Molarity & Dilution Calculator (C1V1=C2V2)
Molarity and dilution calculator. Find molarity from mass, molar mass and volume, or solve a C1V1 = C2V2 dilution for any unknown. Educational only.
Molarity and Dilution Calculator
Leave exactly one field blank and it will be solved.
How to use the molarity and dilution calculator
Choose molarity or dilution
Use "Molarity" to find a solution's concentration from the mass dissolved, or "Dilution" to work out the C₁V₁ = C₂V₂ relationship when diluting a stock.
For molarity, enter mass, molar mass, volume
Type the grams of solute, its molar mass, and the final solution volume. The result is the molarity, plus the moles and a mass-per-volume value.
For dilution, leave one field blank
Enter three of the four values — stock concentration and volume, and final concentration and volume — and leave the unknown blank. The calculator solves for it.
Read and verify
Use the result to weigh out solute or measure stock. For accurate work, make up to volume in a volumetric flask and confirm by measurement where it matters.
Molarity and dilution — the chemist's everyday arithmetic
From grams to moles per litre
Molarity is the most common way to express the concentration of a solution: it is the number of moles of solute dissolved per litre of solution, with units of mol/L, written M. The mole is the bridge between the mass you can weigh and the number of particles that actually react, so chemistry is done in moles even though balances read in grams. To find a molarity you convert the mass of solute to moles by dividing by its molar mass, then divide by the solution volume in litres: M = mass ÷ (molar mass × volume in litres). Dissolving 5.85 g of sodium chloride (molar mass 58.44 g/mol) in water and making it up to one litre, for example, gives 0.1 mol in 1 L, or 0.1 M. The same equation runs in reverse to tell you how much to weigh out for a target concentration — the daily arithmetic of every wet lab.
Dilution is the second everyday operation: making a weaker solution from a stronger stock by adding solvent. The key idea is that diluting changes the volume but not the number of moles of solute already present, so the moles before equal the moles after. Since moles equal concentration times volume, that conservation gives the famous relation C₁V₁ = C₂V₂ — initial concentration times initial volume equals final concentration times final volume. Knowing any three of those four quantities, you can solve for the fourth: most often you want V₁, the volume of stock to take, which is C₂V₂ divided by C₁. Take that volume of stock, add solvent up to the final volume, and you have your dilution.
"Diluting changes the volume, not the moles already dissolved — so concentration times volume is conserved. That single conservation law, C₁V₁ = C₂V₂, underlies every dilution a chemist makes."
Doing it accurately
The equations are exact, but accurate solution-making depends on technique the arithmetic can't capture. Molarity is defined per litre of solution, not per litre of solvent, so you dissolve the solute and then make up to the final volume in a volumetric flask rather than adding solute to a fixed volume of water — the solute itself takes up space. Temperature matters because liquid volumes expand and contract, shifting molarity slightly; this is why some work uses molality (moles per kilogram of solvent), which is temperature-independent. Many solid reagents are hydrates or are not perfectly pure, so the effective molar mass differs from the anhydrous value, and concentrated stock acids are sold by percentage and density rather than molarity, needing a separate conversion. For serial dilutions, small errors compound at each step. None of this changes the formulas, but it means a calculated concentration should be treated as a target that good laboratory technique — accurate weighing, volumetric glassware, and where it matters, verification — turns into a reliable solution. Use this calculator to plan the numbers and learn the relationships, and follow proper procedure for work that counts.
10 Facts About Molarity & Dilution
Molarity = moles of solute ÷ litres of solution.
Moles = mass ÷ molar mass.
Units of molarity are mol/L, written M.
Dilution conserves moles: C₁V₁ = C₂V₂.
Stock volume to take = C₂V₂ ÷ C₁.
Molarity is per litre of solution, not solvent.
Make up to volume in a volumetric flask.
Molality (mol/kg) is temperature-independent.
Hydrates change the effective molar mass.
Errors compound across serial dilutions.
Frequently asked questions
Molarity is the concentration of a solution expressed as moles of solute per litre of solution (mol/L, symbol M). You calculate it by converting the mass of solute to moles (mass divided by molar mass) and dividing by the solution volume in litres. It's the most widely used concentration unit in chemistry because reactions happen in mole ratios, and molarity links the grams you weigh to the moles that react.
C₁V₁ = C₂V₂ says that the moles of solute don't change when you dilute — only the volume and therefore the concentration do. Since moles equal concentration times volume, the product is conserved. Knowing any three of the four values lets you solve for the fourth. Most commonly you want V₁, the volume of stock to dilute: V₁ = C₂V₂ / C₁. Take that volume of stock and add solvent up to the final volume V₂.
Per litre of final solution, not solvent. This matters because the dissolved solute takes up space, so adding solute to exactly one litre of water gives slightly more than one litre of solution and a slightly low molarity. The correct technique is to dissolve the solute in some solvent, then add solvent up to the calibrated mark of a volumetric flask. The calculator assumes you make up to the volume you enter.
Molarity is moles per litre of solution and depends on temperature, because liquid volume changes as it warms or cools. Molality is moles per kilogram of solvent and is temperature-independent, since mass doesn't change with temperature. For most bench work molarity is used and convenient; molality is preferred in precise physical-chemistry measurements such as colligative properties (freezing-point depression, boiling-point elevation) where temperature effects must be removed.
Use the molar mass of the hydrated form, including the water of crystallisation. Copper(II) sulfate pentahydrate, for example, has a molar mass of about 249.7 g/mol, not the 159.6 g/mol of the anhydrous salt — so you need more of the hydrate to get the same moles of copper sulfate. Enter the molar mass that matches the actual reagent on your shelf. Ignoring the water of hydration is a common source of concentration error.
The dilution arithmetic is the same once you know the stock molarity, but concentrated acids are usually sold by weight percent and density, so you first convert that to molarity. Crucially, always add acid to water, never water to acid, because dilution releases a lot of heat and adding water to concentrated acid can cause dangerous spattering or boiling. Follow the safety procedure and use appropriate protection; the calculator handles the numbers, not the hazard.
For molarity, enter mass in grams, molar mass in grams per mole, and volume in litres or millilitres (the calculator converts). For dilution, the concentrations can be in any unit as long as both C values use the same one, and the two volumes use the same unit as each other — because the formula is a ratio, consistent units cancel. The calculator labels volumes in millilitres for clarity, but the relationship holds for any consistent set.
Because small pipetting and volume errors compound at each step of a serial dilution. A 1% error repeated over five steps can accumulate noticeably. Use accurate, calibrated volumetric equipment, mix thoroughly between steps, and where high accuracy matters, prepare key concentrations directly from stock rather than through many serial steps. The arithmetic is exact; the drift comes from technique, so good practice and verification keep concentrations on target.
Use it to plan concentrations and learn the relationships. The formulas are exact, but accurate solutions also depend on technique — correct weighing, volumetric glassware, accounting for purity and hydration, and verification where it matters. This tool is educational; for laboratory or regulated work, follow your validated protocol and confirm critical concentrations experimentally.
No. The values you enter are processed entirely in your browser. Nothing is sent to a server, stored, or shared, and no account is required. The calculation runs on your device only.
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