Methodology

Five matrices, one ratio method

Each converter has its own dimension and base unit. Cross-dimensional conversion is prohibited.

Converter	Base	Standards	Matrix pairs	Non-identity routes
Length	metre	42	1,764	1,722
Weight	gram	42	1,764	1,722
Time	second	26	676	650
Liquid	litre	58	3,364	3,306
Area	square-metre	21	441	420

The matrices contain 8,009 ordered pairs including identity routes and 7,820 useful non-identity routes.

Ratio and uncertainty

For source magnitude b_s and target magnitude b_t, value_t = value_s × (b_s / b_t). Independent relative uncertainties combine as √((u_s/b_s)² + (u_t/b_t)²).

Weight rules

• Mass is the physical quantity; “weight” is retained in the interface because it is the historical and common metrological term.
• Names such as shekel, mina, talent, drachma, and pound are not merged across systems.
• Coin masses are not monetary conversion rates.
• Chinese and Indian representative values carry wider uncertainty because standards changed by regime and textual tradition.

Time rules

• The converter handles durations, not calendar dates or era correlations.
• Egyptian, Greek, and Roman seasonal hours are excluded because their duration changed with daylight, season, and latitude. Equinoctial astronomical hours are separate fixed records.
• Schematic 30-day months and 360-day years are labelled as arithmetic conventions, not observed lunations or complete intercalated calendars.
• Maya Long Count units are fixed day counts; they do not by themselves select a disputed correlation to the Gregorian calendar.

Treasure calculations

Treasure first resolves the selected mass through the Weight matrix to grams. A fineness entered per mille is divided by 1,000, then multiplied by gross mass: fine metal = gross grams × fineness / 1,000. The same calculation is made independently for gold and silver.

• Historical coin presets are dated mass models or measured specimens. They are not exchange rates, purchasing-power estimates, or promises that every coin of that name had one mass.
• Unknown fineness is withheld rather than treated as pure metal. Gold and silver entries must each lie from 0 to 1,000 and cannot total more than 1,000.
• The residual is calculated only from the fineness values supplied. When one metal remains unknown, the residual must not be read as a complete alloy analysis.
• Optional melt value uses prices entered by the reader per troy ounce. The site supplies no market feed or exchange rate and does not infer face value, historical purchasing power, or collector value.

Geometry and interpretation

The pyramid and dodecahedron tools calculate ideal geometry from the dimensions selected. A formula result is mathematically reproducible but does not by itself prove an ancient design intention, an artefact function, or that an ideal solid exactly describes a surviving object. Measured evidence and interpretive claims remain separate throughout the case studies.

Coverage and exclusions

“All ancient units” is not a defensible closed set. The catalogue uses a comprehensive-core rule: include well-attested, distinct, convertible standards from major documented traditions; split materially different regional or chronological standards; exclude units with no stable magnitude or insufficient sourcing.

The Egyptian audit added core length subdivisions, Old versus Middle/New Kingdom area fractions, smaller capacities, and separate Middle and New Kingdom khar values. Hebrew and several Levantine systems remain outside the matrices because competing shekel, mina, and talent standards require corpus-specific identification.

Validation gates

1. Every identifier is unique within its matrix and carries provenance, basis, confidence, and dimensional magnitude.
2. Every ordered pair must round-trip within 1e-12.
3. All unit catalogue links, converter query states, metadata, and internal links must validate.
4. Measured or reconstructed values remain separate from interpretive claims.

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