Molarity Calculator
Enter any two of molarity, moles, or volume to solve for the third — or switch to dilution mode. A live 3D beaker and charts show what the numbers mean.
Reviewed by the ToolNestr Editorial Team — July 2026
Live 3D beaker
Change the moles of solute and the volume of solution — the concentration and the density of dissolved particles update live. Drag to orbit (touch works too).
Concentration graphs
How molarity is calculated
The core definition in one line: molarity is the number of moles of solute divided by the volume of solution in litres — M = n / V. A 1 M solution holds one mole of dissolved substance in every litre.
The formula rearranges three ways, so knowing any two quantities gives the third:
M = n / V
concentration from moles & volume
n = M × V
moles needed for a target M
V = n / M
volume to reach a target M
Most of the time you start from a mass on a balance, not moles. The full chain is: mass → moles (divide by molar mass) → molarity (divide by litres). Written out:
M = (mass ÷ molar mass) ÷ volume(L)
Where the dilution equation comes from: when you add solvent, the moles of solute do not change — only the volume does. Since n = M × V, and n before equals n after, you get the compact rule
M₁V₁ = M₂V₂
That single fact — moles are conserved on dilution — is the reason a small amount of concentrated stock can be diluted to a large, precise working solution.
Worked example 1 — molarity from mass
Given: you dissolve 20 g of sodium hydroxide (NaOH, molar mass 40.00 g/mol) and make it up to 500 mL of solution. What is the molarity?
Worked example 2 — dilution
Given: you have a 12 M stock of hydrochloric acid. How do you make 250 mL of 1 M HCl?
Two ideas that trip students up
1. Dilution keeps the particles, adds the water
Both beakers hold the same number of solute particles. The right one just has more solvent, so the particles are spread thinner — lower molarity, identical moles.
2. Molarity is particles per litre
Each cube is one litre. A 2 M solution simply packs twice as many moles of solute into the same litre as a 1 M solution — concentration is a density of "stuff dissolved."
Molarity of some everyday solutions
Approximate values — useful for a sense of scale of what "how concentrated" actually means.
| Solution | Approx. molarity | Note |
|---|---|---|
| Blood glucose | ~0.005 M | very dilute |
| Seawater (NaCl) | ~0.6 M | salty |
| Household vinegar | ~0.9 M | acetic acid |
| Stomach acid | ~0.1 M | HCl |
| Concentrated HCl (stock) | ~12 M | lab reagent |
| Pure water (as itself) | ~55.5 M | for reference |
Where molarity actually matters
🧪 The lab bench
Almost every wet-lab procedure starts with "prepare X mL of a Y molar solution." Molarity is how chemists communicate concentration unambiguously, and the dilution equation is used dozens of times a day to turn concentrated stocks into precise working solutions.
💊 Medicine and pharmacy
IV fluids, drug formulations and buffers are all defined by concentration. Getting a dilution wrong is not an academic error here — it changes a dose — which is why the M₁V₁ = M₂V₂ calculation is double-checked at every step.
🌊 Environmental testing
Measuring pollutants in water means preparing calibration standards at known molarities by serial dilution. The accuracy of the final reading is only as good as the concentration maths behind the standards.
Common misconceptions
"Molarity is per litre of solvent (water)."
It is per litre of solution — solute plus solvent together, measured after mixing. You dissolve the solute and then make the total volume up to the mark, rather than adding solute to a litre of water.
"Diluting a solution removes some of the solute."
Dilution only adds solvent. The moles of solute are unchanged — they are just spread through a larger volume, so the concentration drops. That conservation of moles is the whole basis of M₁V₁ = M₂V₂.
"Molarity and molality are the same thing."
Molarity is moles per litre of solution and shifts with temperature as the volume changes. Molality is moles per kilogram of solvent and does not, which is why molality is used for boiling-point and freezing-point work.
"Just use millilitres — the number is bigger."
The formula requires litres. Using millilitres without converting inflates your molarity by a factor of 1000. Always divide millilitres by 1000 first.
Formula sources & further reading
The molarity and dilution relationships are standard general-chemistry definitions, traceable to these widely used references:
- • OpenStax, Chemistry 2e — §3.4 "Molarity" (free, peer-reviewed). openstax.org
- • Brown, LeMay & Bursten, Chemistry: The Central Science — Chapter 4, Reactions in Aqueous Solution (Concentrations of Solutions).
- • Zumdahl & Zumdahl, Chemistry — Chapter 4, Types of Chemical Reactions and Solution Stoichiometry.
- • IUPAC — recommended symbol for amount concentration is c (mol/L); "molarity" and the unit symbol M remain in common practical use.
Results are rounded to four significant figures; very small or very large values switch to scientific notation.
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Frequently asked questions
What is molarity?
Molarity (M) is the number of moles of solute per litre of solution: M = mol / L. It is the most common way chemists express the concentration of a solution.
How do I calculate molarity from mass?
First convert the mass of solute to moles using its molar mass (moles = mass ÷ molar mass), then divide by the solution volume in litres. For example, 58.44 g of NaCl is 1 mole; dissolved to make 1 L gives a 1 M solution.
What is the dilution formula?
M₁V₁ = M₂V₂, where M₁ and V₁ are the initial concentration and volume and M₂ and V₂ are the final ones. It works because diluting a solution adds solvent but does not change the number of moles of solute.
What units should I use?
Molarity in mol/L (M), moles in mol, and volume in litres. If your volume is in millilitres, divide by 1000 first — forgetting this is the single most common molarity mistake.
What is the difference between molarity and molality?
Molarity is moles of solute per litre of solution and changes slightly with temperature (because volume changes). Molality is moles of solute per kilogram of solvent and is temperature-independent, so it is preferred for precise or high-temperature work.
Does adding water change the number of moles of solute?
No. Dilution changes the concentration and the volume, but the amount of solute (moles) stays exactly the same. That constant-moles fact is what the dilution equation M₁V₁ = M₂V₂ is built on.