Math Functions

Turso provides all SQLite math functions. These functions operate on numeric values and return REAL unless otherwise noted. If any argument is NULL, the function returns NULL. If any argument is non-numeric and cannot be converted, the function returns NULL or 0.0 depending on the function.

Function Reference

Trigonometric Functions

Function	Description	Return Type
`acos(X)`	Inverse cosine of X in radians. X must be between -1.0 and 1.0	REAL
`asin(X)`	Inverse sine of X in radians. X must be between -1.0 and 1.0	REAL
`atan(X)`	Inverse tangent of X in radians	REAL
`atan2(Y, X)`	Inverse tangent of Y/X in radians, using the signs of both arguments to determine the quadrant	REAL
`cos(X)`	Cosine of X, where X is in radians	REAL
`sin(X)`	Sine of X, where X is in radians	REAL
`tan(X)`	Tangent of X, where X is in radians	REAL

Hyperbolic Functions

Function	Description	Return Type
`acosh(X)`	Inverse hyperbolic cosine of X. X must be >= 1.0	REAL
`asinh(X)`	Inverse hyperbolic sine of X	REAL
`atanh(X)`	Inverse hyperbolic tangent of X. X must be between -1.0 and 1.0	REAL
`cosh(X)`	Hyperbolic cosine of X	REAL
`sinh(X)`	Hyperbolic sine of X	REAL
`tanh(X)`	Hyperbolic tangent of X	REAL

Angle Conversion

Function	Description	Return Type
`degrees(X)`	Convert X from radians to degrees	REAL
`radians(X)`	Convert X from degrees to radians	REAL

Rounding and Truncation

Function	Description	Return Type
`ceil(X)`	Smallest integer not less than X	INTEGER
`ceiling(X)`	Alias for `ceil(X)`	INTEGER
`floor(X)`	Largest integer not greater than X	INTEGER
`trunc(X)`	Integer part of X (truncates toward zero)	INTEGER

Logarithmic and Exponential Functions

Function	Description	Return Type
`exp(X)`	e raised to the power X	REAL
`ln(X)`	Natural logarithm of X. X must be > 0	REAL
`log(X)`	Natural logarithm of X (same as `ln(X)`)	REAL
`log(B, X)`	Logarithm of X with base B. Both must be > 0, B != 1	REAL
`log10(X)`	Base-10 logarithm of X. X must be > 0	REAL
`log2(X)`	Base-2 logarithm of X. X must be > 0	REAL

The single-argument log(X) returns the natural logarithm (base e), matching SQLite behavior. This differs from some other databases where log(X) returns the base-10 logarithm.

Arithmetic Functions

Function	Description	Return Type
`mod(X, Y)`	Remainder of X divided by Y	REAL
`pow(X, Y)`	X raised to the power Y	REAL
`power(X, Y)`	Alias for `pow(X, Y)`	REAL
`sqrt(X)`	Square root of X. X must be >= 0	REAL
`sign(X)`	Returns -1, 0, or +1 for negative, zero, or positive X	INTEGER

Constants

Function	Description	Return Type
`pi()`	Returns the value of pi (3.141592653589793)	REAL

Signatures

acos()

acos(X)

Parameter	Type	Description
`X`	REAL or INTEGER	Value between -1.0 and 1.0

Returns: REAL. The angle in radians whose cosine is X. Returns NULL if X is outside [-1.0, 1.0].

acosh()

acosh(X)

Parameter	Type	Description
`X`	REAL or INTEGER	Value >= 1.0

Returns: REAL. The inverse hyperbolic cosine of X. Returns NULL if X < 1.0.

asin()

asin(X)

Parameter	Type	Description
`X`	REAL or INTEGER	Value between -1.0 and 1.0

Returns: REAL. The angle in radians whose sine is X. Returns NULL if X is outside [-1.0, 1.0].

asinh()

asinh(X)

Parameter	Type	Description
`X`	REAL or INTEGER	Any numeric value

Returns: REAL. The inverse hyperbolic sine of X.

atan()

atan(X)

Parameter	Type	Description
`X`	REAL or INTEGER	Any numeric value

Returns: REAL. The angle in radians whose tangent is X. Result is in the range (-pi/2, pi/2).

atan2()

atan2(Y, X)

Parameter	Type	Description
`Y`	REAL or INTEGER	The y-coordinate
`X`	REAL or INTEGER	The x-coordinate

Returns: REAL. The angle in radians between the positive x-axis and the point (X, Y). Result is in the range (-pi, pi]. Unlike atan(Y/X), atan2 correctly handles all quadrants and the case where X is zero.

atanh()

atanh(X)

Parameter	Type	Description
`X`	REAL or INTEGER	Value between -1.0 and 1.0 (exclusive)

Returns: REAL. The inverse hyperbolic tangent of X. Returns NULL if X is outside (-1.0, 1.0).

ceil() / ceiling()

ceil(X)
ceiling(X)

Parameter	Type	Description
`X`	REAL or INTEGER	Any numeric value

Returns: INTEGER. The smallest integer not less than X.

SELECT ceil(3.2);    -- 4
SELECT ceil(-3.2);   -- -3
SELECT ceiling(5.0); -- 5

cos()

cos(X)

Parameter	Type	Description
`X`	REAL or INTEGER	Angle in radians

Returns: REAL. The cosine of X.

cosh()

cosh(X)

Parameter	Type	Description
`X`	REAL or INTEGER	Any numeric value

Returns: REAL. The hyperbolic cosine of X.

degrees()

degrees(X)

Parameter	Type	Description
`X`	REAL or INTEGER	Angle in radians

Returns: REAL. X converted from radians to degrees.

SELECT degrees(pi());   -- 180.0
SELECT degrees(pi()/2); -- 90.0

exp()

exp(X)

Parameter	Type	Description
`X`	REAL or INTEGER	Exponent

Returns: REAL. The value of e raised to the power X.

SELECT exp(0);   -- 1.0
SELECT exp(1);   -- 2.718281828459045

floor()

floor(X)

Parameter	Type	Description
`X`	REAL or INTEGER	Any numeric value

Returns: INTEGER. The largest integer not greater than X.

SELECT floor(3.7);   -- 3
SELECT floor(-3.2);  -- -4
SELECT floor(5.0);   -- 5

ln()

ln(X)

Parameter	Type	Description
`X`	REAL or INTEGER	Value > 0

Returns: REAL. The natural logarithm (base e) of X. Returns NULL if X <= 0.

SELECT ln(1);         -- 0.0
SELECT ln(exp(1));    -- 1.0
SELECT ln(2);         -- 0.6931471805599453

log()

log(X)
log(B, X)

Parameter	Type	Description
`X`	REAL or INTEGER	Value > 0
`B`	REAL or INTEGER	Base > 0 and != 1 (optional)

Returns: REAL. With one argument, returns the natural logarithm of X (same as ln(X)). With two arguments, returns the logarithm of X in base B.

SELECT log(10);      -- 2.302585... (natural log)
SELECT log(10, 100); -- 2.0 (log base 10 of 100)
SELECT log(2, 256);  -- 8.0 (log base 2 of 256)

log10()

log10(X)

Parameter	Type	Description
`X`	REAL or INTEGER	Value > 0

Returns: REAL. The base-10 logarithm of X. Returns NULL if X <= 0.

SELECT log10(100);   -- 2.0
SELECT log10(1000);  -- 3.0

log2()

log2(X)

Parameter	Type	Description
`X`	REAL or INTEGER	Value > 0

Returns: REAL. The base-2 logarithm of X. Returns NULL if X <= 0.

SELECT log2(256);   -- 8.0
SELECT log2(1024);  -- 10.0

mod()

mod(X, Y)

Parameter	Type	Description
`X`	REAL or INTEGER	Dividend
`Y`	REAL or INTEGER	Divisor

Returns: REAL. The remainder when X is divided by Y. Returns NULL if Y is 0.

SELECT mod(10, 3);    -- 1.0
SELECT mod(10.5, 3);  -- 1.5
SELECT mod(-10, 3);   -- -1.0

pi()

pi()

Takes no parameters. Returns: REAL. The mathematical constant pi (3.141592653589793).

SELECT pi();           -- 3.141592653589793
SELECT 2 * pi() * 5;  -- 31.41592653589793 (circumference of circle with radius 5)

pow() / power()

pow(X, Y)
power(X, Y)

Parameter	Type	Description
`X`	REAL or INTEGER	Base
`Y`	REAL or INTEGER	Exponent

Returns: REAL. X raised to the power Y.

SELECT pow(2, 10);      -- 1024.0
SELECT power(3, 3);     -- 27.0
SELECT pow(100, 0.5);   -- 10.0 (square root)

radians()

radians(X)

Parameter	Type	Description
`X`	REAL or INTEGER	Angle in degrees

Returns: REAL. X converted from degrees to radians.

SELECT radians(180);   -- 3.141592653589793
SELECT radians(90);    -- 1.5707963267948966

sign()

sign(X)

Parameter	Type	Description
`X`	REAL or INTEGER	Any numeric value

Returns: INTEGER. Returns -1 if X is negative, 0 if X is zero, and +1 if X is positive. Returns NULL if X is NULL.

SELECT sign(-42);  -- -1
SELECT sign(0);    -- 0
SELECT sign(3.14); -- 1

sin()

sin(X)

Parameter	Type	Description
`X`	REAL or INTEGER	Angle in radians

Returns: REAL. The sine of X.

sinh()

sinh(X)

Parameter	Type	Description
`X`	REAL or INTEGER	Any numeric value

Returns: REAL. The hyperbolic sine of X.

sqrt()

sqrt(X)

Parameter	Type	Description
`X`	REAL or INTEGER	Value >= 0

Returns: REAL. The square root of X. Returns NULL if X is negative.

SELECT sqrt(144);  -- 12.0
SELECT sqrt(2);    -- 1.4142135623730951

tan()

tan(X)

Parameter	Type	Description
`X`	REAL or INTEGER	Angle in radians

Returns: REAL. The tangent of X.

tanh()

tanh(X)

Parameter	Type	Description
`X`	REAL or INTEGER	Any numeric value

Returns: REAL. The hyperbolic tangent of X. Result is always in the range (-1.0, 1.0).

trunc()

trunc(X)

Parameter	Type	Description
`X`	REAL or INTEGER	Any numeric value

Returns: INTEGER. The integer part of X, removing any fractional digits. Truncates toward zero.

SELECT trunc(3.7);   -- 3
SELECT trunc(-3.7);  -- -3
SELECT trunc(5.0);   -- 5

Examples

Trigonometry

-- Sine and cosine of 45 degrees
SELECT sin(radians(45));  -- 0.7071067811865475
SELECT cos(radians(45));  -- 0.7071067811865476

-- Angle from coordinates
SELECT degrees(atan2(1, 1));  -- 45.0

-- Verify the Pythagorean identity: sin^2 + cos^2 = 1
SELECT pow(sin(1.0), 2) + pow(cos(1.0), 2);  -- 1.0

Rounding

-- Different rounding behaviors
SELECT ceil(2.3), floor(2.3), trunc(2.3);
-- 3, 2, 2

SELECT ceil(-2.3), floor(-2.3), trunc(-2.3);
-- -2, -3, -2

Logarithms

-- Compute the number of bits needed to represent N
SELECT ceil(log2(1000));  -- 10

-- Decibel conversion
SELECT 10 * log10(100);  -- 20.0

-- Verify log identities
SELECT ln(exp(5));  -- 5.0

Distance Calculation

-- Euclidean distance between two points
SELECT sqrt(pow(3 - 0, 2) + pow(4 - 0, 2));
-- 5.0 (3-4-5 triangle)

​Math Functions

​Function Reference

​Trigonometric Functions

​Hyperbolic Functions

​Angle Conversion

​Rounding and Truncation

​Logarithmic and Exponential Functions

​Arithmetic Functions

​Constants

​Signatures

​acos()

​acosh()

​asin()

​asinh()

​atan()

​atan2()

​atanh()

​ceil() / ceiling()

​cos()

​cosh()

​degrees()

​exp()

​floor()

​ln()

​log()

​log10()

​log2()

​mod()

​pi()

​pow() / power()

​radians()

​sign()

​sin()

​sinh()

​sqrt()

​tan()

​tanh()

​trunc()

​Examples

​Trigonometry

​Rounding

​Logarithms

​Distance Calculation

​See Also

Math Functions

Function Reference

Trigonometric Functions

Hyperbolic Functions

Angle Conversion

Rounding and Truncation

Logarithmic and Exponential Functions

Arithmetic Functions

Constants

Signatures

acos()

acosh()

asin()

asinh()

atan()

atan2()

atanh()

ceil() / ceiling()

cos()

cosh()

degrees()

exp()

floor()

ln()

log()

log10()

log2()

mod()

pi()

pow() / power()

radians()

sign()

sin()

sinh()

sqrt()

tan()

tanh()

trunc()

Examples

Trigonometry

Rounding

Logarithms

Distance Calculation

See Also