What it does
When you dilute a solution, you add solvent but the amount of solute stays the same. That one fact lets you work out how much stock to measure, what concentration you'll end up with, or how big the final volume must be. Use it for making working solutions from a lab stock, preparing standards for a calibration curve, or thinning a cleaning or garden concentrate.
How it's calculated
The amount of solute before and after is concentration times volume, so:
V₁ = C₂ × V₂ ÷ C₁ · solvent to add = V₂ − V₁
Dilution factor = C₁ ÷ C₂ = V₂ ÷ V₁
C₁ and V₁ are the stock concentration and the volume of stock you take. C₂ and V₂ are the final concentration and total final volume. Any units work as long as both concentrations use the same kind of unit and both volumes are converted to the same unit; the calculator does those conversions for you. To mix a molar unit (M) with a mass unit (mg/mL or %), it needs the molar mass, because 1 mol/L × molar mass (g/mol) = g/L.
Worked example
You need 100 mL of 0.1 M NaCl from a 1 M stock. V₁ = 0.1 M × 100 mL ÷ 1 M = 10 mL of stock. Put the 10 mL in a volumetric flask or graduated cylinder and add water up to the 100 mL mark, which takes about 90 mL of water. The dilution factor is 1 ÷ 0.1 = 10, a tenfold dilution.
Serial dilutions
A serial dilution repeats the same dilution several times, so each tube is a fixed fraction of the one before. With a factor of 10 and 1 mL per tube, each step moves 0.1 mL into 0.9 mL of diluent. After n steps the concentration is C₀ ÷ factorⁿ:
Cn = C₀ ÷ (factor)n
| Step | From a 1 mM stock, factor 10 | Dilution of stock |
|---|---|---|
| 1 | 0.1 mM (100 µM) | 1 : 10 |
| 2 | 0.01 mM (10 µM) | 1 : 100 |
| 3 | 1 µM | 1 : 1,000 |
| 4 | 100 nM | 1 : 10,000 |
| 5 | 10 nM | 1 : 100,000 |
Limitations
- Volumes don't always add up exactly. Mixing ethanol and water, or diluting strong acids, can give a total a little smaller than the sum. That's why lab procedures say "dilute to the mark" instead of "add 90 mL".
- % here means weight per volume (grams per 100 mL) when converting to mg/mL. Percent by volume (v/v) works fine as long as both concentrations are in % v/v; just don't convert it to mg/mL.
- Safety: when diluting concentrated acids, add the acid slowly to the water, not water to the acid.
- The answer is only as good as your measuring tools. Very small volumes (under about 10 µL) are hard to pipette accurately, so a two-step dilution is often better than one huge one.