The simple answer is that TDS (a measure of "hardness") is not equivalent to siemens (conductance). For a given dissolved solid there will be an approximate proportion where you can "equate" % solute to conductance.
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"Well, I've wrestled with reality for 35 years, Doctor, and I'm happy to state I finally won out over it." Elwood P. Dowd
TDS (total dissolved solids,in a solution) is as the name implies.
μSiemens (or Mho) are unit measure of conductivity. As you probably know water are non-conductive, it is what is dissolved in it that makes it conductive. To arrive at a conductivity value of a solution you will need to measure it's conductivity (the reciprocal of resistance.) by letting current flow through it. If there's a single dissolved solid you may get there by calculating specific conductivity. if there is more dissolve than one dissolve material,it becomes very complicated. Explain what is your application, maybe there's another way we can help you?
A neutral salt will give a conductivity value of approximately 2.5 uS per ppm (or mg/l).
The value will vary depending on the alkalinity of the sample. Carbon dioxide level has an impact.
A base (i.e., very dilute NaOH) will give a reading of about 5.5 uS per mg/l.
An acid (i.e., very dilute HCl) will give a reading of about 7 uS per mg/l.
The conductivity calibration to a specific sample has to be done on that sample. I do not know of any formula that would calculate a specific and accurate conductivity value when knowing the chemical character of the sample, component analysis, pH, etc.
By the way, in 40 plus years in the water treatment industry, I always considered "TDS" as relating to the inorganic constituents of a water sample. The organic content, if present, is typically reported separately.