Concentration Dilution Calculator: Formula and Examples

A concentration dilution calculator works out how much concentrated solution and how much diluent you need to make a target volume at a lower concentration. Enter the starting concentration, target concentration, and final volume; it returns the volume of stock solution required and the amount of diluent to add.

Formula

The standard dilution equation is C₁V₁ = C₂V₂. Rearranging gives V₁ = C₂V₂ / C₁, where C₁ is the stock concentration, V₁ is the volume of stock needed, C₂ is the desired final concentration, and V₂ is the total final volume. The calculator then finds diluent volume as V₂ − V₁.

• C₁: starting or stock concentration, entered as a percentage.
• V₁: volume of stock solution to measure, in milliliters (mL).
• C₂: target concentration, entered as a percentage.
• V₂: total prepared volume, in mL.
• Diluent: liquid added to the stock to reach the final volume, in mL.

The equation assumes the concentration units are compatible and that the final mixture’s volume can be treated as the sum of the measured stock and diluent volumes. Concentration percentages must use the same basis—such as percent by volume in both entries. The calculator’s percentage units cancel in the ratio, so entering 10 and 2 represents 10% and 2%.

Worked Example

Using the calculator’s default values, make 100 mL of a 2% solution from a 10% stock:

1. Stock concentration C₁ = 10%; target concentration C₂ = 2%.
2. Final volume V₂ = 100 mL.
3. Stock volume: V₁ = (C₂ × V₂) / C₁ = (2 × 100) / 10 = 20.00 mL.
4. Diluent: V₂ − V₁ = 100 − 20 = 80.00 mL.

Measure 20 mL of the stock and add diluent until the total mixture reaches 100 mL. This is equivalent to adding about 80 mL only when the volumes combine additively; for greater accuracy, bring the mixture to the final volume rather than relying on the diluent amount alone.

How to Use a Dilution Calculator

Use the calculator when you know the concentration of an available stock and want a specified weaker concentration in a chosen final volume. The result is a volume calculation; it does not identify which liquid is a suitable diluent or whether a particular material can safely or effectively be diluted.

1. Enter the stock concentration from a reliable label or measurement.
2. Enter the desired final concentration, using the same concentration basis.
3. Enter the total final volume, not the amount of diluent.
4. Use the stock-volume result to measure the concentrate, then add diluent to the final volume or measure the calculated diluent where appropriate.

For larger batches, the same proportions apply. If the 10%-to-2% example is scaled from 100 mL to 1,000 mL, the stock requirement becomes 200 mL and the nominal diluent amount becomes 800 mL. Scaling changes quantities, not the concentration ratio.

Reading the Result and Checking Feasibility

The stock volume is the portion of the final mixture that comes from the concentrated solution. The diluent result is the remaining volume under the additive-volume assumption. For a genuine dilution, the target concentration is normally lower than the stock concentration and greater than zero. A target equal to the stock concentration requires no dilution; a target above it cannot be reached by adding diluent alone.

If the stock volume is greater than the requested final volume, check the inputs: that outcome generally means the target is more concentrated than the stock, or the concentrations or volume units were entered incorrectly. A target of zero mathematically gives zero stock, but in practice a zero-concentration solution may simply mean using the diluent alone.

Common Errors and Limitations

• Mixing concentration bases: Do not combine, for example, percent by mass with percent by volume as if they were interchangeable. Read how each concentration is defined.
• Confusing final volume with diluent volume: The requested volume is the total mixture after dilution. It is not the amount of water or other diluent to add.
• Using inconsistent units: Keep volume entries in the same unit. The calculator uses mL; convert liters to milliliters by multiplying by 1,000, or convert both volumes consistently.
• Rounding too early: Keep unrounded values for intermediate calculations, then round the measured amount to match the precision of your equipment.
• Assuming volumes always add exactly: Some mixtures change volume when combined. Where that matters, mix and then adjust to the stated final volume using an appropriate measuring vessel.

The equation is a basic mass-balance calculation, not a chemical compatibility check. It does not account for reaction, evaporation, temperature-related volume changes, density differences, or concentration specifications that require a particular preparation method. Follow the relevant product instructions and laboratory or workplace procedures. Do not assume water is an appropriate diluent for every substance.

Frequently Asked Questions

What is the dilution formula?
The common formula is C₁V₁ = C₂V₂. Solve for stock volume with V₁ = C₂V₂ / C₁, then subtract that volume from the final volume to estimate the diluent amount.

How much water should I add to dilute a solution?
First calculate the stock volume, then subtract it from the desired final volume. The remainder is the nominal amount of diluent if the volumes are additive. For precise preparation, bring the mixture up to the final volume instead.

Can I use the calculator with different units?
Yes, if you convert inputs so the volume values use a consistent unit. This calculator expects mL. The stock and target concentrations must also use the same basis and units.

Can dilution make a solution more concentrated?
No. Adding diluent lowers concentration. To reach a concentration above the stock concentration, you need a more concentrated stock or a different preparation method.

What does a 1:10 dilution mean?
The phrase can be ambiguous: it may mean one part stock brought to ten total parts, or one part stock mixed with ten parts diluent. Check the convention being used. The calculator avoids this ambiguity by asking for actual concentrations and a final volume.

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in stock | Stock concentration | % | 10 | 0
in target | Target concentration | % | 2 | 0
in final | Final volume | mL | 100 | 0
out stockvol | Stock solution needed | mL | target * final / stock | 2
out diluent | Diluent to add | mL | final - stockvol | 2