8.1. Numeric Types
Numeric types consist of two, four, and eightbyte integers, four and eightbyte floatingpoint numbers, and selectableprecision decimals. Table 8.2 lists the available types.
Table 8.2. Numeric Types
Name  Storage Size  Description  Range 

smallint

2 bytes  smallrange integer  32768 to +32767 
integer

4 bytes  typical choice for integer  2147483648 to +2147483647 
bigint

8 bytes  largerange integer  9223372036854775808 to +9223372036854775807 
decimal

variable  userspecified precision, exact  up to 131072 digits before the decimal point; up to 16383 digits after the decimal point 
numeric

variable  userspecified precision, exact  up to 131072 digits before the decimal point; up to 16383 digits after the decimal point 
real

4 bytes  variableprecision, inexact  6 decimal digits precision 
double precision

8 bytes  variableprecision, inexact  15 decimal digits precision 
smallserial

2 bytes  small autoincrementing integer  1 to 32767 
serial

4 bytes  autoincrementing integer  1 to 2147483647 
bigserial

8 bytes  large autoincrementing integer  1 to 9223372036854775807 
The syntax of constants for the numeric types is described in Section 4.1.2 . The numeric types have a full set of corresponding arithmetic operators and functions. Refer to Chapter 9 for more information. The following sections describe the types in detail.
8.1.1. Integer Types #
The types
smallint
,
integer
, and
bigint
store whole numbers, that is, numbers without
fractional components, of various ranges. Attempts to store
values outside of the allowed range will result in an error.
The type
integer
is the common choice, as it offers
the best balance between range, storage size, and performance.
The
smallint
type is generally only used if disk
space is at a premium. The
bigint
type is designed to be
used when the range of the
integer
type is insufficient.
SQL
only specifies the integer types
integer
(or
int
),
smallint
, and
bigint
. The
type names
int2
,
int4
, and
int8
are extensions, which are also used by some
other
SQL
database systems.
8.1.2. Arbitrary Precision Numbers #
The type
numeric
can store numbers with a
very large number of digits. It is especially recommended for
storing monetary amounts and other quantities where exactness is
required. Calculations with
numeric
values yield exact
results where possible, e.g., addition, subtraction, multiplication.
However, calculations on
numeric
values are very slow
compared to the integer types, or to the floatingpoint types
described in the next section.
We use the following terms below: The
precision
of a
numeric
is the total count of significant digits in the whole number,
that is, the number of digits to both sides of the decimal point.
The
scale
of a
numeric
is the
count of decimal digits in the fractional part, to the right of the
decimal point. So the number 23.5141 has a precision of 6 and a
scale of 4. Integers can be considered to have a scale of zero.
Both the maximum precision and the maximum scale of a
numeric
column can be
configured. To declare a column of type
numeric
use
the syntax:
NUMERIC(precision
,scale
)
The precision must be positive, while the scale may be positive or negative (see below). Alternatively:
NUMERIC(precision
)
selects a scale of 0. Specifying:
NUMERIC
without any precision or scale creates an
"
unconstrained
numeric
"
column in which numeric values of any length can be
stored, up to the implementation limits. A column of this kind will
not coerce input values to any particular scale, whereas
numeric
columns with a declared scale will coerce
input values to that scale. (The
SQL
standard
requires a default scale of 0, i.e., coercion to integer
precision. We find this a bit useless. If you're concerned
about portability, always specify the precision and scale
explicitly.)
Note
The maximum precision that can be explicitly specified in
a
numeric
type declaration is 1000. An
unconstrained
numeric
column is subject to the limits
described in
Table 8.2
.
If the scale of a value to be stored is greater than the declared scale of the column, the system will round the value to the specified number of fractional digits. Then, if the number of digits to the left of the decimal point exceeds the declared precision minus the declared scale, an error is raised. For example, a column declared as
NUMERIC(3, 1)
will round values to 1 decimal place and can store values between 99.9 and 99.9, inclusive.
Beginning in
PostgreSQL
15, it is allowed
to declare a
numeric
column with a negative scale. Then
values will be rounded to the left of the decimal point. The
precision still represents the maximum number of nonrounded digits.
Thus, a column declared as
NUMERIC(2, 3)
will round values to the nearest thousand and can store values between 99000 and 99000, inclusive. It is also allowed to declare a scale larger than the declared precision. Such a column can only hold fractional values, and it requires the number of zero digits just to the right of the decimal point to be at least the declared scale minus the declared precision. For example, a column declared as
NUMERIC(3, 5)
will round values to 5 decimal places and can store values between 0.00999 and 0.00999, inclusive.
Note
PostgreSQL
permits the scale in a
numeric
type declaration to be any value in the range
1000 to 1000. However, the
SQL
standard requires
the scale to be in the range 0 to
precision
.
Using scales outside that range may not be portable to other database
systems.
Numeric values are physically stored without any extra leading or
trailing zeroes. Thus, the declared precision and scale of a column
are maximums, not fixed allocations. (In this sense the
numeric
type is more akin to
varchar(
than to
n
)
char(
.) The actual storage
requirement is two bytes for each group of four decimal digits,
plus three to eight bytes overhead.
n
)
In addition to ordinary numeric values, the
numeric
type
has several special values:
Infinity
Infinity
NaN
These are adapted from the IEEE 754 standard, and represent
"
infinity
"
,
"
negative infinity
"
, and
"
notanumber
"
, respectively. When writing these values
as constants in an SQL command, you must put quotes around them,
for example
UPDATE table SET x = 'Infinity'
.
On input, these strings are recognized in a caseinsensitive manner.
The infinity values can alternatively be spelled
inf
and
inf
.
The infinity values behave as per mathematical expectations. For
example,
Infinity
plus any finite value equals
Infinity
, as does
Infinity
plus
Infinity
; but
Infinity
minus
Infinity
yields
NaN
(not a
number), because it has no welldefined interpretation. Note that an
infinity can only be stored in an unconstrained
numeric
column, because it notionally exceeds any finite precision limit.
The
NaN
(not a number) value is used to represent
undefined calculational results. In general, any operation with
a
NaN
input yields another
NaN
.
The only exception is when the operation's other inputs are such that
the same output would be obtained if the
NaN
were to
be replaced by any finite or infinite numeric value; then, that output
value is used for
NaN
too. (An example of this
principle is that
NaN
raised to the zero power
yields one.)
Note
In most implementations of the
"
notanumber
"
concept,
NaN
is not considered equal to any other numeric
value (including
NaN
). In order to allow
numeric
values to be sorted and used in treebased
indexes,
PostgreSQL
treats
NaN
values as equal, and greater than all non
NaN
values.
The types
decimal
and
numeric
are
equivalent. Both types are part of the
SQL
standard.
When rounding values, the
numeric
type rounds ties away
from zero, while (on most machines) the
real
and
double precision
types round ties to the nearest even
number. For example:
SELECT x, round(x::numeric) AS num_round, round(x::double precision) AS dbl_round FROM generate_series(3.5, 3.5, 1) as x; x  num_round  dbl_round ++ 3.5  4  4 2.5  3  2 1.5  2  2 0.5  1  0 0.5  1  0 1.5  2  2 2.5  3  2 3.5  4  4 (8 rows)
8.1.3. FloatingPoint Types #
The data types
real
and
double precision
are
inexact, variableprecision numeric types. On all currently supported
platforms, these types are implementations of
IEEE
Standard 754 for Binary FloatingPoint Arithmetic (single and double
precision, respectively), to the extent that the underlying processor,
operating system, and compiler support it.
Inexact means that some values cannot be converted exactly to the internal format and are stored as approximations, so that storing and retrieving a value might show slight discrepancies. Managing these errors and how they propagate through calculations is the subject of an entire branch of mathematics and computer science and will not be discussed here, except for the following points:

If you require exact storage and calculations (such as for monetary amounts), use the
numeric
type instead. 
If you want to do complicated calculations with these types for anything important, especially if you rely on certain behavior in boundary cases (infinity, underflow), you should evaluate the implementation carefully.

Comparing two floatingpoint values for equality might not always work as expected.
On all currently supported platforms, the
real
type has a
range of around 1E37 to 1E+37 with a precision of at least 6 decimal
digits. The
double precision
type has a range of around
1E307 to 1E+308 with a precision of at least 15 digits. Values that are
too large or too small will cause an error. Rounding might take place if
the precision of an input number is too high. Numbers too close to zero
that are not representable as distinct from zero will cause an underflow
error.
By default, floating point values are output in text form in their
shortest precise decimal representation; the decimal value produced is
closer to the true stored binary value than to any other value
representable in the same binary precision. (However, the output value is
currently never
exactly
midway between two
representable values, in order to avoid a widespread bug where input
routines do not properly respect the roundtonearesteven rule.) This value will
use at most 17 significant decimal digits for
float8
values, and at most 9 digits for
float4
values.
Note
This shortestprecise output format is much faster to generate than the historical rounded format.
For compatibility with output generated by older versions
of
PostgreSQL
, and to allow the output
precision to be reduced, the
extra_float_digits
parameter can be used to select rounded decimal output instead. Setting a
value of 0 restores the previous default of rounding the value to 6
(for
float4
) or 15 (for
float8
)
significant decimal digits. Setting a negative value reduces the number
of digits further; for example 2 would round output to 4 or 13 digits
respectively.
Any value of extra_float_digits greater than 0 selects the shortestprecise format.
Note
Applications that wanted precise values have historically had to set extra_float_digits to 3 to obtain them. For maximum compatibility between versions, they should continue to do so.
In addition to ordinary numeric values, the floatingpoint types have several special values:
Infinity
Infinity
NaN
These represent the IEEE 754 special values
"
infinity
"
,
"
negative infinity
"
, and
"
notanumber
"
, respectively. When writing these values
as constants in an SQL command, you must put quotes around them,
for example
UPDATE table SET x = 'Infinity'
. On input,
these strings are recognized in a caseinsensitive manner.
The infinity values can alternatively be spelled
inf
and
inf
.
Note
IEEE 754 specifies that
NaN
should not compare equal
to any other floatingpoint value (including
NaN
).
In order to allow floatingpoint values to be sorted and used
in treebased indexes,
PostgreSQL
treats
NaN
values as equal, and greater than all
non
NaN
values.
PostgreSQL
also supports the SQLstandard
notations
float
and
float(
for specifying
inexact numeric types. Here,
p
)
p
specifies
the minimum acceptable precision in
binary
digits.
PostgreSQL
accepts
float(1)
to
float(24)
as selecting the
real
type, while
float(25)
to
float(53)
select
double precision
. Values of
p
outside the allowed range draw an error.
float
with no precision specified is taken to mean
double precision
.
8.1.4. Serial Types #
Note
This section describes a PostgreSQLspecific way to create an autoincrementing column. Another way is to use the SQLstandard identity column feature, described at CREATE TABLE .
The data types
smallserial
,
serial
and
bigserial
are not true types, but merely
a notational convenience for creating unique identifier columns
(similar to the
AUTO_INCREMENT
property
supported by some other databases). In the current
implementation, specifying:
CREATE TABLEtablename
(colname
SERIAL );
is equivalent to specifying:
CREATE SEQUENCEtablename
_colname
_seq AS integer; CREATE TABLEtablename
(colname
integer NOT NULL DEFAULT nextval('tablename
_colname
_seq') ); ALTER SEQUENCEtablename
_colname
_seq OWNED BYtablename
.colname
;
Thus, we have created an integer column and arranged for its default
values to be assigned from a sequence generator. A
NOT NULL
constraint is applied to ensure that a null value cannot be
inserted. (In most cases you would also want to attach a
UNIQUE
or
PRIMARY KEY
constraint to prevent
duplicate values from being inserted by accident, but this is
not automatic.) Lastly, the sequence is marked as
"
owned by
"
the column, so that it will be dropped if the column or table is dropped.
Note
Because
smallserial
,
serial
and
bigserial
are implemented using sequences, there may
be "holes" or gaps in the sequence of values which appears in the
column, even if no rows are ever deleted. A value allocated
from the sequence is still "used up" even if a row containing that
value is never successfully inserted into the table column. This
may happen, for example, if the inserting transaction rolls back.
See
nextval()
in
Section 9.17
for details.
To insert the next value of the sequence into the
serial
column, specify that the
serial
column should be assigned its default value. This can be done
either by excluding the column from the list of columns in
the
INSERT
statement, or through the use of
the
DEFAULT
key word.
The type names
serial
and
serial4
are
equivalent: both create
integer
columns. The type
names
bigserial
and
serial8
work
the same way, except that they create a
bigint
column.
bigserial
should be used if you anticipate
the use of more than 2
^{
31
}
identifiers over the
lifetime of the table. The type names
smallserial
and
serial2
also work the same way, except that they
create a
smallint
column.
The sequence created for a
serial
column is
automatically dropped when the owning column is dropped.
You can drop the sequence without dropping the column, but this
will force removal of the column default expression.