Conductance & Water-Quality Converter

Conductance is a younger idea than resistance. Georg Ohm published his eponymous law in 1827, and the ohm became the operational unit by which engineers thought about wire and coil. It took two more generations to realise that flipping the ratio — describing how easily a path lets charge through, rather than how stiffly it opposes it — is sometimes the more useful frame.

The Siemens family did more to shape industrial electricity than almost any other in the nineteenth century. Werner von Siemens (1816-1892) and his brothers Wilhelm and Friedrich founded Siemens & Halske in 1847, built early telegraph lines across Europe and Asia, invented the dynamo independently of Pacinotti, and ran a research program that pumped out instruments, cables, and electric trams from Berlin and London. The CGPM honoured them in 1971 by naming the SI unit of conductance the siemens.

Before that, electrical engineers had been using mho — Ohm spelled backwards — for decades. The name is attributed to William Thomson, Lord Kelvin, who liked the playfulness and the typographic mirror. Heinrich Hertz, the discoverer of radio waves, also helped codify a coherent unit system for the late nineteenth century. For engineers building amplifiers in the era of vacuum tubes, "millimhos per volt" was simply how you spoke about transconductance.

The General Conference on Weights and Measures finally settled it on 14 October 1971, adopting the siemens (S) as the SI derived unit of electrical conductance. One siemens is one ampere per volt, which is the same as one inverse ohm. The mho continued to appear in American semiconductor datasheets through the 1990s — many old transistor spec sheets still use it — but textbooks gradually standardised on S.

The other half of conductance's modern story is biological. In 1952 Alan Hodgkin and Andrew Huxley published their landmark mathematical model of the squid giant axon action potential, expressing the membrane in terms of time- and voltage-dependent conductances for sodium and potassium ions. Their work won the 1963 Nobel Prize. Yet their model lumped millions of channels together; nobody had ever measured a single ion channel.

That changed in 1976, when Erwin Neher and Bert Sakmann in Göttingen pressed a fire-polished glass micropipette against a frog muscle cell and made a gigaohm seal. With essentially no leakage, they could resolve picoampere current pulses lasting milliseconds — the opening and closing of individual acetylcholine receptors. They had measured one channel's conductance: a few tens of picosiemens. The pair received the 1991 Nobel Prize, and patch clamp became the foundational tool of modern neuroscience.

Today conductance is measured in fabs (ultrapure water at 0.055 µS/cm baseline), in estuarine ecology (brackish water 5-30 mS/cm), in agronomy (soil EC), in semiconductor datasheets (gm in mS), and in single-molecule biophysics (sub-picosiemens). The same number, scaled across 27 orders of magnitude, talks to all of them. That is why this tool refuses to be a single generic form — drag the bar in your domain and let the SI engine handle the rest.