Pharmaceutical Chemistry

Molarity Calculator

Work out the molarity of a solution, or how much solid or liquid to use for a target molarity.

I want to calculate

Molar concentration

0.0171mol/L (M)

Moderately dilute solution

Inputs

Substance type

Molecular weight (MW)

g/mol

From the label or formula, e.g. NaCl 58.44, glucose 180.16.

Amount of solid

The mass you weighed out.

Final volume of solution

The volume you make the solution up to.

In other units

Millimolar17.11mM

Micromolar17111.57μM

Nanomolar17111567.42nM

Working

Your values substituted into the formula.

Molecular weight58.44g/mol

Final volume1 L = 1.0000L

M = (1 g = 1.0000 g) / (58.44 × 1.0000)

Common solutions

Tap one to load it as a target molarity.

Solution	MW (g/mol)	Amount
	58.44	58.44in 1L
	36.46	8.3 mL*in 1L
	40.00	20.00in 1L
	372.24	3.7224in 1L
	157.60	157.60in 1L

*For 37% concentrated HCl (specific gravity 1.19)

For solids

M = (mass in g) / (MW × volume in L)

For liquids

M = (A × sg × purity%) / (MW × V)

M molarity (mol/L) · MW molecular weight (g/mol) · mass mass of solid, converted to grams · A amount of liquid (mL) · sg specific gravity (g/mL) · purity% percentage purity, as a decimal · V final volume, converted to litres.

To find the required amount

Mass (g) = M_target × MW × V(L)

Volume (mL) = (M_target × MW × V(L)) / (sg × purity%)

For a liquid, A × sg gives the grams of liquid and × purity gives the grams of the actual solute in it; dividing by MW turns grams into moles.

Worked example: weighing sodium bicarbonate for a 0.2 M solution

A practical asks for 250 mL of 0.2 M sodium bicarbonate (NaHCO₃, MW 84.01 g/mol) to use as a mild base in an acid–base experiment. How much solid do you weigh? (Illustrative values.)

Mode / substance: Amount from target molarity · Solid
Target molarity: 0.2 mol/L
Molecular weight, MW: 84.01 g/mol
Final volume: 250 mL

Write the formula
Mass (g) = M × MW × V(L)
Convert the volume to litres
V = 250 mL × 0.001 = 0.2500 L
Moles needed
n = M × V = 0.2 mol/L × 0.2500 L = 0.05 mol
Convert moles to grams
Mass = 0.05 mol × 84.01 g/mol = 4.2005 g

Weigh 4.2005 g of NaHCO₃ (about 4.20 g on a two-decimal balance), dissolve and make up to 250 mL.

The calculator prints 4.2005 g and the instruction "Dissolve and make up to 250 mL for 0.2 M". Dissolve the solid in less than 250 mL of water and then make up to the mark in a volumetric flask; adding 4.2 g to 250 mL of water gives slightly more than 250 mL of solution and so slightly less than 0.2 M.

Common mistakes

Using the molecular weight of a different form from the one you weigh — an anhydrous MW for a hydrate (CuSO₄·5H₂O is 249.68, anhydrous CuSO₄ is 159.61 g/mol), or the free base for a salt.

Leaving the volume in mL in the formula. M × MW × 250 instead of × 0.250 gives an answer 1000 times too large; the calculator converts for you only if the unit selector matches what you typed.

Adding the solute to the full final volume of solvent instead of making up to volume. Molarity is per litre of solution, not per litre of solvent.

For a concentrated liquid reagent, ignoring specific gravity and purity: 37% HCl is not 'pure HCl', and 1 mL of it does not weigh 1 g.

Confusing molarity (mol/L of solution) with molality (mol/kg of solvent) or with normality, which counts equivalents rather than moles.

Assumptions and limitations

Molarity changes slightly with temperature because the solution's volume does; volumetric glassware is calibrated at a stated temperature, usually 20 °C.

The liquid-reagent formula uses the label's specific gravity and % w/w assay; a bottle that has absorbed water or lost gas (concentrated HCl, ammonia) is weaker than the label says, so standardise by titration when the exact concentration matters.

The result is only as good as the purity of the solid. A 98% pure reagent weighed as if it were 100% gives a solution about 2% weaker.

Guide: Dilution and Concentration CalculationsThe concept in full, with practice questions.mg/mL ↔ Molarity CalculatorConvert a molar concentration to the mg/mL figure a drug label or assay uses.Dilution Calculator (C₁V₁ = C₂V₂)Dilute the stock you have just made to a working concentration.Percentage Solution Calculator (w/v, w/w, v/v)When the method states strength as % w/v rather than mol/L.

References

International Union of Pure and Applied Chemistry. Compendium of Chemical Terminology (the 'Gold Book'). Source
Bureau International des Poids et Mesures. The International System of Units (SI Brochure). 9th ed. Sèvres: BIPM; 2019. Source
Sinko PJ, editor. Martin's Physical Pharmacy and Pharmaceutical Sciences. 8th ed. Philadelphia: Wolters Kluwer; 2023.

Common questions

The final volume of solution. Dissolve the solute in less solvent, then make up to the mark in a volumetric flask. Adding the solute to the full volume of solvent gives a slightly lower molarity.

Concentrated reagents are sold by volume but are not pure: conc. HCl is about 37% w/w with sg 1.19. Volume × sg gives grams of liquid, and × purity gives grams of HCl itself.

The MW of exactly what you weigh. CuSO₄·5H₂O is 249.68 g/mol, not the 159.61 g/mol of anhydrous CuSO₄ — using the wrong one gives an error of more than 50%.

1 M = 1,000 mM = 1,000,000 μM = 1,000,000,000 nM. Very small results are shown in scientific notation, e.g. 2.775e-7 M is 277.53 nM.

Prepared by the PharmaWallah student team. Verify results with your textbook or instructor. Report an error · Editorial policy