Quinaria

A quinaria (plural: quinariae) is a Roman unit of area, roughly equal to 4.2 square centimetres (0.65 in²).[1] Its primary use was to measure the cross-sectional area of pipes in Roman water distribution systems. A "one quinaria" pipe is 2.31 centimetres (0.91 in) in diameter.

In Roman times, there was considerable ambiguity regarding the origin of the name, and the actual value of a quinaria. According to Frontinus:[2]

...Those who refer (the quinaria) to Vitruvius and the plumbers, declare that it was so named from the fact that a flat sheet of lead 5 digits wide, made up into a round pipe, forms this ajutage. But this is indefinite, because the plate, when made up into a round shape, will be extended on the exterior surface and contracted on the interior surface. The most probable explanation is that the quinaria received its name from having a diameter of 5/4 of a digit...

In other words, Vitruvius claimed that the name was derived from a pipe created from a flat sheet of lead "5 digits wide", roughly 9.25 centimetres (3.64 in), but Frontinus contested the definitiveness of this because the exterior circumference of the resulting pipe would be larger than the interior circumference. According to Frontinus, the name and value is derived from a pipe having a diameter of "5/4 of a digit". Using Vitruvius' standard, the value of a quinaria is 6.81 square centimetres (1.056 sq in), and the resulting pipe would have a diameter of 2.94 centimetres (1.16 in).

The importance of this measure was that water taxes in ancient Rome were based on the size of the supply pipe.[3] See also: Water theft § Roman period.