Molarity · w/w

Molarity calculator from grams or percent w/w

Weigh out the right grams before the batch fails titration.

Enter grams, volume and molar mass, or a percent w/w stock with its density, and get the molarity and the dilution volume.

Last updated 2026-09-27. Math runs in your browser, no data leaves your computer.

Molarity from mass and volume

Use this part when you are weighing a solid or a neat liquid into a volumetric flask. Pick whether you want the molarity of what you made or the grams to weigh out for a target.

Both directions use the same three numbers, so switching the mode only changes which field the tool reads.

Use the molar mass of the exact form you weigh, including any water of crystallisation, because a hydrate like CuSO4·5H2O weighs 249.677 g/mol against 159.60 for the anhydrous salt.

This is the volume after you make up to the mark, not the volume of water you added, since the solute itself takes up space in the flask.

Correct the weighed mass for purity first if the reagent is below 100% assay, otherwise the molarity comes out high by the same margin.

Percent w/w to molarity

Use this part for a bought stock such as 36% hydrochloric acid, where the label gives percent by weight and you need moles per liter. Pick a preset to fill typical values, then overwrite them with the numbers on your own SDS or certificate of analysis.

Preset densities come from published reference tables at 20 to 25 degrees Celsius, and your lot will differ slightly, so the numbers on your own SDS Section 9 win every time.

Read the assay from the certificate of analysis for the drum or tote in front of you, since commercial grades are sold as a range.

Specific gravity against water is close enough to g/mL for this purpose, and the tool converts lb per US gallon for you.

Use the molar mass of the active species only, so HCl rather than the water it is dissolved in.

Add the working strength you want and the tool tells you how much stock to measure, which saves a second calculation at the bench.

Always add acid to water when you make the dilution, because the heat released can boil water poured onto concentrated acid.

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General guidance only. Verify against the cited primary sources before you commit to a shipment, declaration, or contract.

Where molarity math goes wrong

Most bench errors with bought acids come from reading percent w/w as if it were grams per 100 mL. A 36% hydrochloric acid holds 36 g of HCl in every 100 g of liquid, and because a milliliter of that liquid weighs about 1.18 g, a liter carries noticeably more acid than the label suggests at first glance. The batch comes out strong, the titration fails the specification, and the lot sits in quarantine while someone works out why.

The tool runs three formulas side by side. Molarity from a weighed solid is grams divided by molar mass and by liters. A percent stock converts through M = (percent / 100) x density x 1,000 / molar mass, with density in g/mL. The dilution uses C1 x V1 = C2 x V2, so the stock volume equals target molarity times final volume divided by stock molarity.

Molar masses in the presets are summed from the IUPAC abridged standard atomic weights published by the Commission on Isotopic Abundances and Atomic Weights. Preset densities are examples from published tables: hydrochloric acid from the Perry's handbook table at 20 degrees Celsius, phosphoric acid 85% from Christensen and Reed (1955) at 25 degrees Celsius, and sulfuric, nitric and acetic acid from the reference values cited in each acid's Wikipedia entry. The lb/gal factor of 0.1198264 kg/L comes from NIST Special Publication 811.

Worked example: 1 L of 1 M hydrochloric acid

The booking. A plant lab needs 1 L of 1 M HCl for a pickling bath check and has a drum of 36% acid on the shelf. The technician reads 36% as 36 g per 100 mL, which gives 360 g/L divided by 36.458 g/mol, or 9.874 M, and measures 1,000 / 9.874 = 101.3 mL of stock into the flask. On paper the arithmetic looks tidy and the flask is made up to the mark.

The failure. Percent w/w is grams per 100 g, not per 100 mL, and at 1.179 g/mL the stock actually runs 0.36 x 1.179 x 1,000 / 36.458 = 11.64 M. Those 101.3 mL deliver 1.179 moles, so the solution is 18% strong and every result read against it is wrong by the same margin. The choice is either to remake the standard from the right number or to accept a bath check that nobody can defend in an audit.

The fix. Run the stock through the percent w/w section with the density from the SDS and the tool returns 11.64 M, and a dilution to 1 M in 1,000 mL needs 1,000 / 11.64 = 85.9 mL of stock. The technician measures 85.9 mL into water, makes up to the mark, and the check titration lands on 1 M within the method tolerance.

Need the molar mass of a hydrate or a salt with brackets in the formula before you start? The molar mass calculator parses formulas like CuSO4·5H2O against the IUPAC atomic weights and also converts grams to moles.

Mixing two strengths of the same product in a tank rather than a flask? The blending calculator gives the amount of each strength to hit a target percent, by weight or by volume.

Frequently asked

What is the formula for molarity?

Molarity is moles of solute per liter of finished solution, so M = mass in grams divided by (molar mass in g/mol times volume in liters). To weigh out a target instead, grams = M times liters times molar mass. For 2 L of 0.5 M sodium hydroxide at 39.997 g/mol that comes to 39.997 g.

How do I convert percent w/w to molarity?

Multiply the mass fraction by the density in g/mL and by 1,000 to get grams of solute per liter, then divide by the molar mass. For 36% hydrochloric acid at a density of 1.179 g/mL that is 0.36 times 1.179 times 1,000 divided by 36.458, or 11.64 M.

Why does the calculator need density for percent solutions?

Percent w/w tells you grams of solute per 100 g of solution, while molarity counts per liter. Density is the bridge between mass and volume, and a 36% acid at 1.179 g/mL packs 18% more solute into a liter than someone reading 36% as grams per 100 mL would expect. Take the density from Section 9 of the SDS or the certificate of analysis for your lot.

Does temperature change molarity?

Yes, because the solution volume expands as it warms while the moles of solute stay fixed. The preset densities are quoted at 20 or 25 degrees Celsius, so a stock stored in a hot warehouse will read slightly weaker per liter. For release testing, titrate the stock against a primary standard instead of trusting the label.

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