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

Hyperbolic Functions

Angle Conversion

Rounding and Truncation

Logarithmic and Exponential Functions

Arithmetic Functions

Constants

Signatures

acos()

acos(X)

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

acosh()

acosh(X)

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

asin()

asin(X)

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

asinh()

asinh(X)

Returns: REAL. The inverse hyperbolic sine of X.

atan()

atan(X)

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

atan2()

atan2(Y, X)

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)

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

ceil() / ceiling()

ceil(X)
ceiling(X)

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)

Returns: REAL. The cosine of X.

cosh()

cosh(X)

Returns: REAL. The hyperbolic cosine of X.

degrees()

degrees(X)

Returns: REAL. X converted from radians to degrees.

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

exp()

exp(X)

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

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

floor()

floor(X)

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)

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)

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)

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)

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)

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)

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)

Returns: REAL. X converted from degrees to radians.

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

sign()

sign(X)

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)

Returns: REAL. The sine of X.

sinh()

sinh(X)

Returns: REAL. The hyperbolic sine of X.

sqrt()

sqrt(X)

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)

Returns: REAL. The tangent of X.

tanh()

tanh(X)

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

trunc()

trunc(X)

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)

See Also

• Expressions for arithmetic operators
• Aggregate Functions for SUM, AVG, MIN, MAX
• Data Types for REAL and INTEGER storage classes