Why this page exists
Anyone can put a formula in a web page. Nothing on the surface of a calculator tells you whether the arithmetic behind it was checked, guessed, or copied from a site that guessed. So rather than asking you to trust the readout, this page describes the machinery — plainly enough that you can judge it, and specifically enough that you could catch us being wrong.
Every formula exists twice
Each instrument's mathematics is implemented in two places by design: once in TypeScript, which runs in your browser, and once in Python, which never leaves our build machine. The two share no code. Before any page is published, the same inputs are pushed through both and the answers must agree to roughly twelve significant figures. They must also agree about failure — dividing by zero has to be refused by both, for the same reason.
This sounds like over-engineering for a percentage calculator, and for one page it would be. The point is scale: when 3,900 sheets share one engine, a subtle error in that engine is an error in thousands of pages at once. Two implementations that must agree turn a silent, systematic mistake into a build that stops.
Cited test cases, not self-confirmation
Every instrument carries a small file of test cases: specific inputs with the answers they must produce. At least one case per instrument is a golden case — its expected value comes from outside our own code. A published physical constant, an exact-by-construction identity, a worked example from a standard reference, or arithmetic done by hand on paper.
"I computed it with the formula I am testing" is explicitly not an acceptable source, because it proves only that the code agrees with itself. The distinction is not theoretical: while building the first instruments, this rule caught two hand-computed expectations that were simply wrong, and a variable-naming collision that would have silently broken a statistics page.
What the pages promise
- The formula is shown. Not a description of it — the equation, typeset, with every symbol defined, plus the substituted working for the numbers you entered.
- Undefined stays undefined. When a result does not exist — division by zero, an impossible measurement — the readout blanks and states the reason. It is never filled with a plausible-looking figure.
- Units are converted, not assumed. Values are normalised to SI internally, so entering 154 pounds and 5 foot 8 gives exactly what 69.9 kilograms and 172.7 centimetres gives.
- Sources are listed. Where an instrument encodes a published standard or clinical formula, the reference is named on the page so you can check the origin yourself.
How the writing is made
Explanations are written from the formula and the specification of each instrument — never adapted from another calculator site's text. Before publishing, every page is compared against the rest of our own corpus to catch near-duplicate prose, and against the corresponding page on the largest competitor to confirm our explanation is independent of theirs. Pages that fail either check are rewritten, not published.
Where we are fallible
Verification narrows the space for error; it does not eliminate it. A formula can be implemented correctly in both languages and still be the wrong formula for your situation. Published equations — particularly in health — are population averages that may fit you poorly. Financial figures here exclude the fees, taxes and local rules that make a real quote differ. And a cited source can itself be outdated.
So: these instruments are for arithmetic you can check, not for decisions you should not make alone. If you find a figure you believe is wrong, please tell us — a specific, reproducible disagreement is the most valuable thing anyone can send us.
Current state
3718 instruments are in service and pass every check described above. 3,900 are catalogued and queued. We publish an instrument only once its formula, its test cases and its explanation have all passed — which is why the bench fills slowly and the category pages honestly separate what is built from what is not.