Formulas Complex

Complex Formulas — Constants, Operators, and Functions

This page lists the constants, operators, and functions available when writing value formulas. Use the {key} syntax to insert other values (for example, {health} or {baseValue}).

Constants

• pi — π (approximately 3.14159265)
• e — Euler's number (approximately 2.71828)

Operators

Operator	Description
-	Subtraction (also unary negation, e.g. -{key})
+	Addition
*	Multiplication
/	Division
^	Exponentiation (power)
%	Modulus (remainder), e.g. 11 % 2 → 1

Use parentheses () to control evaluation order. Operator precedence follows typical math rules (exponents, multiplication/division/modulus, addition/subtraction).

Functions

Function	Description
abs(x)	Absolute value
ceil(x)	Round up to nearest integer
floor(x)	Round down to nearest integer
round(x)	Round to nearest integer
sqrt(x)	Square root
sq(x)	Square (x * x)
sign(x)	1 if x>0, -1 if x<0, 0 if x==0
sin(x)	Sine — x in radians
cos(x)	Cosine — x in radians
tan(x)	Tangent — x in radians
asin(x)	Arc-sine — returns radians
acos(x)	Arc-cosine — returns radians
atan(x)	Arc-tangent — returns radians
sinh(x)	Hyperbolic sine
cosh(x)	Hyperbolic cosine
tanh(x)	Hyperbolic tangent
min(x, y, ...)	Minimum of the given numbers
max(x, y, ...)	Maximum of the given numbers
sum(x, y, ...)	Sum of the given numbers
avg(x, y, ...)	Average of the given numbers
ln(x)	Natural logarithm (base e)
log(x)	Base-10 logarithm
random()	Returns a pseudo-random number in the range [0, 1)

Notes:

• Trigonometric functions use radians. Convert degrees to radians with * pi / 180.
• Use sq(x) or the exponent x ^ 2 for squares; cubes are x ^ 3.
• random() returns a pseudo-random float between 0 (inclusive) and 1 (exclusive).

Examples

• Average of two values: ( {a} + {b} ) / 2
• Clamp a value between 0 and a max: max(0, min({value}, {max}))
• Weighted value: ({base} * 0.7 + {bonus} * 0.3)
• Convert degrees to radians for trig: sin({angle} * pi / 180)
• Conditional-like (using sign): max(0, sign({damage}) * {damage}) — ensures damage is non-negative