the402 x402 endpoint directory

List every physical constant in the dataset, or only those in a given category (universal, adopted, electromagnetic, a

Search the constants table by key, symbol or name substring. Exact matches rank first, then prefix matches, then subst

Look up a physical constant by its key (e.g. "speed-of-light"), symbol (e.g. "c") or exact name. Returns the CODATA 20

Compute the molar mass (g/mol) of a chemical formula. Supports nested parentheses and brackets, element multipliers, a

Search the periodic table by name or symbol substring. Exact matches rank first, then prefix matches, then substring m

Look up a periodic-table element by exactly one of `symbol` (e.g. "Fe"), `name` (e.g. "iron") or atomic `number` (1..1

Poisson distribution with rate `lambda` (> 0, ≤ 1e9). `function` selects the mass (pmf), cumulative distribution (cdf)

Binomial distribution with `trials` (n ≥ 0, ≤ 1e6) and success `probability` (0..1). `function` selects the mass (pmf)

Student's t distribution with df degrees of freedom (> 0). `function` selects the density (pdf), cumulative distributi

Normal distribution with optional mean (default 0) and standard deviation sd (default 1). `function` selects the densi

Parse an A1 range like "A1:C10" into its start and end cells (normalized so start is the top-left) and its extent — ro

Convert between a spreadsheet column letter and its 1-based index in either direction. Provide exactly one of `letter`

Build an A1-style cell reference from 1-based row and column numbers, optionally marking the row and/or column absolut

Parse an A1-style cell reference (e.g. "B3" or "$AA$100") into 1-based row and column numbers, plus the column letters

The n-th Catalan number Cₙ = C(2n, n)/(n+1), counting balanced bracketings, binary trees, and many other structures. R

Multinomial coefficient (k1+k2+…)! / (k1! k2! …) — the number of ways to partition n = Σki items into labelled groups

Binomial coefficient nCr = n!/(r!(n-r)!), the number of unordered r-subsets of n. Requires r ≤ n and min(r, n-r) ≤ 100

Number of ordered arrangements of r items from n, nPr = n!/(n-r)!. Requires r ≤ n and r ≤ 10000.

Exact factorial n! for 0 ≤ n ≤ 20000, returned as a decimal string with its digit count.

Compute (base ^ exponent) mod modulus efficiently for arbitrary-precision integers. The modulus must be positive.

Euler's totient φ(n) — the count of integers in [1, n] coprime to n — for a positive integer ≤ 10^15 (it is computed f

Miller-Rabin primality test (with witnesses that are exact for all 64-bit integers) on an arbitrary-precision integer.

Prime-factorize a positive integer (≤ 10^15 so the computation is always fast). Returns the prime factors with exponen

Least common multiple of two or more positive integers (arbitrary precision).

Greatest common divisor of two or more non-negative integers (arbitrary precision).

Split the input into parts on each match of a RE2 pattern. An optional limit caps the number of parts (0 = unlimited).

Replace matches of a RE2 pattern with a replacement string. Replaces all matches by default (set all=false for first-o

Find the first match (or all matches with all=true) of a RE2 pattern, returning each match's text, start/end offsets,

Test whether a RE2 pattern matches anywhere in the input. Returns { matched }. RE2 guarantees linear-time evaluation,

Build an otpauth:// provisioning URI (the string encoded in authenticator QR codes) for a totp or hotp secret. Include

Verify a submitted TOTP code against a base32 secret, scanning ±window time steps (default ±1) to tolerate clock drift

Generate an RFC 4226 counter-based HMAC one-time password from a base32 secret and counter. Configurable digits (6–10,

Generate an RFC 6238 time-based one-time password from a base32 secret. Uses the current time by default, or an explic

Infer a JSON Schema (draft-07) from an example value, walking objects and arrays recursively. Set detectFormat=true to

Validate a JSON value against a JSON Schema (draft-07, with the standard string formats enabled). An invalid schema is

Ordinary-least-squares linear regression of y on x: slope, intercept, correlation r and coefficient of determination r

Pearson correlation coefficient and covariance of two equal-length paired series. Rejected as a clean 400 if the lengt

Evaluate one or more percentiles (0–100) of a numeric sample using linear interpolation between order statistics (the

Full descriptive summary of a numeric sample: count, sum, min/max/range, mean, median, mode(s), variance, standard dev

Euclidean, Manhattan and Chebyshev distance between two 2-D points.

Area (shoelace formula), perimeter and centroid of a simple polygon given its vertices in order. Vertices are treated

Area (Heron's formula), perimeter and interior angles of a triangle from its three side lengths. Sides that violate th

Area, perimeter and diagonal of a rectangle from its width and height.

Diameter, circumference and area of a circle from its radius.

Internal rate of return (per period) of a series of cash flows, solved with a bounded bisection. Requires at least one

Net present value of a series of cash flows discounted at a per-period rate. cashflows[0] is the time-0 flow (typicall

Present value of a future sum and/or a level annuity, given a per-period rate and number of periods. Set dueAtBeginnin

Future value of a present sum and/or a level annuity, given a per-period rate and number of periods. Set dueAtBeginnin

Grow a principal by simple or compound interest over a number of years. Compound interest uses compoundsPerYear compou

Compute the level monthly payment, total paid and total interest of a fully-amortizing loan. Handles a 0% rate. Set sc