Methodology

The engine

Every calculator on this site runs on a deterministic math engine written in JavaScript and executed in your browser. Deterministic means: the same inputs always produce the same outputs, through fixed arithmetic and algebra, no language model, no guessing, no randomness.

Steps and answers come from one computation

Each engine function returns two things together: the result and the steps that produced it. Because both are generated by the same code path, the steps shown can never contradict the answer, a common failure mode of AI-only solvers, where the explanation is generated separately from the number.

Testing

Every engine function ships with unit tests covering normal inputs, invalid inputs, and boundary cases: division by zero, zero and negative values, single-value data sets, complex roots, vertical lines, and identity/contradiction equations. Tests run automatically before any release.

Limitations

• Tools state their scope on-page. The derivative and integral calculators handle polynomials; trigonometric and exponential functions are not yet supported.
• Floating-point arithmetic has finite precision (about 15–17 significant digits). Results display up to 6 significant decimals; exact forms (fractions, multiples of π) are shown alongside where meaningful.
• These are educational tools. For safety-critical, financial, or engineering decisions, verify with independent computation, see the disclaimer.