Molarity, Mass, and Volume Calculator — Solve for Concentration, Volume, or Mass
The core relationship used in solution preparation:
Mass (g) = Concentration (mol/L) × Volume (L) × Molecular Weight (g/mol)
Given any two of the three variables, the third can be solved. The tool handles common unit conversions automatically so you don’t have to count zeros.
Common pitfalls:
- Use the molecular weight for the correct salt form. Many reagents are sold as hydrochlorides, sodium salts, or hydrates — their molecular weights differ substantially from the free base. Use the formula weight (FW) on the bottle label, not the MW of the parent compound.
- Hydrated reagents (e.g., CuSO₄·5H₂O) must use the hydrated molecular weight, or the actual concentration will be lower than intended.
- Solubility is a separate constraint. A successful calculation does not mean the compound will dissolve. DMSO stock solutions are typically 10–100 mM; for poorly water-soluble compounds, check solubility before you start.
- Proteins and antibodies are usually specified in mg/mL rather than mol/L. Converting requires an accurate molecular weight — glycosylation increases the actual MW above the theoretical value.
Example calculation
To prepare 100 mL of 1 mol/L NaCl (FW 58.44):
Mass = 1 mol/L × 0.1 L × 58.44 g/mol = 5.844 g
Dissolve 5.844 g and bring the volume up to 100 mL — do not add 100 mL of water.
“Bring to volume” is not the same as “add water”
The solute itself occupies volume. Dissolving 5.844 g of NaCl increases the volume by roughly 2 mL, so adding 100 mL of water gives ~102 mL of solution, making the concentration about 2% low. This is negligible for dilute solutions but matters when preparing high-concentration stocks.
Correct procedure: add roughly 80% of the target volume of solvent, dissolve completely, then bring to the final volume mark.
Three types of percent concentration
This is the most commonly glossed-over distinction — the three notations give very different values:
| Notation | Meaning | Example |
|---|---|---|
| % (w/v) | grams per 100 mL of solution | 10% SDS = 10 g / 100 mL |
| % (w/w) | grams per 100 g of solution | Concentrated HCl 37% (w/w) |
| % (v/v) | mL per 100 mL of solution | 70% ethanol |
Molecular biology reagents typically use w/v; acid/base reagents on bottle labels are usually w/w; organic solvents are typically v/v. When a paper writes “10%” without specifying, judge by the convention for that reagent — if in doubt, check the original protocol.
ppm equals mg/L in dilute aqueous solutions because water density is ~1 g/mL. This does not hold in non-aqueous systems.
FAQ
Why is my prepared solution at the wrong concentration?
The most common cause is using the wrong molecular weight: when a reagent is a hydrochloride salt, sodium salt, or hydrate, the actual MW differs from the parent compound. Always use the FW printed on the bottle label.
How do I convert a protein concentration from mg/mL to M?
You need an accurate molecular weight. For recombinant proteins, the theoretical MW can be calculated from the amino acid sequence, but the actual MW of glycosylated proteins is higher than the theoretical value.
Why use the FW on the bottle instead of the compound's molecular weight?
Reagents are commonly sold as hydrochlorides, sodium salts, or hydrates, and the MW can differ substantially from the free base. For example, dopamine hydrochloride has an FW roughly 20% higher than dopamine itself — weighing by the free-base MW means your actual concentration will be about 20% low. The formula weight on the label is the MW of the powder you are actually weighing.
The calculation says it should work — why won't it dissolve?
Solubility is a physical limit independent of the calculation. DMSO stocks are typically kept at 10–100 mM precisely because the compound precipitates above that. Temperature, pH, and ionic strength all affect solubility — it is common for a compound to precipitate on ice but dissolve normally at room temperature.
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