMT=]fmt [, IOSTAT=ios] [, ERR=err] [, END=s]) list_of_variables
      write([UNIT=]u, [FMT=]fmt [, IOSTAT=ios] [, ERR=err] [, END=s]) list_of_variables

where s is the label which we will goto when end-of-file is encountered.

Non-ANSI Fortran

Most Fortran 77 compliers will accept the following non-ANSI syntax

  • The do-continue loop can use end do in place of continue
  • Loops:
      while (logical expr) do
      do while (logical expr) 
  • Support of include statement to insert another file, just like the #include in C

Fortran 90

Fortran 90 is a superset of Fortran 77. New features include:

  • Programs are bracketed by program myname and end program
  • Fortran 90 introduces the do-end do loop and also the select case statement:
      end do
      select case (number)
      case (:less_than_this, this, this, from_this:to_this, greater_than_this:)
      case (only_this)
      case default
      end select
  • One may use the expression if (logical expr) exit to halt the loop.
  • Supports the matrix addition, subtraction and multiplication
  • Language features: Supports the recursive function call, definition of structures (C-struct-like), dynamic allocation of memory, pointers, and operator overloading.
  • Symbolic names are now up to 31 characters, instead of 6.
  • End-of-line comments are allowed, start with !.
  • Semi-colons can be used to separate multiple statements in the same line.
  • Strings can be quoted with double quotation marks in addition to apostrophes.
  • New form of relational operators:
    .GE. .GT. .LE. .LT. .EQ. .NE.
    >=   >    <=   <    ==   /=
  • Implicit variable declaration can be done by specifying implicit none at the beginning of declaration block
  • New way of defining variable and assigning initial values:
    real :: num1 = 1.0     ! with initial value
    real :: num2           ! without initial value
    integer :: num3

In case the file is with extension .f90 or free-format is specified, the following rules hold:

  • A statement line can be as long as 132 characters
  • Comments must start with !, even at the first column
  • To continue a statement, use & at the end of each statement. Comment is allowed after &
  • If we break strings into two lines, put & at the end of first line and another & at the beginning of the second line. No comments allowed.
  • Spaces are significant. Hence 1 000 000 no longer means a million.


    author = {Clive G. Page},
    year = 1987,
    publisher = {Messrs Pitman},
    title = {Professional Programmer's Guide to Fortran 77},
    note = {Now available as},
    pdf = {},
    url = {}
    author = {Erik Boman and Sarah T. Whitlock and Paul H. Hargrove},
    title = {Fortran 77 Tutorial },
    note = {Stanford University},
    url = {},
    year = 1995

Further reading for Fortran 90:

    author = {Clive G. Page},
    year = 2001,
    title = {Fortran 90 for Fortran 77 Programmers},
    url = {},
    pdf = {},
    author = {Michael Metcalf},
    title = {Fortran 90 Tutorial},
    year = 1995,
    url = {},
    pdf = {},