How to Use the PPM Dilution Formula C1V1 = C2V2

For a simple dilution where the concentration basis stays compatible, the standard relationship is:

C₁ is the starting or stock concentration, V₁ is the volume of stock used, C₂ is the target concentration, and V₂ is the final total volume.

Calculate the stock volume

If the stock concentration, target concentration, and final volume are known:

For example, suppose you have a 1,000 PPM stock and want 100 mL of a 50 PPM solution.

Measure 5 mL of the stock and bring the solution to a final volume of 100 mL with the appropriate diluent. The calculation assumes the PPM basis is compatible between the stock and final solution.

Why final volume matters

V₂ is the final volume of the diluted solution. It is not simply the amount of solvent added. If 5 mL of stock is brought to a final volume of 100 mL, the final volume is 100 mL.

Tenfold and other simple dilutions

A tenfold dilution reduces concentration by a factor of 10. A 1,000 PPM stock therefore becomes 100 PPM after a tenfold dilution. A hundredfold dilution would reduce it to 10 PPM.

The same idea can be expressed as a dilution factor:

For 1,000 PPM to 10 PPM, the dilution factor is 100.

Serial dilution

When the target concentration is much lower than the available stock, several smaller dilution steps may be easier to measure accurately. Each step has its own concentration and volume. The overall dilution factor is the product of the individual step factors.

For example, two tenfold dilutions produce a 100-fold overall dilution. Starting at 1,000 PPM, the first step gives 100 PPM and the second gives 10 PPM.

What can make C1V1 = C2V2 inappropriate?

The equation assumes that the concentration quantities are defined on a compatible basis and that the dilution process does not introduce a relevant change that the simple relationship ignores. Problems can arise if density, composition, temperature, reaction, evaporation, or a change in concentration basis matters to the method.

Do not use the equation to convert arbitrary mass-based PPM into volume-based concentration without the physical information needed to connect them.

Preparation checklist

1. Confirm the stock concentration and its basis.
2. Confirm the target concentration uses the same basis.
3. Choose a practical final volume.
4. Calculate V₁ before measuring.
5. Use appropriate volumetric equipment for the required precision.
6. Bring the solution to the final volume, then mix thoroughly.
7. Record the stock, target, volume, and dilution steps.

For the arithmetic, use the PPM Dilution Calculator. For repeated dilution steps, see Serial Dilution and Dilution Factor.