r3.mapcalc - GRASS manual
Author: GRASS Development Team
Description: r3.mapcalc: Raster map calculator.
Keywords: raster, algebra

## NAME

r3.mapcalc - Raster map calculator.

## KEYWORDS

raster, algebra

## SYNOPSIS

r3.mapcalc
r3.mapcalc --help
r3.mapcalc [-sl] [expression=string] [region=string] [file=name] [seed=integer] [nprocs=integer] [--overwrite] [--help] [--verbose] [--quiet] [--ui]

### Flags:

-s
  Generate random seed (result is non-deterministic) [deprecated]
  This flag is deprecated and will be removed in a future release. Seeding is automatic or use parameter seed.
-l
  List input and output maps
--overwrite
  Allow output files to overwrite existing files
--help
  Print usage summary
--verbose
  Verbose module output
--quiet
  Quiet module output
--ui
  Force launching GUI dialog

### Parameters:

expression=string
  Expression to evaluate
region=string
  The computational region that should be used.
  Options: current, intersect, union
  Default: current
  current: current uses the current region of the mapset
  intersect: intersect computes the intersection region between all input maps and uses the smallest resolution
  union: union computes the union extent of all map regions and uses the smallest resolution
file=name
  File containing expression(s) to evaluate
seed=integer
  Seed value for the random number generator
  Using the same seed ensures identical results, while a randomly generated seed produces different outcomes in each run.
nprocs=integer
  Number of threads for parallel computing
  0: use OpenMP default; >0: use nprocs; <0: use MAX-nprocs
  Default: 0

## DESCRIPTION

r3.mapcalc performs arithmetic on raster map layers. New raster map layers can be created which are arithmetic expressions involving existing raster map layers, integer or floating point constants, and functions.

### Program use

r3.mapcalc expression have the form:

result = expression

where result is the name of a raster map layer to contain the result of the calculation and expression is any legal arithmetic expression involving existing raster map layers (except result itself), integer or floating point constants, and functions known to the calculator. Parentheses are allowed in the expression and may be nested to any depth. result will be created in the user's current mapset.

As expression= is the first option, it is the default. This means that passing an expression on the command line is possible as long as the expression is quoted and a space is included before the first = sign. Example ('foo' is the resulting map):

    r3.mapcalc "foo = 1"

or:

    r3.mapcalc 'foo = 1'

An unquoted expression (i.e. split over multiple arguments) won't work, nor will omitting the space before the = sign:

    r3.mapcalc 'foo=1'
    Sorry, <foo> is not a valid parameter

If no options are given, it manufactures "file=-" (which reads from stdin), so you can continue to use e.g.:

    r3.mapcalc < file

or:

    r3.mapcalc <<EOF
    foo = 1
    EOF

But unless you need compatibility with previous versions, use file= explicitly, e.g.:

    r3.mapcalc file=file

or:

    r3.mapcalc file=- <<EOF
    foo = 1
    EOF

The formula entered to r3.mapcalc by the user is recorded both in the result map title (which appears in the category file for result) and in the history file for result.

Some characters have special meaning to the command shell. If the user is entering input to r3.mapcalc on the command line, expressions should be enclosed within single quotes. See NOTES, below.

### Operators and order of precedence

The following operators are supported:

         Operator   Meaning                    Type        Precedence
         --------------------------------------------------------------
         -          negation                   Arithmetic  12
         ~          one's complement           Bitwise     12
         !          not                        Logical     12
         ^          exponentiation             Arithmetic  11
         %          modulus                    Arithmetic  10
         /          division                   Arithmetic  10
         *          multiplication             Arithmetic  10
         +          addition                   Arithmetic   9
         -          subtraction                Arithmetic   9
         <<         left shift                 Bitwise      8
         >>         right shift                Bitwise      8
         >>>        right shift (unsigned)     Bitwise      8
         >          greater than               Logical      7
         >=         greater than or equal      Logical      7
         <          less than                  Logical      7
         <=         less than or equal         Logical      7
         ==         equal                      Logical      6
         !=         not equal                  Logical      6
         &          bitwise and                Bitwise      5
         |          bitwise or                 Bitwise      4
         &&         logical and                Logical      3
         &&&        logical and[1]             Logical      3
         ||         logical or                 Logical      2
         |||        logical or[1]              Logical      2
         ?:         conditional                Logical      1

(modulus is the remainder upon division)

[1] The &&& and ||| operators handle null values differently to other operators. See the section entitled NULL support below for more details.

The operators are applied from left to right, with those of higher precedence applied before those with lower precedence. Division by 0 and modulus by 0 are acceptable and give a NULL result. The logical operators give a 1 result if the comparison is true, 0 otherwise.

### 3D Grid names

Anything in the expression which is not a number, operator, or function name is taken to be a 3D grid name. Examples:

    volume
    x3
    3d.his

Most GRASS raster map layers and 3D grids meet this naming convention. However, if a 3D grid has a name which conflicts with the above rule, it should be quoted. For example, the expression

    x = a-b

would be interpreted as: x equals a minus b, whereas

    x = "a-b"

would be interpreted as: x equals the 3D grid named a-b

Also

    x = 3107

would create x filled with the number 3107, while

    x = "3107"

would copy the 3D grid 3107 to the 3D grid x.

Quotes are not required unless the 3D grid names look like numbers or contain operators, OR unless the program is run non-interactively. Examples given here assume the program is run interactively. See NOTES, below.

r3.mapcalc will look for the 3D grids according to the user's current mapset search path. It is possible to override the search path and specify the mapset from which to select the 3D grid. This is done by specifying the 3D grid name in the form:

    name@mapset

For example, the following is a legal expression:

    result = x@PERMANENT / y@SOILS

The mapset specified does not have to be in the mapset search path. (This method of overriding the mapset search path is common to all GRASS commands, not just r3.mapcalc.)

### The neighborhood modifier

3D grids are data base files stored in voxel format, i.e., three-dimensional matrices of float/double values. In r3.mapcalc, 3D grids may be followed by a neighborhood modifier that specifies a relative offset from the current cell being evaluated. The format is map[r,c,d], where r is the row offset, c is the column offset and d is the depth offset. For example, map[1,2,3] refers to the cell one row below, two columns to the right and 3 levels below of the current cell, map[-3,-2,-1] refers to the cell three rows above, two columns to the left and one level below of the current cell, and map[0,1,0] refers to the cell one column to the right of the current cell. This syntax permits the development of neighborhood-type filters within a single 3D grid or across multiple 3D grids.

### Functions

The functions currently supported are listed in the table below. The type of the result is indicated in the last column. F means that the functions always results in a floating point value, I means that the function gives an integer result, and * indicates that the result is float if any of the arguments to the function are floating point values and integer if all arguments are integer.

    function                description                                     type
    ---------------------------------------------------------------------------
    abs(x)                  return absolute value of x                      *
    acos(x)                 inverse cosine of x (result is in degrees)      F
    asin(x)                 inverse sine of x (result is in degrees)        F
    atan(x)                 inverse tangent of x (result is in degrees)     F
    atan(x,y)               inverse tangent of y/x (result is in degrees)   F
    ceil(x)                 the smallest integral value not less than x     *
    cos(x)                  cosine of x (x is in degrees)                   F
    double(x)               convert x to double-precision floating point    F
    eval([x,y,...,]z)       evaluate values of listed expr, pass results to z
    exp(x)                  exponential function of x                       F
    exp(x,y)                x to the power y                                F
    float(x)                convert x to single-precision floating point    F
    floor(x)                the largest integral value not greater than x   *
    graph(x,x1,y1[x2,y2..]) convert the x to a y based on points in a graph F
    graph2(x,x1[,x2,..],y1[,y2..])
                            alternative form of graph()                     F
    if                      decision options:                               *
    if(x)                   1 if x not zero, 0 otherwise
    if(x,a)                 a if x not zero, 0 otherwise
    if(x,a,b)               a if x not zero, b otherwise
    if(x,a,b,c)             a if x > 0, b if x is zero, c if x < 0
    int(x)                  convert x to integer [ truncates ]              I
    isnull(x)               check if x = NULL
    log(x)                  natural log of x                                F
    log(x,b)                log of x base b                                 F
    max(x,y[,z...])         largest value of those listed                   *
    median(x,y[,z...])      median value of those listed                    *
    min(x,y[,z...])         smallest value of those listed                  *
    mod(x,y)                return the modulus (the remainder) of x/y       *
    mode(x,y[,z...])        mode value of those listed                      *
    nmax(x,y[,z...])        largest value of those listed, excluding NULLs  *
    nmedian(x,y[,z...])     median value of those listed, excluding NULLs   *
    nmin(x,y[,z...])        smallest value of those listed, excluding NULLs *
    nmode(x,y[,z...])       mode value of those listed, excluding NULLs     *
    not(x)                  1 if x is zero, 0 otherwise
    pow(x,y)                x to the power y                                *
    rand(a,b)               random value x : a <= x < b                     *
    round(x)                round x to nearest integer                      I
    round(x,y)              round x to nearest multiple of y
    round(x,y,z)            round x to nearest y*i+z for some integer i
    sin(x)                  sine of x (x is in degrees)                     F
    sqrt(x)                 square root of x                                F
    tan(x)                  tangent of x (x is in degrees)                  F
    xor(x,y)                exclusive-or (XOR) of x and y                   I

    Internal variables:
     row()                  current row of moving window                    I
     col()                  current col of moving window                    I
     depth()                return current depth                            I
     nrows()                number of rows in computation region            I
     ncols()                number of columns in computation region         I
     ndepths()              number of depth levels in computation region    I
     x()                    current x-coordinate of moving window           F
     y()                    current y-coordinate of moving window           F
     z()                    return current z value                          F
     ewres()                current east-west resolution                    F
     nsres()                current north-south resolution                  F
     tbres()                current top-bottom resolution                   F
     area()                 area of current cell in square meters           F
     null()                 NULL value

Note, that the row(), col() and depth() indexing starts with 1.

### Floating point values in the expression

Floating point numbers are allowed in the expression. A floating point number is a number which contains a decimal point:

        2.3   12.0   12.   .81

Floating point values in the expression are handled in a special way. With arithmetic and logical operators, if either operand is float, the other is converted to float and the result of the operation is float. This means, in particular that division of integers results in a (truncated) integer, while division of floats results in an accurate floating point value. With functions of type * (see table above), the result is float if any argument is float, integer otherwise.

Note: If you calculate with integer numbers, the resulting map will be integer. If you want to get a float result, add the decimal point to integer number(s).

If you want floating point division, at least one of the arguments has to be a floating point value. Multiplying one of them by 1.0 will produce a floating-point result, as will using float():

          r3.mapcalc "ratio = float(soil.4 - soil.3) / soil.3)"

### NULL support

- Division by zero should result in NULL.
- Modulus by zero should result in NULL.
- NULL-values in any arithmetic or logical operation should result in NULL. (however, &&& and ||| are treated specially, as described below).
- The &&& and ||| operators observe the following axioms even when x is NULL:

          x &&& false == false
          false &&& x == false
          x ||| true == true
          true ||| x == true

- NULL-values in function arguments should result in NULL (however, if(), eval() and isnull() are treated specially, as described below).
- The eval() function always returns its last argument
- The situation for if() is:

      if(x)
          NULL if x is NULL; 0 if x is zero; 1 otherwise
      if(x,a)
          NULL if x is NULL; a if x is non-zero; 0 otherwise
      if(x,a,b)
          NULL if x is NULL; a if x is non-zero; b otherwise
      if(x,n,z,p)
          NULL if x is NULL; n if x is negative;
      z if x is zero; p if x is positive

- The (new) function isnull(x) returns: 1 if x is NULL; 0 otherwise. The (new) function null() (which has no arguments) returns an integer NULL.
- Non-NULL, but invalid, arguments to functions should result in NULL.

      Examples:
      log(-2)
      sqrt(-2)
      pow(a,b) where a is negative and b is not an integer

NULL support: Please note that any math performed with NULL cells always results in a NULL value for these cells. If you want to replace a NULL cell on-the-fly, use the isnull() test function in a if-statement.

Example: The users wants the NULL-valued cells to be treated like zeros. To add maps A and B (where B contains NULLs) to get a map C the user can use a construction like:

    C = A + if(isnull(B),0,B)

NULL and conditions:

For the one argument form:

    if(x) = NULL        if x is NULL
    if(x) = 0        if x = 0
    if(x) = 1        otherwise (i.e. x is neither NULL nor 0).

For the two argument form:

    if(x,a) = NULL        if x is NULL
    if(x,a) = 0        if x = 0
    if(x,a) = a        otherwise (i.e. x is neither NULL nor 0).

For the three argument form:

    if(x,a,b) = NULL    if x is NULL
    if(x,a,b) = b        if x = 0
    if(x,a,b) = a        otherwise (i.e. x is neither NULL nor 0).

For the four argument form:

    if(x,a,b,c) = NULL    if x is NULL
    if(x,a,b,c) = a        if x > 0
    if(x,a,b,c) = b        if x = 0
    if(x,a,b,c) = c        if x < 0

More generally, all operators and most functions return NULL if *any* of their arguments are NULL.
The functions if(), isnull() and eval() are exceptions.
The function isnull() returns 1 if its argument is NULL and 0 otherwise. If the user wants the opposite, the ! operator, e.g. "!isnull(x)" must be used.

All forms of if() return NULL if the first argument is NULL. The 2, 3 and 4 argument forms of if() return NULL if the "selected" argument is NULL, e.g.:

    if(0,a,b) = b    regardless of whether a is NULL
    if(1,a,b) = a    regardless of whether b is NULL

eval() always returns its last argument, so it only returns NULL if the last argument is NULL.

Note: The user cannot test for NULL using the == operator, as that returns NULL if either or both arguments are NULL, i.e. if x and y are both NULL, then "x == y" and "x != y" are both NULL rather than 1 and 0 respectively.
The behaviour makes sense if the user considers NULL as representing an unknown quantity. E.g. if x and y are both unknown, then the values of "x == y" and "x != y" are also unknown; if they both have unknown values, the user doesn't know whether or not they both have the same value.

## NOTES

### Usage from command line

Extra care must be taken if the expression is given on the command line. Some characters have special meaning to the UNIX shell. These include, among others:

    * ( ) > & |

It is advisable to put single quotes around the expression; e.g.:

    'result = volume * 2'

Without the quotes, the `*`, which has special meaning to the UNIX shell, would be altered and r3.mapcalc would see something other than the `*`.

### Multiple computations

In general, it's preferable to do as much as possible in each r3.mapcalc command using multi-line input.

### Backwards compatibility

For the backwards compatibility with GRASS 6, if no options are given, it manufactures `file=-` (which reads from stdin), so you can continue to use e.g.:

    r3.mapcalc < file

or:

    r3.mapcalc <<EOF
    foo = 1
    EOF

But unless you need compatibility with previous GRASS versions, use `file=` explicitly, as stated above.

When the map name contains uppercase letter(s) or a dot which are not allowed to be in module option names, the r3.mapcalc command will be valid also without quotes:

    r3.mapcalc volume_A=1
    r3.mapcalc volume.1=1

However, this syntax is not recommended as quotes as stated above more safe. Using quotes is both backwards compatible and valid in future.

### Interactive input in command line

For formulas that the user enters from standard input (rather than from the command line), a line continuation feature now exists. If the user adds a backslash to the end of an input line, r3.mapcalc assumes that the formula being entered by the user continues on to the next input line. There is no limit to the possible number of input lines or to the length of a formula.

If the r3.mapcalc formula entered by the user is very long, the map title will contain only some of it, but most (if not all) of the formula will be placed into the history file for the result map.

When the user enters input to r3.mapcalc non-interactively on the command line, the program will not warn the user not to overwrite existing map layers. Users should therefore take care to assign program outputs raster map names that do not yet exist in their current mapsets.

### 3D GRID mask handling

r3.mapcalc follows the common GRASS behavior of raster mask handling, so the mask is only applied when reading an existing GRASS raster map. This implies that, for example, the command:

    r3.mapcalc "volume_amplified = volume * 3"

create a map with NULL cells for the masked-out cells if raster mask is active.

However, when creating a map which is not based on any map, e.g. a map from a constant:

    r3.mapcalc "volume_const = 200.0"

the created raster map is limited only by a computation region but it is not affected by an active raster mask. This is expected because, as mentioned above, the mask is only applied when reading, not when writing a raster map. If the raster mask should be applied in this case, an `if()` function including the mask raster should be used, e.g. (assuming the mask is called `MASK`):

    r3.mapcalc "volume_const = if(MASK, 200.0, null())"

When testing expressions related to mask handling keep in mind that when the raster mask is active, you don't see data in masked areas even if they are not NULL. See r3.mask for details.

### Random number generator initialization

The pseudo-random number generator used by the rand() function can be initialised to a specific value using the seed option. This can be used to replicate a previous calculation.

Alternatively, it can be initialised from the system time and the PID using the -r flag. This should result in a different seed being used each time.

In either case, the seed will be written to the map's history, and can be seen using r.info.

If you want other people to be able to verify your results, it's preferable to use the seed option to supply a seed which is either specified in the script or generated from a deterministic process such as a pseudo-random number generator given an explicit seed.

Note that the rand() function will generate a fatal error if neither the seed option nor the -s flag are given.

## EXAMPLES

To compute the average of two 3D grids a and b:

    ave = (a + b)/2

To form a weighted average:

    ave = (5*a + 3*b)/8.0

To produce a binary representation of the 3D grid a so that category 0 remains 0 and all other categories become 1:

    mask = a != 0

This could also be accomplished by:

    mask = if(a)

To mask 3D grid b by 3D grid a:

    result = if(a,b)

To change all values below 5 to NULL, keep value otherwise:

    newmap = if(map < 5, null(), map)

The graph() function allows users to specify a x-y conversion using pairs of x,y coordinates. In some situations a transformation from one value to another is not easily established mathematically, but can be represented by a 2-D graph and then linearly interpolated. The graph() function provides the opportunity to accomplish this. An x-axis value is provided to the graph function along with the associated graph represented by a series of x,y pairs. The x values must be monotonically increasing (each larger than or equal to the previous). The graph function linearly interpolates between pairs. Any x value lower the lowest x value (i.e. first) will have the associated y value returned. Any x value higher than the last will similarly have the associated y value returned. Consider the request:

    newmap = graph(map, 1,10, 2,25, 3,50)

X (map) values supplied and y (newmap) values returned:

    0, 10
    1, 10
    1.5, 17.5
    2.9, 47.5
    4, 50
    100, 50

## KNOWN ISSUES

The result variable on the left hand side of the equation should not appear in the expression on the right hand side.

    mymap = if( mymap > 0, mymap, 0)

Any maps generated by a r3.mapcalc command only exist after the entire command has completed. All maps are generated concurrently, row-by-row (i.e. there is an implicit "for row in rows {...}" around the entire expression). Thus the `#`, `@`, and `[ ]` operators cannot be used on a map generated within same r3.mapcalc command run.

    newmap = oldmap * 3.14
    othermap = newmap[-1, 0] / newmap[1, 0]

Continuation lines must end with a `\` and have no trailing white space (blanks or tabs). If the user does leave white space at the end of continuation lines, the error messages produced by r3.mapcalc will be meaningless and the equation will not work as the user intended. This is particularly important for the `eval()` function.

Currently, there is no comment mechanism in r3.mapcalc. Perhaps adding a capability that would cause the entire line to be ignored when the user inserted a # at the start of a line as if it were not present, would do the trick.

The function should require the user to type "end" or "exit" instead of simply a blank line. This would make separation of multiple scripts separable by white space.

r3.mapcalc does not print a warning in case of operations on NULL cells. It is left to the user to utilize the `isnull()` function.

## REFERENCES

r.mapcalc: An Algebra for GIS and Image Processing, by Michael Shapiro and Jim Westervelt, U.S. Army Construction Engineering Research Laboratory (March/1991).

Performing Map Calculations on GRASS Data: r.mapcalc Program Tutorial, by Marji Larson, Michael Shapiro and Scott Tweddale, U.S. Army Construction Engineering Research Laboratory (December 1991)

Neteler, M. (2001): Volume modelling of soils using GRASS GIS 3D tools. - in: Brovelli, M. (ed.)(2001): The Geomatics Workbook N. 2. Politecnico di Milano, Italy (ISSN 1591-092X) (PDF)

## SEE ALSO

g.region, r3.colors, r.mapcalc

## AUTHORS

Tomas Paudits & Jaro Hofierka, funded by GeoModel s.r.o., Slovakia
tpaudits@mailbox.sk, hofierka@geomodel.sk

Glynn Clements

## SOURCE CODE

Available at: r3.mapcalc source code (history)

Latest change: Friday Apr 17 01:04:26 2026 in commit: 32a143358df26b2e518b03c7e0d79541e8d1e5b1

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© 2003-2026 GRASS Development Team, GRASS 8.5.1dev Reference Manual