Every protocol that mentions a dilution is really asking the same question: how much of what, into how much of what? Getting it wrong by a factor of ten is the single most common laboratory error, and the reason is usually a phrase that means something slightly different from what most people hear.
Conservation of solute
Dilution does not remove any solute — it adds solvent. So the amount in before equals the amount after:
C₁ × V₁ = C₂ × V₂
Solve for whichever variable you do not know. Keep both volumes in the same unit and both concentrations in the same unit, and the units cancel on their own.
The dilution factor is C₁ ÷ C₂: a 10× dilution from a 10 mg/mL stock gives 1 mg/mL. Note the direction — a factor of 10 from a 10 mg/mL stock is 1 mg/mL, not 100.
Worked example: 100 mL of 2 mg/mL from a 10 mg/mL stock
V₁ = (C₂ × V₂) ÷ C₁ = (2 × 100) ÷ 10 = 20 mL.
So you pipette 20 mL of stock and add 80 mL of diluent to reach 100 mL total. Both sides of the equation check: 10 × 20 = 200 and 2 × 100 = 200 — the same mass of drug in both cases, as it must be. The dilution calculator reports the stock volume, the diluent to add, the factor and the check together, so a protocol can be verified before touching a pipette.
"1:5" is a trap
Protocols say "dilute 1:5" and people routinely interpret it as adding five volumes of diluent to one of stock. That is actually a 1:6 dilution. The correct reading of a 1:5 dilution is one part stock to four parts diluent, giving five times the original volume — the ratio is of parts to total, not to what you add.
The same ambiguity surrounds "1 in 10", which almost always means one part in ten total, so 1 volume of stock made up to 10 volumes with diluent. The dilution factor is the reliable check: if you believe you are making a 1:5, the concentrations should differ by exactly 5×, and if they do not, the reading was wrong.
Serial dilutions: covering ranges no single step can
A serial dilution steps down in series — each tube dilutes the one before. The factors multiply, which is what makes them powerful:
A 1:10 dilution done three times gives 1:1000, because 10 × 10 × 10 = 1000.
The practical limit is arithmetic. A single 1:100,000 dilution would require a volume of 100,000 parts, which is physically absurd; five serial 1:100 steps are routine and give 1:10¹⁰, achievable in five tubes. This is how standards spanning many orders of magnitude get built, and it is why a clinical lab produces a dilution series rather than one heroic flask.
The discipline it requires is simple: use a fresh pipette at each step, and mix each tube thoroughly. Carrying residual solution from a previous step silently contaminates the next, and the error compounds exactly as the factors do.
Two things dilution cannot do
You cannot dilute up. If your target concentration is higher than your stock, no volume arithmetic will get you there — you need a more concentrated stock, or a different method. The calculator flags this rather than returning a negative volume, which is a useful guard.
The final volume is always a sum. You cannot end up with less volume than you started with. If a calculation says otherwise, either a concentration is wrong or the units are mismatched.
Accuracy and the practical checks
Three habits make dilutions reliable. Check the factor afterwards: measure the concentration if you can, and confirm it differs from the stock by exactly the intended factor. Watch the volume arithmetic: "20 mL stock plus 80 mL diluent" is right; "20 mL stock plus 100 mL diluent" is a 1:6 dilution and the error will not announce itself.
And use glassware of the right class. Volumetric glassware is calibrated "to contain" at a specific temperature and should not be used to deliver an exact volume of anything — for precise work, deliver into a separate vessel. Volumetric pipettes are calibrated to deliver and should be let down the wall and allowed to drain. The best arithmetic in the world does not survive using a 10 mL beaker for a 2.000 mL aliquot.
Percent dilutions and the same maths restated
A dilution is often quoted as a percentage, and it is the same arithmetic in different clothing. A 1:10 dilution is a 10-fold dilution, meaning the final concentration is 10% of the stock — so the stock has been diluted to 10%, or "a 1-in-10 solution". Consistency in the phrasing is what matters: 1:10, 1 in 10, 1/10 and 10% all mean the same thing here, while 1:11 would not.
Percentage form is usually easier to reason about when combining steps. A 1:10 followed by a 1:5 is a 10% × 20% = 2% overall, and expressing each step as a percentage makes the multiplication obvious. This is the same asymmetry insight as the percent change guide, applied to concentration: each step is relative to whatever came before, not to the original stock.
Mixed solutions and the wrong-but-plausible answer
One error deserves naming because it produces a reasonable-looking number. If you mix a solution with plain diluent and then try to treat the mixture as if it were the new stock for a further dilution, the volume bookkeeping silently breaks — the amount of solute per litre changed twice, not once.
The safe habit is to track two things for every solution and never discard them: the amount of solute and the total volume. The concentration is derived from those two whenever needed, and any dilution step becomes the one-line check solute_before = solute_after. Carrying the concentration alone is what makes such mistakes easy to make and hard to see.
One habit that prevents nearly every mistake
Write the factor next to each step as you go, and verify at the end that the concentrations differ by exactly the expected ratio. Almost every dilution error is a factor that drifted by ten somewhere along the line, and a written factor is the cheapest way to catch it.
Frequently asked questions
What is the dilution formula C1V1 = C2V2?
It states that the amount of solute before dilution equals the amount after: stock concentration × stock volume = final concentration × final volume. Solve it for whichever value you do not know.
How much diluent should I add?
Final volume minus stock volume. To make 100 mL of a 2 mg/mL solution from a 10 mg/mL stock you need 20 mL of stock plus 80 mL of diluent — the final volume is the sum of both.
Can I make a solution more concentrated than my stock?
No. Dilution can only reduce concentration. If your target is higher than the stock, you need a more concentrated starting solution.
What is a serial dilution?
A series of dilutions where each step dilutes the previous one. A 1:10 dilution repeated three times gives a total 1:1000 dilution, because the dilution factors multiply.