Dilution Calculator by Volume: Mix a Target Solution

A dilution calculator by volume works out how much concentrated stock solution and how much diluent to combine to make a chosen final volume at a lower concentration. Enter the stock concentration, target concentration, and final volume; the calculator returns the stock volume and the diluent volume to add.

Formula

The standard dilution relationship is C₁V₁ = C₂V₂. Rearranging it gives the stock volume, V₁ = (C₂ × V₂) ÷ C₁. The diluent volume is V₂ − V₁ when the stated final volume is the total volume of the finished mixture.

• C₁ is the stock solution concentration, in grams per liter (g/L) in this calculator.
• V₁ is the volume of stock solution required, in liters (L).
• C₂ is the target concentration, in g/L.
• V₂ is the desired final solution volume, in L.

The concentration units must match, and the volume units must match. The formula assumes the stock and target concentrations describe the same dissolved substance and use a compatible concentration basis. For example, do not treat a mass-per-volume concentration such as g/L as though it were a percentage by volume.

Worked Example

Using the default values—100 g/L stock, a 20 g/L target, and 1 L final volume:

1. Calculate the stock volume: V₁ = (20 g/L × 1 L) ÷ 100 g/L = 0.2 L.
2. Calculate the diluent volume: 1 L − 0.2 L = 0.8 L.
3. Combine 0.2 L of stock with enough diluent to bring the mixture to a final volume of 1 L. Under the calculator’s simple volume-addition assumption, that is 0.8 L of diluent.

The calculator therefore reports 0.200 L of stock solution and 0.800 L of diluent. The stock volume is 200 mL and the diluent volume is 800 mL. Check: 100 g/L × 0.2 L = 20 g of solute, and 20 g ÷ 1 L = 20 g/L.

How to Use a Dilution Calculator by Volume

1. Find the stock concentration from the solution label, preparation record, or other reliable source.
2. Choose a target concentration that is lower than the stock concentration.
3. Enter the desired final volume and use consistent units. This calculator uses g/L for concentrations and L for volumes.
4. Read the stock volume, then measure the diluent. For greater accuracy, add diluent until the mixture reaches the desired final volume rather than assuming the separate liquid volumes add perfectly.

The calculator describes a mathematical mixing calculation; it does not identify the substance, verify the stock label, or determine whether a particular solution is suitable for a specific purpose. If the target is not lower than the stock concentration, the requested mixture cannot be made by diluting that stock alone.

Understanding the Result and Its Limits

“Diluent to add” is often used as shorthand for the difference between final volume and stock volume. In routine calculations, that is a useful estimate. However, some mixtures do not finish at exactly the sum of their measured starting volumes. Dissolving a solid or mixing certain liquids can change the total volume. When a precise final concentration matters, measure the stock and then add diluent until the mixture reaches the specified final volume.

The calculation also assumes that the concentration is uniform and that no solute is lost, reacted, or removed during mixing. It does not account for temperature-related volume changes, density differences, evaporation, or measurement uncertainty. Follow the applicable preparation procedure and use measuring equipment suitable for the required precision.

Common Mistakes and Unit Conversions

• Mixing concentration units: Convert both concentrations to the same unit first. For example, 1 g/L equals 1 mg/mL, but 1 g/L does not equal 1 mg/L.
• Mixing volume units: Convert milliliters to liters or liters to milliliters before calculating. There are 1,000 mL in 1 L; the ratio itself does not change when both volumes use the same unit.
• Entering a percentage without defining it: Percent can mean mass per mass, volume per volume, or mass per volume. These are not interchangeable without the relevant density and definition.
• Rounding too early: Keep extra digits during intermediate steps, then round the measured quantities to what your equipment can reliably measure.
• Requesting an impossible target: A target concentration above the stock concentration produces a calculated stock volume greater than the desired final volume. Dilution alone cannot achieve that result.

For example, if a stock is labeled 5 g/L and the target is 10 g/L, the stock is already less concentrated than the requested target. You would need a more concentrated stock or a different preparation method; adding diluent cannot raise concentration.

Frequently Asked Questions

What is the dilution formula?
The usual relationship is C₁V₁ = C₂V₂. Use it to find the volume of a known stock solution needed to make a lower-concentration solution at a specified final volume.

How much water do I add when diluting a solution?
For a simple volume-addition estimate, subtract the stock volume from the desired final volume. For an accurately specified final volume, add water or another appropriate diluent until the mixture reaches that final volume.

Can I use this calculator with percentages?
Only if the stock and target percentages use the same definition and basis. Convert them consistently, and do not assume that percent by mass, percent by volume, and mass per volume mean the same thing.

Can dilution make a solution more concentrated?
No. Adding diluent lowers concentration. A target above the stock concentration cannot be reached by dilution alone.

What if the stock and target use different units?
Convert them to compatible concentration units before entering them. The dilution equation works only when both concentration values refer to the same substance and measurement basis.

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in stock | Stock concentration | g/L | 100 | 0
in target | Target concentration | g/L | 20 | 0
in final | Final volume | L | 1 | 0
out stockvol | Stock solution needed | L | target * final / stock | 3
out diluent | Diluent to add | L | final - stockvol | 3