Concentration units: mg/mL, µg/µL and molarity

The simplest concentration unit is mass of solute per volume of solution: grams per litre, milligrams per millilitre, micrograms per microlitre. These three are the same number written three ways, because each step down in mass (g → mg → µg) is matched by the same step down in volume (L → mL → µL):

• 1 g/L = 1 mg/mL = 1 µg/µL
• 1 mg/mL = 1,000 µg/mL = 1 µg/µL
• 1 µg/mL = 1 ng/µL

The slip to watch for is mixing a step in the numerator with no step in the denominator. "1 mg/mL is 1,000 µg/µL" is wrong by a factor of a thousand, and it is a very easy thing to write down in a hurry.

Molarity is moles of solute per litre of solution, written M. It counts molecules rather than mass, which is why it is the unit chemistry prefers: two solutions at the same molarity contain the same number of molecules per volume, whatever those molecules weigh. Millimolar (mM) is one thousandth of a mole per litre; micromolar (µM) one millionth; nanomolar (nM) one billionth.

The bridge between mass and molarity is molecular weight, in grams per mole. Divide mass concentration in g/L by molecular weight in g/mol and you have molarity in mol/L. Multiply molarity by molecular weight and you are back to g/L.

Take a hypothetical solute with a molecular weight of 1,000 g/mol, purely to keep the arithmetic visible:

• A solution at 1 mg/mL is 1 g/L. Divide by 1,000 g/mol: 1 mmol/L, or 1 mM.
• A solution at 10 µg/mL is 0.01 g/L. Divide by 1,000 g/mol: 0.00001 mol/L, which is 10 µM.
• A solution at 1 µM is 0.000001 mol/L. Multiply by 1,000 g/mol: 0.001 g/L, which is 1 µg/mL.

Do the conversion in base units (g, L, mol) and convert prefixes at the end. Trying to carry "µ" and "m" through the division is where the powers of ten go missing.

A compound can be described by more than one molecular weight: the free molecule, or the molecule together with a counter-ion or salt form. They differ, and using the wrong one shifts every molarity calculation by the same proportion. The certificate of analysis names the compound as tested; if the name includes a salt form, that is the form the mass on the label refers to. See how to read a certificate of analysis. Relatedly, a purity figure by HPLC is an area percent, not a mass fraction — what HPLC purity actually measures explains why that matters for any calculation that starts from a labelled mass.

The single most effective habit is to write every unit on every line and cancel them like algebra. If the units do not cancel to the unit you wanted, the arithmetic is wrong, however clean the numbers look. It takes ten seconds and it catches the thousand-fold error every time. Record the calculation in the notebook, not on a scrap — see a lab notebook and chain of custody for reference materials.

A calculation is only as precise as its least precise input. A mass read from a balance to three significant figures does not become more precise by being divided by a molecular weight quoted to six; the result should be reported to three. Rounding at each step compounds error, so carry full precision through the arithmetic and round once, at the end, to the precision the inputs justify. This matters most when a result is later compared with a specification: the purity on a certificate is reported to a stated precision, and a laboratory's own figure should be reported to a comparable one before the two are set side by side. The quality page describes what the certificate reports; the returns policy describes what happens when a laboratory's own independent result disagrees materially with it.

This is arithmetic. It is not a preparation, dilution or usage instruction for any material sold on this site, and we publish none. Handling and preparation are the responsibility of the qualified researcher, under the laboratory's own procedures. All material is supplied for in-vitro laboratory research only — see research use only.