Dilution Calculator
Work out how much stock solution and diluent to mix for a target concentration and volume using C₁V₁ = C₂V₂, with the dilution factor and fold dilution.
Comment utiliser cette calculatrice
- 1Enter the concentration of your stock solution.
- 2Enter the concentration and volume you want to end up with.
- 3Read the volume of stock to measure out and the diluent to add.
- 4Measure the stock, then add diluent up to the final volume — not the other way around.
Comment ça marche
Dilution — C₁V₁ = C₂V₂
C₁V₁ = C₂V₂ V₁ = (C₂ × V₂) ÷ C₁ — stock volume to use diluent = V₂ − V₁ dilution factor = C₁ ÷ C₂ = V₂ ÷ V₁
Diluting a solution changes its concentration but not the amount of solute it contains — you are only adding more solvent. That conservation of solute is exactly what the dilution equation C₁V₁ = C₂V₂ expresses: the concentration times the volume (which equals the moles of solute) is the same before and after. Given a concentrated stock of known concentration C₁, and a target concentration C₂ and volume V₂, the equation rearranges to tell you the volume of stock to take, V₁ = C₂V₂ ÷ C₁. The rest of the final volume is made up with diluent. Because the same units appear on both sides, they cancel, so the equation works with molarity, mass concentration, or percentage as long as you are consistent. The dilution factor, C₁ ÷ C₂, summarises how much the solution is being diluted — a factor of 10 is a 'ten-fold' dilution.
Exemple détaillé
To make 100 mL of 1 M solution from a 10 M stock, V₁ = (1 × 100) ÷ 10 = 10 mL of stock, topped up with 90 mL of diluent. That is a ten-fold (1:10) dilution — the dilution factor is 10 ÷ 1 = 10, matching the final volume divided by the stock volume, 100 ÷ 10.
Dilution Calculator : le guide complet
The idea behind C₁V₁ = C₂V₂
Dilution is one of the most common operations in any laboratory, and the equation behind it is one of the simplest in chemistry — yet its logic is worth understanding rather than memorising. When you dilute a solution, you add solvent but no new solute. The number of solute molecules stays exactly the same; they are just spread through a larger volume, which is what lowers the concentration. Concentration multiplied by volume gives the total amount of solute, so if that amount is unchanged, C₁V₁ must equal C₂V₂. The whole equation is just a statement that solute is conserved.
Seen this way, solving a dilution problem is never a matter of recalling which value goes where. You know three of the four quantities and want the fourth, so you rearrange the equation accordingly. Most often you know the stock concentration and the target concentration and volume, and you solve for the stock volume to use. But the same equation just as easily tells you the final concentration if you dilute a fixed volume of stock into a fixed final volume, or how much a solution has been diluted from its concentration change.
Getting the technique right
A correct calculation still needs correct technique, and there is a common pitfall. The equation gives the volume of stock and, by subtraction, the volume of diluent — but you should not simply combine the full stock volume with the full diluent volume and assume the total is right. Volumes of solutions do not always add perfectly, especially at higher concentrations, and small measurement errors accumulate. The proper method is to measure the calculated stock volume into a container, then add diluent until the total reaches the target final volume, ideally to a calibrated mark.
For precise work this means using a volumetric flask, which has a single etched line marking an exact volume. Pipette the stock into the flask, then top up with solvent to the line, mixing as you go. This 'add to volume' approach guarantees the final volume is exactly V₂, which is what the target concentration depends on. For rough or non-critical dilutions the distinction matters less, but the habit of diluting to a final volume rather than adding a fixed amount of diluent is what separates reliable results from slightly-off ones.
Dilution factors and serial dilutions
The dilution factor — the stock concentration divided by the final concentration — is a compact way to describe how much a solution has been diluted, and it appears constantly in science. A factor of 10 means the solution is one-tenth as concentrated, often written as a 1:10 or 'ten-fold' dilution. Thinking in factors is handy because they multiply: diluting ten-fold and then ten-fold again gives a hundred-fold dilution overall, which is the basis of serial dilution.
Serial dilution — making a series of stepwise dilutions, each from the last — is how scientists reach very low concentrations accurately. Trying to dilute a solution a millionfold in a single step would require measuring an impractically tiny volume of stock, inviting large errors. Instead, six successive ten-fold dilutions achieve the same millionfold reduction, each step using easily measured volumes. This technique is fundamental to microbiology for counting bacteria, to immunology for antibody titres, and to any field needing a controlled range of concentrations. Every step is just another application of C₁V₁ = C₂V₂.
Questions fréquentes
How do I use the C1V1 = C2V2 formula?
Identify the three values you know and solve for the fourth. To find the stock volume for a target, rearrange to V₁ = (C₂ × V₂) ÷ C₁. For 100 mL of 1 M from a 10 M stock, that's (1 × 100) ÷ 10 = 10 mL of stock, plus 90 mL of diluent.
Why does C1V1 equal C2V2?
Because dilution adds solvent but no new solute, the amount of solute is conserved. Concentration times volume equals the amount of solute, so it must be the same before and after: C₁V₁ = C₂V₂. The concentration falls only because the same solute is spread through a larger volume.
Should I add the stock to the diluent or vice versa?
Measure the stock volume, then add diluent up to the final volume — don't combine the full stock and full diluent amounts. Volumes don't always add perfectly, and the target concentration depends on hitting an exact final volume, ideally measured to a mark in a volumetric flask.
What is a dilution factor?
The dilution factor is the stock concentration divided by the final concentration (equivalently, final volume divided by stock volume). A factor of 10 is a ten-fold or 1:10 dilution. Factors multiply, which is why serial dilutions — repeated steps — reach very low concentrations accurately.