Molarity Calculator: Mass to Weigh and Concentration

Molarity is the number of moles of a substance per liter of finished solution. It is the unit almost every lab recipe uses, written M for mol/L, and it answers the question people ask at the balance most often: how many grams go into the flask?

How to use the calculator

The panel opens in the "mass to weigh" mode. A second mode, "concentration", runs the sum the other way.

1. Under "Solve for", pick mass to weigh or concentration.
2. In mass to weigh mode, enter the target concentration and choose its unit (M, mM, µM, nM or pM). In concentration mode, enter the mass dissolved instead, in g, mg or µg.
3. Enter the final volume and its unit (L, mL, µL or nL). This is the volume of the finished solution, not the water you start with.
4. Enter the molar mass (MW) in g/mol. Take it from the label or the certificate of analysis. If you only have the formula, the molar mass calculator works it out.

The result appears straight away. If a box is empty or zero, the mass mode asks for values above zero instead of giving a result. In mass mode you get the mass to weigh, shown in g, mg or µg depending on size, plus the amount of solute in moles. In concentration mode you get the molarity in whichever unit gives a readable number. Under both results the formula line repeats the sum with your numbers in it, so you can check each step.

The molarity formula

Molarity is moles divided by liters, and moles are grams divided by molar mass. Put the two together and you get the mass to weigh:

c = n / V and n = m / MW, so m = c × V × MW

Before multiplying, the calculator converts your entries to these base units: 100 mM becomes 0.1 mol/L and 500 mL becomes 0.5 L. For the concentration mode it rearranges the same equation to c = m / (MW × V).

Molarity units

1 M is 1 mol/L, which older textbooks write as mol/dm³. Biology works mostly in smaller units, each a thousand times smaller than the last: 1 M = 1,000 mM = 1,000,000 µM, and on down to nM and pM.

Worked example with the default values

The calculator opens on a common request: 500 mL of 100 mM sodium chloride, with a molar mass of 58.44 g/mol.

1. Convert the concentration: 100 mM is 0.1 mol/L.
2. Convert the volume: 500 mL is 0.5 L.
3. Moles needed: 0.1 mol/L × 0.5 L = 0.05 mol.
4. Mass: 0.05 mol × 58.44 g/mol = 2.922 g.

The tool shows "Mass to weigh: 2.922 g" and "= 0.05 mol of solute". Switch to concentration mode and its defaults run the check in reverse: 2.922 g dissolved to a final 500 mL with a molar mass of 58.44 gives 100 mM.

To make it, weigh 2.922 g, dissolve it in roughly 400 mL of water, then bring the volume up to the 500 mL mark in a volumetric flask or cylinder.

Common mistakes

• Adding the solid to the full 500 mL of water. Molarity counts the finished volume, so dissolve in less and make up to the mark. The difference is small for dilute salts and large for concentrated ones.
• Using the anhydrous molar mass for a hydrate. Calcium chloride dihydrate is 147.01 g/mol, not the 110.98 of the dry salt, because the crystal water is part of what you weigh. The hint under the molar mass box says the same.
• A factor of 1,000 from the unit picker. Typing 100 while the unit still says M asks for a 100 molar solution and returns 2,922 g. Check the unit before the number.
• Ignoring purity. If the certificate says 98 percent, divide the calculated mass by 0.98.
• Weighing a liquid reagent as if it were a powder. For liquids, convert grams to milliliters with the density, or use a percent v/v recipe in the ppm and percent calculator.

Limits

Volume expands slightly as a solution warms, so molarity shifts with temperature. For work where that matters, such as freezing point measurements, molality is the steadier unit. The tool also assumes the solute dissolves completely and that the molar mass you enter matches the exact form in the bottle. It does not dilute an existing stock; for that, use the dilution calculator.

FAQ

What is molarity?

Molarity is the amount of a solute in moles per liter of solution. A 1 M sodium chloride solution holds 58.44 g of NaCl in every liter of finished solution. It is the standard way to state concentration in chemistry and biology recipes.

How do you calculate molarity from grams?

Divide the grams by the molar mass to get moles, then divide the moles by the final volume in liters. For 2.922 g of NaCl in 0.5 L, that is 2.922 ÷ 58.44 = 0.05 mol, and 0.05 ÷ 0.5 = 0.1 M, or 100 mM.

What are the units of molarity?

Molarity is written M, short for mol/L. Lab protocols also use mM (millimolar, one thousandth of a molar), µM (micromolar), nM (nanomolar) and pM (picomolar). Each step down is a factor of 1,000.

Is molarity the same as molality?

No. Molarity is moles per liter of solution, while molality is moles per kilogram of solvent. In dilute water solutions the two numbers are close, but they move apart as the solution gets more concentrated.

Why does the calculator ask for the hydrate's molar mass?

Many salts are sold as hydrates, with water molecules locked into the crystal. That water is weighed along with the salt, so a mole of the hydrate weighs more than a mole of the dry compound. Using the anhydrous value for a hydrate leaves the solution weaker than planned.