Formula Atlas
Most calculator sites organise by topic. Underneath, the mathematics does not respect those boundaries — one amortisation formula serves a mortgage, a car loan and a boat loan alike, filed under three different categories. This is a map of what our calculators actually share, and it grows as more of the catalog is mapped.
10 formula families · 13 calculators · 1 spanning more than one category
Amortising loan payment
2 hubsSimon Stevin published the first printed interest tables, including the present value of an annuity — the relationship this payment formula inverts. Until then such tables were guarded as trade secrets by lenders.Simon Stevin, Tafelen van Interest, Antwerp·1582
Body mass index
Adolphe Quetelet proposed weight divided by height squared while studying the statistical distribution of human measurements — he was describing populations, not diagnosing individuals. Ancel Keys coined the name 'body mass index' 137 years later, and noted in the same paper that it was only adequate as a population measure.Adolphe Quetelet, Sur l'homme et le développement de ses facultés, Paris (1835); Ancel Keys et al., 'Indices of relative weight and obesity', Journal of Chronic Diseases 25(6) (1972)·1835, named 1972
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Area of a circle
Archimedes proved that a circle's area equals that of a right triangle whose height is the radius and whose base is the circumference, and bounded π between 3+10/71 and 3+1/7 by comparing inscribed and circumscribed 96-gons.Archimedes, Measurement of a Circle, Propositions 1 and 3·c. 250 BCE
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Compound growth with regular contributions
The present-value-of-an-annuity relationship this inverts appeared in Simon Stevin's printed interest tables, and Richard Witt's Arithmeticall Questions extended it to series of payments in English three decades later.Simon Stevin, Tafelen van Interest, Antwerp (1582); Richard Witt, Arithmeticall Questions, London (1613)·1582–1613
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Heron's formula for the area of a triangle
Heron of Alexandria set out this formula with a worked proof in his Metrica, deriving a triangle's area from its three sides alone — no angle and no height required.Heron of Alexandria, Metrica, Book I, Proposition 8·c. 60 CE
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The ideal gas law
Émile Clapeyron combined Boyle's, Charles' and Avogadro's separate observations into one equation of state, introducing the constant that carries the relationship between the amount of gas and its energy.Émile Clapeyron, 'Mémoire sur la puissance motrice de la chaleur', Journal de l'École Polytechnique, vol. 14·1834
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Ohm's law
Georg Ohm published the proportionality between current and voltage after measuring it on wires of varying length, using a thermocouple for a steady source. The work was poorly received at first — his own ministry considered it insufficiently rigorous.Georg Simon Ohm, Die galvanische Kette, mathematisch bearbeitet, Berlin·1827
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Percentage change
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The Pythagorean theorem
Euclid's proof arranges the three squares around the triangle and shows the two smaller ones can be cut and rearranged to fill the largest. Babylonian tablet Plimpton 322 lists Pythagorean triples roughly a thousand years earlier, so the relationship was in use long before it was proved.Euclid, Elements, Book I, Proposition 47·c. 300 BCE
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Simple interest
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Each of these calculators shows its full derivation — every step, why the step exists, and where the formula came from. The atlas grows as more families are mapped.