# Arithmetic

# Arithmetic Operators

MySQL provides the following arithmetic operators

Operator	Name	Example
`+`	Addition	`SELECT 3+5;` -> 8 `SELECT 3.5+2.5;` -> 6.0 `SELECT 3.5+2;` -> 5.5
`-`	Subtraction	`SELECT 3-5;` -> -2
`*`	Multiplication	`SELECT 3 * 5;` -> 15
`/`	Division	`SELECT 20 / 4;` -> 5 `SELECT 355 / 113;` -> 3.1416 `SELECT 10.0 / 0;` -> NULL
`DIV`	Integer Division	`SELECT 5 DIV 2;` -> 2
`%` or `MOD`	Modulo	`SELECT 7 % 3;` -> 1 `SELECT 15 MOD 4` -> 3 `SELECT 15 MOD -4` -> 3 `SELECT -15 MOD 4` -> -3 `SELECT -15 MOD -4` -> -3 `SELECT 3 MOD 2.5` -> 0.5

# BIGINT

If the numbers in your arithmetic are all integers, MySQL uses the BIGINT (signed 64-bit) integer data type to do its work. For example:

select (1024 * 1024 * 1024 * 1024 *1024 * 1024) + 1 -> 1,152,921,504,606,846,977

and

select (1024 * 1024 * 1024 * 1024 *1024 * 1024 * 1024 -> BIGINT out of range error

# DOUBLE

If any numbers in your arithmetic are fractional, MySQL uses 64-bit IEEE 754 floating point arithmetic (opens new window). You must be careful when using floating point arithmetic, because many floating point numbers are, inherently, approximations rather than exact values (opens new window).

# Mathematical Constants

# Pi

The following returns the value of PI formatted to 6 decimal places. The actual value is good to DOUBLE;

SELECT PI();    -> 3.141593

# Trigonometry (SIN, COS)

Angles are in Radians, not Degrees. All computations are done in IEEE 754 64-bit floating point (opens new window). All floating point computations are subject to small errors, known as machine ε (epsilon) errors (opens new window), so avoid trying to compare them for equality. There is no way to avoid these errors when using floating point; they are built in to the technology.

If you use DECIMAL values in trigonometric computations, they are implicitly converted to floating point, and then back to decimal.

# Sine

Returns the sine of a number X expressed in radians

SELECT SIN(PI()); -> 1.2246063538224e-16

# Cosine

Returns the cosine of X when X is given in radians

SELECT COS(PI()); -> -1

# Tangent

Returns the tangent of a number X expressed in radians. Notice the result is very close to zero, but not exactly zero. This is an example of machine ε.

SELECT TAN(PI());   -> -1.2246063538224e-16

# Arc Cosine (inverse cosine)

Returns the arc cosine of X if X is in the range -1 to 1

SELECT ACOS(1);    -> 0
SELECT ACOS(1.01); -> NULL

# Arc Sine (inverse sine)

Returns the arc sine of X if X is in the range -1 to 1

SELECT ASIN(0.2); -> 0.20135792079033

# Arc Tangent (inverse tangent)

ATAN(x) returns the arc tangent of a single number.

SELECT ATAN(2); -> 1.1071487177941

ATAN2(X, Y) returns the arc tangent of the two variables X and Y. It is similar to calculating the arc tangent of Y / X. But it is numerically more robust: t functions correctly when X is near zero, and the signs of both arguments are used to determine the quadrant of the result.

Best practice suggests writing formulas to use ATAN2() rather than ATAN() wherever possible.


ATAN2(1,1);    -> 0.7853981633974483 (45 degrees)
 ATAN2(1,-1);   -> 2.356194490192345  (135 degrees)
 ATAN2(0, -1);  -> PI  (180 degrees)  don't try ATAN(-1 / 0)... it won't work

# Cotangent

Returns the cotangent of X

SELECT COT(12); -> -1.5726734063977

# Conversion

SELECT RADIANS(90) -> 1.5707963267948966
SELECT SIN(RADIANS(90)) -> 1
SELECT DEGREES(1), DEGREES(PI()) -> 57.29577951308232, 180

# Rounding (ROUND, FLOOR, CEIL)

# Round a decimal number to an integer value

For exact numeric values (e.g. DECIMAL): If the first decimal place of a number is 5 or higher, this function will round a number to the next integer away from zero. If that decimal place is 4 or lower, this function will round to the next integer value closest to zero.

SELECT ROUND(4.51) -> 5
SELECT ROUND(4.49) -> 4
SELECT ROUND(-4.51) -> -5

For approximate numeric values (e.g. DOUBLE): The result of the ROUND() function depends on the C library; on many systems, this means that ROUND() uses the round to the nearest even rule:

SELECT ROUND(45e-1) -> 4  -- The nearest even value is 4
SELECT ROUND(55e-1) -> 6  -- The nearest even value is 6

# Round up a number

To round up a number use either the CEIL() or CEILING() function

SELECT CEIL(1.23)    -> 2
SELECT CEILING(4.83) -> 5

# Round down a number

To round down a number, use the FLOOR() function

SELECT FLOOR(1.99) -> 1

FLOOR and CEIL go toward / away from -infinity:

SELECT FLOOR(-1.01), CEIL(-1.01) -> -2 and -1
SELECT FLOOR(-1.99), CEIL(-1.99) -> -2 and -1

# Round a decimal number to a specified number of decimal places.

SELECT ROUND(1234.987, 2) -> 1234.99
SELECT ROUND(1234.987, -2) -> 1200

The discussion of up versus down and "5" applies, too.

# Raise a number to a power (POW)

To raise a number x to a power y, use either the POW() or POWER() functions

SELECT POW(2,2); => 4
SELECT POW(4,2); => 16

# Square Root (SQRT)

Use the SQRT() function. If the number is negative, NULL will be returned

SELECT SQRT(16); -> 4
SELECT SQRT(-3); -> NULL

# Random Numbers (RAND)

# Generate a random number

To generate a pseudorandom floating point number between 0 and 1, use the RAND() function

Suppose you have the following query

SELECT i, RAND() FROM t;

This will return something like this

i	RAND()
1	0.6191438870682
2	0.93845168309142
3	0.83482678498591

# Random Number in a range

To generate a random number in the range a <= n <= b, you can use the following formula

FLOOR(a + RAND() * (b - a + 1))

For example, this will generate a random number between 7 and 12

SELECT FLOOR(7 + (RAND() * 6));

A simple way to randomly return the rows in a table:

SELECT * FROM tbl ORDER BY RAND();

These are pseudorandom numbers.

The pseudorandom number generator in MySQL is not cryptographically secure. That is, if you use MySQL to generate random numbers to be used as secrets, a determined adversary who knows you used MySQL will be able to guess your secrets more easily than you might believe.

# Absolute Value and Sign (ABS, SIGN)

Return the absolute value of a number

SELECT ABS(2);   -> 2
SELECT ABS(-46); -> 46

The sign of a number compares it to 0.

Sign	Result	Example
-1	n < 0	`SELECT SIGN(42);` -> 1
0	n = 0	`SELECT SIGN(0);` -> 0
1	n > 0	`SELECT SIGN(-3);` -> -1

SELECT SIGN(-423421); -> -1

# Remarks

MySQL, on most machines, uses 64-bit IEEE 754 floating point arithmetic (opens new window) for its calculations.

In integer contexts it uses integer arithmetic.

RAND() is not a perfect random number generator. It is mainly used to quickly generate pseudorandom numbers

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