How we build and check calculators
An answer is only worth something if it is right. This is exactly what each calculator goes through before it is published.
The maths is separate from the page
Every calculator is a pure function: values in, a worked solution out. It lives in one file, independent of the page around it, so it can be tested directly rather than through a browser.
Tests check a property, not a saved answer
Comparing against a stored expected answer only proves the code has not changed. So each engine is checked against an independent computation instead: a factorisation is multiplied back out and compared coefficient by coefficient, a derivative is compared against a numeric difference quotient, a simplified square root must satisfy out² × rest = n with no square factor left. A wrong answer cannot pass by agreeing with itself.
A second implementation confirms the first
The same cases are run again in a different language, using its own standard library for exact fractions and statistics. Both implementations have to agree.
Human review before publication
A qualified mathematician checks the maths, the wording of every step and the common mistakes section before a calculator goes live. The review date is shown on the page.
Saying so when it cannot answer
A calculator that guesses is worse than one that declines. When an expression has no integer factorisation, or an input is outside what the tool covers, it says that plainly and explains why.