The formula
How to calculate dilution
The dilution equation follows from a simple fact: diluting a solution adds solvent but no solute, so the number of moles before and after is the same. Concentration times volume is constant.
Take the calculated stock volume, then make up to the final volume with diluent — do not add the diluent volume to the stock volume. For most aqueous dilutions the two approaches agree closely, but the first is correct.
The inputs, one by one:
- Stock concentration (M)
- Target concentration (M)
- Final volume needed (ml)
Everything recalculates as you type, and the numbers in the address bar update with it, so a link to this page carries your figures with it.
The calculation runs on exactly the numbers currently in the fields above, recomputed in full each time — there is no dependency on the order values are entered in, so adjusting one input to test a scenario and then changing it back leaves the result exactly where it started.
Why dilution matters
A dilution calculation gets used both to check work already done by hand and to explore how a formula behaves without redoing the algebra every time an input changes — this page exists for both, since the underlying arithmetic is the same either way.
Beyond a single check, the same calculation is worth rerunning whenever a measured input changes — a new reading, a corrected value, an updated assumption — since the result here always reflects exactly what is currently in the fields above rather than a value calculated once and then left stale.
It is worth remembering that a formula is only ever as good as the assumptions built into it, and most of the standard equations used across science and statistics carry at least one simplifying assumption — a linear approximation, an idealised gas, a normally distributed error term — that holds well in most ordinary cases and breaks down at the extremes. The result here reflects the standard formula exactly; whether that formula's assumptions are appropriate for your particular situation is a separate judgement worth making deliberately rather than assuming automatically.
In practice, a formula like this one is most often reached for at the exact moment a manual calculation needs checking against a deadline — a lab report due, a problem set to submit — which is precisely the situation where a small arithmetic slip is easiest to miss and most costly to leave uncorrected. Running the same inputs through an independent calculator catches that class of error reliably.
Worked example
Take the figures the calculator starts with:
- Stock concentration: 2 M
- Target concentration: 0.25 M
- Final volume needed: 500 ml
That gives:
- Stock volume to take: 62.5 ml
- Diluent to add: 437.5 ml
- Dilution factor: 8 ×
The figures above are the calculator's own default values, shown purely so the working is visible rather than hidden — the same steps apply exactly to your own numbers, entered in the fields at the top of this page.
Reading the result
A dilution factor of 8 is often written as 1:8, though that notation is ambiguous: some authors mean one part stock to eight parts diluent, giving a factor of 9. Stating the factor removes the ambiguity.
Where this goes wrong. For serial dilutions the factors multiply. Three successive 1-in-10 steps give a 1,000-fold dilution, not 30-fold, and pipetting error compounds at every step.
A result that is wrong by an exact factor of ten, a hundred or a similar round number is almost always a units error rather than a mistake in the formula itself — checking each input against the unit stated beside it is the fastest way to track it down.
Calculate the stock volume with C₁V₁ = C₂V₂, transfer it to a volumetric flask, then make up to the final volume with solvent. Mix thoroughly before use.
Yes, provided both concentrations are in the same units. The relationship holds for molarity, percentage, parts per million or anything else proportional to the amount of solute.
The headline figure is stock volume to take. With 2 M stock concentration, 0.25 M target concentration and 500 ml final volume needed, that comes to 62.5 ml. Change any field and the figure moves with it.
Generally, no more than the least precise input justifies — a result reported to six decimal places from inputs measured to two significant figures is implying a precision the calculation does not actually have. The calculator shows full precision so you can round appropriately for your own use.
Yes — the equation shown in the formula section above is the standard form used in textbooks and reference material for this calculation, not a simplified or approximate version.
Yes, in the sense that it applies the correct standard formula and returns an accurate result for the inputs given — but check your own course or publication's requirements for how results should be rounded, presented and referenced, since those conventions vary and are not something a calculator can know on your behalf.