Percent Dilution Calculator: Formula and Examples

A percent dilution calculator works out how much solvent to add to a solution to reach a chosen lower concentration. Enter the starting concentration, target concentration, and starting volume; it returns the final volume and the amount of solvent to add.

Formula

The calculation uses conservation of solute: the amount of dissolved material stays the same when solvent is added. In symbols, C₁V₁ = C₂V₂.

• C₁ is the starting concentration, expressed as a percentage.
• V₁ is the starting solution volume, in millilitres (mL).
• C₂ is the target concentration, expressed as a percentage.
• V₂ is the final solution volume, in mL, after dilution.
• Solvent to add is V₂ − V₁.

Rearranging gives V₂ = V₁ × C₁ / C₂, and solvent to add = V₁ × (C₁ / C₂ − 1). The percentage values can be entered as ordinary percentage numbers, such as 10 and 2, because their ratio is unchanged if both are converted to fractions. The formula assumes the same concentration basis is used for both values and that volumes are additive.

Worked Example

With the calculator’s default values, dilute 100 mL of a 10% solution to 2%:

1. Calculate the final volume: V₂ = 100 mL × 10 ÷ 2 = 500 mL.
2. Subtract the starting volume: solvent to add = 500 mL − 100 mL = 400 mL.

The calculator therefore returns 400.00 mL of solvent to add, with a final solution volume of 500.00 mL. This is the main distinction to keep in mind: “amount to add” is not the same as “final volume.”

What Percent Dilution Means

Dilution lowers the concentration of a solution by adding solvent, while leaving the quantity of solute unchanged. For example, adding water to a salt solution increases its total volume and reduces the amount of salt per unit volume. It does not remove salt.

Percent concentration can refer to different conventions. Common forms include mass per volume (such as grams per 100 mL), mass per mass (grams per 100 g), and volume per volume (mL per 100 mL). The calculator does not convert between these definitions; it compares the numerical concentrations you enter. Use matching units and the same percentage convention for the starting and target concentrations.

When to Use This Calculator

Use it when you know a solution’s starting concentration and volume and want to prepare a weaker solution by adding solvent. It is useful for straightforward dilution planning, classroom exercises, and other non-specialized calculations where the assumptions fit.

• Enter the original concentration in “Starting concentration.”
• Enter the desired, lower concentration in “Target concentration.”
• Enter the quantity of original solution in “Starting volume.”
• Read “Solvent to add” as the calculated addition and “Final volume” as the resulting total.

Although the inputs and output here use mL, the same formula works with litres, US fluid ounces, or other volume units. Keep all volume quantities in one unit: if you enter 1 L as 1,000 mL, the answer will also be in mL. A US fluid ounce is a volume unit; it should not be confused with an ounce by weight.

Limits and Common Mistakes

The target concentration must be greater than zero and no greater than the starting concentration for a dilution by adding solvent. If the target is higher than the starting concentration, the formula returns a negative addition, signalling that adding solvent cannot achieve the requested result. A concentration of zero cannot be reached by adding a finite volume of solvent according to this formula.

• Confusing added volume with final volume: A 100 mL starting sample diluted to 500 mL needs 400 mL added, not 500 mL.
• Mixing percentage bases: Do not compare, for instance, a mass-by-volume percentage with a volume-by-volume percentage as though they were identical.
• Mixing units: Use a single volume unit throughout and convert before calculating if needed.
• Rounding too early: Keep intermediate values unrounded when doing a manual calculation, then round the measured amount sensibly for the equipment being used.
• Assuming volumes always add exactly: The formula treats the final volume as the starting volume plus solvent. Some mixtures contract or expand, so the measured final volume may differ.

The calculation also assumes the original solution is homogeneous and that adding solvent does not change the amount of solute through reaction, evaporation, precipitation, or another process. It is a mathematical estimate, not a substitute for a procedure that specifies how a particular mixture must be prepared.

Frequently Asked Questions

How do I calculate how much water to add?
Use V₂ = V₁ × C₁ / C₂ to find the desired final volume, then subtract the starting volume: water to add = V₂ − V₁. This assumes water is the appropriate solvent and the percentage basis remains consistent.

Is a 1:10 dilution the same as 10%?
Not necessarily. A 1:10 dilution can mean one part stock brought to ten total parts, which is one-tenth of the stock concentration. In other contexts, people use “1:10” to mean one part stock plus ten parts diluent. State whether the ratio describes total parts or parts added.

Can I use this calculator for a target concentration higher than the starting concentration?
No. Adding solvent only lowers concentration. To reach a higher concentration, you would need a different method, such as adding solute or removing solvent, with a calculation appropriate to that process.

Does the calculator work with litres or ounces?
Yes. The formula is unit-independent as long as the starting volume and the result use the same unit. Convert to a consistent unit before using the calculator, which displays its volume answers in mL.

Why might the measured final volume differ from the result?
The formula assumes volumes add directly. Real mixtures can change volume when combined, and measurement precision, temperature, or incomplete mixing can also affect the observed result.

Related

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in c1 | Starting concentration (%) | % | 10 | 0
in c2 | Target concentration (%) | % | 2 | 0
in v1 | Starting volume | mL | 100 | 0
out add | Solvent to add | mL | v1 * (c1 / c2 - 1) | 2
out vf | Final volume | mL | v1 * c1 / c2 | 2