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()
| Parameter | Type | Description |
|---|
X | REAL or INTEGER | Value between -1.0 and 1.0 |
acosh()
| Parameter | Type | Description |
|---|
X | REAL or INTEGER | Value >= 1.0 |
asin()
| Parameter | Type | Description |
|---|
X | REAL or INTEGER | Value between -1.0 and 1.0 |
asinh()
| Parameter | Type | Description |
|---|
X | REAL or INTEGER | Any numeric value |
atan()
| Parameter | Type | Description |
|---|
X | REAL or INTEGER | Any numeric value |
atan2()
| Parameter | Type | Description |
|---|
Y | REAL or INTEGER | The y-coordinate |
X | REAL or INTEGER | The x-coordinate |
atan(Y/X), atan2 correctly handles all quadrants and the case where X is zero.
atanh()
| Parameter | Type | Description |
|---|
X | REAL or INTEGER | Value between -1.0 and 1.0 (exclusive) |
ceil() / ceiling()
| Parameter | Type | Description |
|---|
X | REAL or INTEGER | Any numeric value |
SELECT ceil(3.2); -- 4
SELECT ceil(-3.2); -- -3
SELECT ceiling(5.0); -- 5
cos()
| Parameter | Type | Description |
|---|
X | REAL or INTEGER | Angle in radians |
cosh()
| Parameter | Type | Description |
|---|
X | REAL or INTEGER | Any numeric value |
degrees()
| Parameter | Type | Description |
|---|
X | REAL or INTEGER | Angle in radians |
SELECT degrees(pi()); -- 180.0
SELECT degrees(pi()/2); -- 90.0
exp()
| Parameter | Type | Description |
|---|
X | REAL or INTEGER | Exponent |
SELECT exp(0); -- 1.0
SELECT exp(1); -- 2.718281828459045
floor()
| Parameter | Type | Description |
|---|
X | REAL or INTEGER | Any numeric value |
SELECT floor(3.7); -- 3
SELECT floor(-3.2); -- -4
SELECT floor(5.0); -- 5
ln()
| Parameter | Type | Description |
|---|
X | REAL or INTEGER | Value > 0 |
SELECT ln(1); -- 0.0
SELECT ln(exp(1)); -- 1.0
SELECT ln(2); -- 0.6931471805599453
log()
| Parameter | Type | Description |
|---|
X | REAL or INTEGER | Value > 0 |
B | REAL or INTEGER | Base > 0 and != 1 (optional) |
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()
| Parameter | Type | Description |
|---|
X | REAL or INTEGER | Value > 0 |
SELECT log10(100); -- 2.0
SELECT log10(1000); -- 3.0
log2()
| Parameter | Type | Description |
|---|
X | REAL or INTEGER | Value > 0 |
SELECT log2(256); -- 8.0
SELECT log2(1024); -- 10.0
mod()
| Parameter | Type | Description |
|---|
X | REAL or INTEGER | Dividend |
Y | REAL or INTEGER | Divisor |
SELECT mod(10, 3); -- 1.0
SELECT mod(10.5, 3); -- 1.5
SELECT mod(-10, 3); -- -1.0
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()
| Parameter | Type | Description |
|---|
X | REAL or INTEGER | Base |
Y | REAL or INTEGER | Exponent |
SELECT pow(2, 10); -- 1024.0
SELECT power(3, 3); -- 27.0
SELECT pow(100, 0.5); -- 10.0 (square root)
radians()
| Parameter | Type | Description |
|---|
X | REAL or INTEGER | Angle in degrees |
SELECT radians(180); -- 3.141592653589793
SELECT radians(90); -- 1.5707963267948966
sign()
| Parameter | Type | Description |
|---|
X | REAL or INTEGER | Any numeric value |
SELECT sign(-42); -- -1
SELECT sign(0); -- 0
SELECT sign(3.14); -- 1
sin()
| Parameter | Type | Description |
|---|
X | REAL or INTEGER | Angle in radians |
sinh()
| Parameter | Type | Description |
|---|
X | REAL or INTEGER | Any numeric value |
sqrt()
| Parameter | Type | Description |
|---|
X | REAL or INTEGER | Value >= 0 |
SELECT sqrt(144); -- 12.0
SELECT sqrt(2); -- 1.4142135623730951
tan()
| Parameter | Type | Description |
|---|
X | REAL or INTEGER | Angle in radians |
tanh()
| Parameter | Type | Description |
|---|
X | REAL or INTEGER | Any numeric value |
trunc()
| Parameter | Type | Description |
|---|
X | REAL or INTEGER | Any numeric value |
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)
See Also
