How Tallytopia Calculates Results

Last updated: July 2026

One engine, every calculator

Every calculator on Tallytopia is a formal definition — its inputs, formula steps and display formats — executed by a single deterministic calculation engine built on the open-source mathjs library. There is no per-calculator code to drift out of date: the same engine that computes your result also computes every number in our reference tables, so a table can never disagree with the calculator above it.

AI never does the math

The question bar uses AI for exactly two jobs: recognising which calculator answers your question, and reading the numbers out of your sentence. The arithmetic itself always runs through the deterministic engine. An AI language model never computes, estimates or rounds any result you see.

Every step is shown

Results come with their working: each intermediate step of the formula is displayed and updates live as you change inputs. If you disagree with an assumption, change it and watch the calculation rebuild — nothing is hidden behind the answer.

Published formulas and sources

Wherever a standard exists, we use it and name it: the standard amortization formula for loans and mortgages, Mifflin-St Jeor for BMR, the Devine formula for ideal weight, the US Navy circumference method for body fat, Epley for one-rep max, Riegel for race prediction, the Cooper test for VO₂ max, MET values from the Compendium of Physical Activities, WHO ranges for BMI, and Kepler's third law for orbits. Astronomy constants come from NASA's planetary fact sheets; tax rates cite each country's published standard and reduced rates. Each calculator's page states its formula and assumptions in plain language.

Automated accuracy tests

The formulas are guarded by an automated test suite that runs before every release. It pins calculators to independently known values — the classic $1,995.91 payment on a 30-year $300,000 mortgage at 7%, the International Space Station's 93-minute orbit, Earth's 11.19 km/s escape velocity — and recomputes every cell of every reference table on the site. A change that alters any of those numbers cannot ship.

Rounding and display

Values are computed at full floating-point precision and rounded only for display, at the precision stated on each page (currency to the cent, rates as shown). Intermediate steps display rounded but calculate unrounded, so totals can differ from hand-recomputing the displayed steps by a cent.

Limits and corrections

Calculators simplify: a mortgage page models principal and interest, not your lender's fee schedule; health estimates are population formulas, not diagnoses. Results are informational only — not financial, medical or legal advice. If you believe a result is wrong, email hello@tallytopia.com with the inputs you used — verified errors are fixed and noted.

See also: about Tallytopia and the full calculator directory.