Reference

Functions

Functions take arguments in parentheses, separated by commas. Each argument can itself be an expression.

avg(99, 34, 65, 213, 45, 123)
max(10m, 30k, 7.7m)
bayes(0.01, 0.9, 0.05)
derivative(2x^2, x)

Math and number theory

Function	Description	Example
`abs(x)`	Absolute value	`abs(-234)`
`sum(...)`	Add all arguments, unit-aware	`sum(12, 23, 52)`
`fraction(x)`	Reduced fraction	`fraction(0.625)`
`mixed fraction(x)`	Mixed-number fraction	`mixed fraction(7/3)`
`isprime(x)`	Primality test	`isprime(91)`
`factors(x)`	All positive divisors	`factors(28)`

Statistics

Function	Description	Example
`avg(...)` / `mean(...)`	Arithmetic mean	`avg(70, 80, 90)`
`median(...)`	Middle value	`median(2, 4, 4, 6)`
`range(...)`	Largest minus smallest	`range(2, 4, 10)`
`variance(...)`	Population variance	`variance(2, 4, 4, 6)`
`standard deviation(...)`	Population standard deviation	`standard deviation(2, 4, 4)`
`harmonic mean(...)`	Harmonic mean	`harmonic mean(8, 12, 15)`
`geometric mean(...)`	Geometric mean	`geometric mean(8, 12, 15)`

Sets and combinatorics

Function / operator	Description	Example
`max(...)`	Maximum value, unit-aware	`max(10m, 30k, 7.7m)`
`min(...)`	Minimum value, unit-aware	`min(12 meters, 12 miles)`
`lcm(...)`	Least common multiple	`lcm(12, 15, 18, 25)`
`gcd(...)`	Greatest common divisor	`gcd(12, 15, 18, 25)`
`perm`	Permutations, order matters	`10 perm 3`
`comb`	Combinations, order ignored	`10 comb 3`

Probability

Function	Description	Example
`P(x)`	Probability literal between 0 and 1	`P(10%)`
`conditional(pAandB, pB)`	Conditional probability P(A\|B)	`conditional(0.12, 0.3)`
`bayes(prior, likelihood, fp)`	Bayes posterior P(H\|E)	`bayes(0.01, 0.9, 0.05)`
`odds(p)`	Odds for a probability	`odds(0.75)`
`probability from odds(o)`	Probability implied by odds	`probability from odds(3)`
`binomial(n, k, p)`	Exactly k successes in n trials	`binomial(10, 3, 0.5)`
`expected value(v1, p1, ...)`	Weighted sum of value/probability pairs	`expected value(10, 0.5, 20, 0.5)`

Finance

Function	Description	Example
`simple interest(p, r, t)`	Interest only	`simple interest(10000, 5%, 2 years)`
`compound interest(p, r, t, n)`	Compound interest earned	`compound interest(1000, 10%, 2 years)`
`future value(p, r, t, n)`	Principal plus compound growth	`future value(1000, 10%, 2 years)`
`present value(fv, r, t, n)`	Present value of a future amount	`present value(1210, 10%, 2 years)`
`cagr(start, end, t)`	Compound annual growth rate	`cagr(1000, 2000, 10 years)`
`emi(p, r, t)`	Monthly amortizing loan payment	`emi(500000, 6.5%, 30 years)`
`mortgage(p, r, t)`	Alias for `emi`	`mortgage(500000, 6.5%, 30 years)`
`loan payment(p, r, t)`	Alias for `emi`	`loan payment(500000, 6.5%, 30 years)`
`loan interest(p, r, t)`	Total interest paid	`loan interest(100000, 12%, 1 year)`
`future value annuity(pmt, r, t, n)`	Future value of equal payments	`future value annuity(1000, 10%, 3 years)`
`present value annuity(pmt, r, t, n)`	Present value of equal payments	`present value annuity(500, 8%, 10 years, 12)`
`roi(initial, final)`	Return on investment	`roi(1000, 1500)`
`apy(rate, frequency)`	Effective annual yield	`apy(12%, 12)`
`profit margin(revenue, cost)`	Profit as a percent of revenue	`profit margin(200, 150)`
`markup(cost, price)`	Markup over cost	`markup(150, 200)`
`break even(fixed, price, variable)`	Units needed to break even	`break even(10000, 50, 30)`
`runway(cash, burn)`	Months of cash runway	`runway(100000, 8000)`
`doubling time(rate)`	Rule-of-72 estimate in years	`doubling time(8%)`
`tip(bill, rate)`	Tip amount	`tip(80, 18%)`
`tip total(bill, rate)`	Bill including the tip	`tip total(80, 18%)`
`discount(price, rate)`	Sale price after a discount (alias `sale price`)	`discount(200, 25%)`
`sales tax(price, rate)`	Tax on a price	`sales tax(100, 8%)`
`price with tax(price, rate)`	Price including tax	`price with tax(100, 8%)`
`npv(rate, cf0, cf1, ...)`	Net present value of a cashflow series	`npv(10%, -1000, 500, 500, 500)`
`irr(cf0, cf1, ...)`	Internal rate of return, as a percent	`irr(-1000, 500, 500, 500)`
`depreciation(cost, salvage, life)`	Straight-line depreciation per year	`depreciation(10000, 1000, 5)`

Health and fitness

Body-composition and fitness metrics. Inputs accept weight/height units. See Health & Fitness for the formula standards.

Function	Description	Example
`bmi(weight, height)`	Body Mass Index	`bmi(70, 1.75)`
`bmr male(w, h, age)` / `bmr female(...)`	Basal metabolic rate, kcal/day	`bmr male(80, 180, 30)`
`tdee(bmr, factor)`	Total daily energy expenditure	`tdee(1780, 1.55)`
`body fat male(w, h, age)` / `body fat female(...)`	Body fat % (Deurenberg)	`body fat male(80, 1.8, 30)`
`ideal weight male(height)` / `ideal weight female(...)`	Ideal weight, kg (Devine)	`ideal weight male(180 cm)`
`max heart rate(age)`	Maximum heart rate, bpm	`max heart rate(30)`
`target heart rate(age, intensity)`	Target heart-rate zone, bpm	`target heart rate(30, 70%)`
`calories burned(met, weight, minutes)`	Calories for an activity	`calories burned(8, 70, 30)`
`water intake(weight)`	Suggested daily water	`water intake(70 kg)`

Symbolic algebra

Function	Description	Example
`simplify(expr)`	Collect like terms	`simplify(2x^2 - 4x^2)`
`derivative(expr, variable)`	Derivative	`derivative(2x^2, x)`
`diff(expr, variable)`	Alias for `derivative`	`diff(sin(x), x)`
`integrate(expr, variable)`	Indefinite integral	`integrate(2x^2 + 3x, x)`
`integral(expr, variable)`	Alias for `integrate`	`integral(2x^2 + 3x, x)`
`integrate(expr, variable, a, b)`	Definite integral	`integrate(2x^2, x, 0, 5)`
`limit(expr, variable, point)`	Limit	`limit(sin(x)/x, x, 0)`

IP addresses

Function	Description	Example
`ipv4(n)`	Build IPv4 address from integer	`ipv4(3232235777)`
`ipv6(n)`	Build IPv6 address from integer	`ipv6(1)`
`network(cidr)`	Network address	`network(192.168.1.130/24)`
`broadcast(cidr)`	Broadcast address	`broadcast(192.168.1.0/24)`
`netmask(cidr)`	Subnet mask	`netmask(10.0.0.0/24)`
`subnetmask(cidr)`	Alias for `netmask`	`subnetmask(10.0.0.0/24)`
`wildcard(cidr)`	Inverse mask	`wildcard(192.168.1.0/24)`
`firsthost(cidr)`	First usable host	`firsthost(192.168.1.0/24)`
`lasthost(cidr)`	Last usable host	`lasthost(192.168.1.0/24)`
`hosts(cidr)`	Usable host count	`hosts(192.168.1.0/24)`
`addresses(cidr)`	Total address count	`addresses(192.168.1.0/24)`
`prefix(maskOrCidr)`	Prefix length	`prefix(255.255.255.0)`
`version(address)`	IP version, `4` or `6`	`version(2001:db8::1)`
`contains(cidr, address)`	Subnet membership	`contains(192.168.1.0/24, 192.168.1.5)`
`isprivate(address)`	Private address test	`isprivate(10.1.2.3)`
`ispublic(address)`	Public address test	`ispublic(8.8.8.8)`
`isloopback(address)`	Loopback test	`isloopback(127.0.0.1)`
`ismulticast(address)`	Multicast test	`ismulticast(224.0.0.1)`

Trigonometry and logarithms

These take the value after the name, and parentheses are optional for plain numeric arguments. See Trigonometry and Logarithms for details.

Group	Names
Basic trig	`sin`, `cos`, `tan`, `sec`, `csc`, `cot`
Inverse	`asin`, `acos`, `atan`, `asec`, `acsc`, `acot`
Hyperbolic	`sinh`, `cosh`, `tanh`, `sech`, `csch`, `coth`
Inverse hyperbolic	`asinh`, `acosh`, `atanh`, `asech`, `acsch`, `acoth`
Logarithms	`log` / `loge` (natural), `log10`, `log2`

Geometry

Shape area, perimeter/circumference, surface area, volume, and line slope. Length units on the arguments carry into the result. See Geometry.

Function	Description	Example
`circle area(r)`	π·r²	`circle area(5)`
`circle circumference(r)`	2·π·r (alias `circle perimeter`)	`circle circumference(5)`
`square area(s)` / `square perimeter(s)`	Square area / perimeter	`square area(4)`
`rectangle area(w, h)` / `rectangle perimeter(w, h)`	Rectangle area / perimeter	`rectangle area(3, 4)`
`triangle area(base, height)`	½·base·height (or Heron from three sides)	`triangle area(3, 4, 5)`
`trapezoid area(a, b, h)`	½·(a + b)·h	`trapezoid area(4, 6, 3)`
`parallelogram area(base, height)`	base × height	`parallelogram area(5, 3)`
`ellipse area(a, b)`	π·a·b	`ellipse area(3, 2)`
`sphere volume(r)` / `sphere surface area(r)`	Sphere volume / area (alias `sphere area`)	`sphere volume(3)`
`cube volume(s)` / `cube surface area(s)`	Cube volume / surface area	`cube volume(3)`
`cylinder volume(r, h)` / `cylinder surface area(r, h)`	Cylinder volume / surface area	`cylinder volume(2, 5)`
`cone volume(r, h)` / `cone surface area(r, h)`	Cone volume / surface area	`cone volume(2, 6)`
`rectangular prism volume(l, w, h)`	Box volume (alias `box volume`)	`box volume(2, 3, 4)`
`pyramid volume(l, w, h)`	1/3·l·w·h	`pyramid volume(3, 3, 9)`
`slope(x1, y1, x2, y2)`	Slope of a line	`slope(0, 0, 2, 4)`

Coordinate systems

Constructors build points; a single point argument converts it. See Coordinate Systems for to-conversions and arithmetic.

Function	Description	Example
`point(...)`	Cartesian point/vector (also `cartesian`, `vector`)	`point(1, 2, 3)`
`polar(r, θ)`	2-D polar point (θ in degrees)	`polar(5, 90)`
`cylindrical(r, θ, z)`	3-D cylindrical point	`cylindrical(2, 90, 5)`
`spherical(ρ, θ, φ)`	3-D spherical point	`spherical(1, 90, 0)`
`minkowski(t, x, y, z)`	Spacetime point (−,+,+,+)	`minkowski(1, 2, 3, 4)`
`distance(a, b)`	Distance between two points	`distance(point(0,0), point(3,4))`
`magnitude(v)` / `norm(v)`	Length from the origin	`magnitude(point(3,4))`
`midpoint(a, b)`	Midpoint of two points	`midpoint(point(0,0), point(4,6))`
`dot(a, b)`	Dot product (scalar)	`dot(point(1,2,3), point(4,5,6))`
`cross(a, b)`	Cross product of two 3-D vectors	`cross(point(1,0,0), point(0,1,0))`
`angle(a, b)`	Angle between two vectors (degrees)	`angle(point(1,0), point(0,1))`
`normalize(v)`	Unit vector	`normalize(point(3,4))`
`interval(p, q)`	Signed Minkowski interval s²	`interval(minkowski(5,0,0,0), minkowski(0,3,0,0))`
`atan2(y, x)`	Two-argument arctangent (degrees)	`atan2(1, 1)`
`hypot(...)`	Euclidean norm √(x²+y²+…)	`hypot(3, 4)`

Matrices

Take a matrix literal [1 2, 3 4] (space = column, comma/semicolon = row). See Matrices for arithmetic and the full set.

Function	Description	Example
`transpose(A)`	Transpose	`transpose([1 2 3, 4 5 6])`
`determinant(A)` / `det(A)`	Determinant of a square matrix	`determinant([1 2, 3 4])`
`inverse(A)` / `inv(A)`	Inverse of an invertible matrix	`inverse([4 7, 2 6])`
`adjugate(A)` / `adj(A)`	Classical adjoint	`adjugate([1 2, 3 4])`
`trace(A)`	Sum of the diagonal	`trace([1 2, 3 4])`
`rank(A)`	Rank	`rank([1 2, 2 4])`
`rref(A)`	Reduced row-echelon form	`rref([1 2 3, 4 5 6, 7 8 9])`
`minor(A, i, j)`	(i, j) minor (1-indexed)	`minor([1 2 3, 4 5 6, 7 8 10], 1, 1)`
`cofactor(A, i, j)`	(i, j) cofactor (1-indexed)	`cofactor([1 2 3, 4 5 6, 7 8 10], 1, 2)`
`identity(n)` / `eye(n)`	n×n identity	`identity(3)`
`zeros(n)` / `zeros(r, c)`	Zero matrix	`zeros(2, 3)`
`ones(n)` / `ones(r, c)`	All-ones matrix	`ones(2, 2)`
`diag(...)` / `diag(A)`	Build / extract a diagonal	`diag(1, 2, 3)`
`size(A)` / `shape(A)`	Dimensions `[rows cols]`	`size([1 2 3, 4 5 6])`
`rows(A)` / `cols(A)`	Row / column count	`rows([1 2 3, 4 5 6])`
`hadamard(A, B)`	Element-wise product	`hadamard([1 2, 3 4], [10 20, 30 40])`
`linsolve(A, b)`	Solve A·x = b	`linsolve([2 1, 1 3], [5, 10])`
`eigenvalues(A)` / `eigvals(A)`	Eigenvalues (approximate)	`eigenvalues([2 1, 1 2])`
`eigenvectors(A)` / `eigvecs(A)`	Eigenvectors as columns	`eigenvectors([2 0, 0 3])`

Visualization

Produce a graph rendered below the editor. See Graphing.

Function	Description	Example
`draw(...)`	Graph curves `y=f(x)`, complex numbers, or points (alias `plot`)	`draw(x^2)`
`plot(...)`	Alias for `draw`	`plot(sin(x), cos(x))`

Random

Draw random values. In the app the result freezes (a hidden managed seed) so it stays stable across edits; hover the function name to reveal the seed and re-roll. See Random & IDs.

Function	Description	Example
`random()`	Real number in `[0, 1)`	`random()`
`random(max)`	Whole number from `0` to `max`	`random(6)`
`random(min, max)`	Whole number from `min` to `max`	`random(10, 100)`
`uuid()`	UUID — v7 by default; `uuid(4)` / `uuid(7)`	`uuid()`
`nanoid()`	URL-safe id; `nanoid(n)` sets length	`nanoid()`
`coin()`	`"heads"` or `"tails"`	`coin()`
`randombool()`	`true` or `false`	`randombool()`
`pick(...)`	One argument chosen at random	`pick(1, 2, 3)`
`randomcolor()`	A random colour	`randomcolor()`

Hashing

Deterministic hashes and checksums of a quoted string (or a number). Returns a lowercase hex digest. See Hashing.

Function	Description	Example
`md5(text)`	MD5 (128-bit)	`md5("hello")`
`sha1(text)`	SHA-1 (160-bit)	`sha1("hello")`
`sha256(text)`	SHA-256 (256-bit)	`sha256("hello")`
`sha384(text)`	SHA-384 (384-bit)	`sha384("hello")`
`sha512(text)`	SHA-512 (512-bit)	`sha512("hello")`
`sha3(text)`	SHA3-256 (alias `sha3_256`)	`sha3("hello")`
`ripemd160(text)`	RIPEMD-160 (160-bit)	`ripemd160("hello")`
`crc32(text)`	CRC32 checksum	`crc32("hello")`

Color constructors

rgb(...), rgba(...), and hsl(...) build colors. See Colors.

rgb(12, 124, 201)
rgba(12, 124, 201, 0.5)
hsl(60, 0.03703, 0.1058)

Constants and special values

pi, e, and i can be used anywhere a compatible number is expected. i is the imaginary unit for complex arithmetic.

2 * pi
e ^ 2
i^2

Function names are generally case-insensitive. Labels are case-sensitive.