Converting Between Concentration Units Without Losing Your Mind
A reagent's concentration might be given as molarity on one label, percent w/v on another, and mg/mL in a third protocol — and converting between them correctly requires knowing the molecular weight, not just the numbers on the page.
The units, and what they actually mean
- Molarity (M) — moles of solute per litre of solution
- % w/v — grams of solute per 100 mL of solution (e.g., 0.9% w/v = 0.9 g per 100 mL)
- mg/mL — a direct mass-per-volume measure, equivalent to % w/v × 10
- ppm (parts per million) — for dilute aqueous solutions, approximately equal to mg/L (since 1 L of water weighs almost exactly 1 kg)
Key conversion formulas
mg/mL to Molarity: divide by molecular weight (g/mol), result is mol/L
Molarity to mg/mL: multiply by molecular weight
| Convert from | To | Formula |
|---|---|---|
| % w/v | mg/mL | × 10 |
| mg/mL | % w/v | ÷ 10 |
| mg/mL | Molarity (M) | ÷ molecular weight (g/mol) |
| Molarity (M) | mg/mL | × molecular weight (g/mol) |
| ppm (dilute aqueous) | mg/L | ≈ same numeric value |
Why molecular weight is the piece people forget
Converting to or from molarity always requires the compound's molecular weight — % w/v and mg/mL don't need it since they're both simple mass-based units, but molarity is a molar unit (moles, not mass), so the conversion has to account for how much a mole of that specific substance weighs.
⚠️ Double-check which form of the compound you're using. A hydrate (e.g., CaCl₂·2H₂O) has a different molecular weight than the anhydrous form (CaCl₂) — using the wrong one silently introduces an error in every molarity conversion.
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