A conductivity meter measures how easily current crosses a centimetre of water. Ions carry that current, so the reading tracks how many ions are dissolved — but the meter cannot tell one ion from another, and it has never weighed anything. Turning its number into a mass takes a correlation, and the correlation is honest about being one.

$\mathrm{TDS} = k\,\mathrm{EC}$ — T-D-S equals k E-C. $\mathrm{TDS}$ is the total dissolved solids in mg/L, the mass that would be left if you evaporated a litre to dryness. $\mathrm{EC}$ is the electrical conductivity in µS/cm, referenced to 25 °C. $k$ is the TDS/EC factor, a bare ratio, typically 0.55 to 0.70 for natural waters. Solve for whichever of the three the day needs: the TDS from a reading, the conductivity a mg/L limit corresponds to, or your own $k$ once a laboratory has weighed one sample for you.

$k$ is not a constant of nature. Sodium-chloride-dominated waters sit near the bottom of that band; carbonate and sulphate waters near the top, because those ions carry more mass per unit of charge they conduct with. A plant that calibrates its own $k$ against one gravimetric result has earned the right to trust its meter for a year.

The units will catch you before the chemistry does. 1 mS/cm = 1000 µS/cm. Tower and boiler panels are usually scaled in µS/cm, RO and DI panels in mS/cm or MΩ·cm, and the same water logged in the wrong prefix reads like a different plant.

At the pure end the trade flips the scale over entirely. $\rho = \dfrac{1}{\sigma}$ — rho equals one over sigma. $\sigma$ — sigma — is the conductivity, $\rho$ — rho — the resistivity, and they are exact reciprocals. The reason the pairing survives is arithmetic convenience: in µS/cm and MΩ·cm the reciprocal needs no scaling at all. 0.055 µS/cm is 18.2 MΩ·cm, the theoretical purity of water at 25 °C and the number every laboratory polisher is judged against. And note which way each scale runs: purer water conducts less and resists more, so a rising resistivity and a falling conductivity are the same good news.