Is there any documentation on the expression language supported by Spotlight calculations?

Question

As most know, you can type mathematical expressions into Spotlight and it will show the result, which you can copy with Cmd-C to paste into other applications. It's mostly intuitive, especially to programmers who are used to notations like ^ and ** for exponentation, but not everything is obvious.

For instance, in a comment to this answer someone pointed out that the expression 1 & -1 produces the unexpected result 0; if -1 is interpreted as its twos-complement representation, that would be 11111..., and bitwise AND with 1 should produce 1, not 0. Some languages like C simply don't specify the result of bitwise operations on negative numbers.

Is there any public documentation of all the operators and functions supported by this calculator, and the way it interprets the operands? I've been trying to find it with google, but the best I could find is a brief mention that you can enter mathematical expressions here; the examples it gives are trivial (one multiplication and one division), and there's no link to more detailed documentation.

Answer 1

Not sure if there is an Apple document on this at all but here are some of the mathematical functions and symbols you can use in formulas while making calculations with Spotlight of macOS Ventura (13.4.1) with examples and the results returned:

Basic: 1 + 1 = 2, 1 - 1 = 0, 2 * 3 = 6, 6 / 2 = 3
Precendence: 2 + 3 * 5 = 17
Parentheses: (1 + 1) / 2 = 2
Multiplication (Implied): 2(8+1) = 18
Absolute Value: abs(-1.1) = fabs(-1.1) = 1.1
Percentage: 25% = 0.25, 60 * 25% = 15
Include unit in formula: 5 miles * 4 = 20 miles
Include a unit conversion in formula: 5 miles * 4 in km = 32.19 kilometers
Use a rate with units in a formula: 20 mph * 5 hours = 100 miles
Modulus (Remainder): 5 % 2 = 1
Base 10 and Natural Logarithms: log(10) = 1, ln(e) = 1,
Exponentiation: 2^3 = 2 ** 3 = 8
Exponentiation (Natural Base): e^2 = e ** 2 = exp(2) = 7,3890560989
Square and Cube Roots: sqrt(4) = 2, cbrt(27) = 3
Factorial: 3! = 6
Trigonometric (Radian): sin(pi/2) = 1, cos(pi) = -1, tan(pi/4) = 1
Trigonometric (Degree): sind(90) = 1, cosd(180) = -1, tand(45) = 1
Trigonometric (Degree): sin(90deg) = 1, cos(180deg) = -1, tan(45deg) = 1
Inverse Trigonometric (Radian): arcsin(1) = 1,57 radians, arccos(-1) = 3,14 radians, arctan(1) = 0,79 radians
Inverse Trigonometric (Degree): arcsind(1) = 90 degrees, arccosd(-1) = 180 degrees, tand(1) = 45 degrees
Hyperbolic: sinh(1) = 1.1752011936, cosh(0) = 1, tanh(0) = 0
Inverse Hyperpolic: arcsinh(1) = 0.881373587; arccosh(1) = 0, arctanh(0.5) = 0.5493061443
Rounding: ceil(1.2) = 2, floor(1.2) = 1, round(1.6) = 2
Bitwise Operators: 3 & 5 = 3 and 5 = 1, 3 | 5 = 3 or 5 = 7, 3 xor 5 = 6
Error and Complementary Error Functions: erf(1) = 0.8427007929, erfc(1) = 0.1572992071

One can combine any of the above symbols or operators, using parentheses for correct prioritization whenever necessary, as shown in the example below:

ln(e **  (4 / sind(90))) = 4

Though the constants pi and e are allowed, variables are not.

To get a result into clipboard, just press Command ⌘+C once the result appears. A calculation result is not shown when the formula is not proper or the outcome is undefined.

Credits:

1. "Spotlight calculator can do more than simple arithmetic" by Eren Jeager of Reddit, 2013
2. "Advanced Calculations With Spotlight" by MacMost, 2016
3. "Advanced Math Calculations Using Spotlight" by MacMost, 2023