Tank Dilution Calculator: Mix to a Target Concentration

A tank dilution calculator determines how much concentrated solution and how much water to combine to reach a target concentration in a chosen final tank volume. Enter the stock concentration, desired concentration, and final volume; the calculator returns the stock-solution volume and the amount of diluent to add.

Formula

The dilution relationship is C₁V₁ = C₂V₂. Rearranging gives V₁ = C₂V₂ ÷ C₁, where C₁ is the stock concentration in mg/L, V₁ is the stock-solution volume in L, C₂ is the target concentration in mg/L, and V₂ is the final mixture volume in L. The diluent volume is V₂ − V₁, assuming the final mixture volume is the specified volume.

Concentration units must match, and the stock, target, and final-volume units must be used consistently. This calculator expresses concentration in mg/L and volume in L. If the stock is given in another unit, convert it first; for example, 1 g/L equals 1,000 mg/L. For dilute water-based solutions, mg/L is often numerically close to parts per million (ppm), but that approximation is not universal, especially for solutions with a substantially different density.

Worked Example

Using the calculator’s defaults:

• Stock concentration, C₁ = 1,000 mg/L
• Target concentration, C₂ = 100 mg/L
• Final volume, V₂ = 100 L

First calculate stock volume: V₁ = (100 mg/L × 100 L) ÷ 1,000 mg/L = 10 L. Then calculate diluent: 100 L − 10 L = 90 L. The result is 10.00 L of stock solution and 90.00 L of diluent, for a nominal final volume of 100 L.

How Tank Dilution Works

Dilution lowers concentration by distributing a measured amount of solute through a larger total volume. The equation assumes that the amount of solute taken from the stock remains in the mixture: the stock’s concentration multiplied by the stock volume equals the final concentration multiplied by the final volume.

For example, if a stock solution contains 1,000 mg of a substance per litre, 10 L contains 10,000 mg. In a final 100 L mixture, those 10,000 mg correspond to 100 mg/L. Adding 100 L of water to 10 L of stock would instead make about 110 L, so it would not produce the 100 L final volume used in this example.

The formula works for many liquid dilution tasks when concentration is defined consistently and the mixture is uniform. It does not establish whether a target concentration is appropriate for a particular process, material, or organism; that target must come from a reliable, task-specific source.

When to Use the Calculator

Use it when you know the stock concentration and the desired final concentration and volume. It can help plan a batch before filling a tank, or calculate a smaller test batch using the same concentration ratio.

• For a smaller batch, reduce the final volume and keep the stock and target concentrations unchanged. The required stock amount scales with the final volume.
• If you know the volumes already measured, use the same relationship to check the expected concentration: C₂ = C₁V₁ ÷ V₂.
• If the desired final volume is not fixed, first decide how much finished mixture is needed; the calculator treats the entered volume as the final total, not the amount of water.

Tank capacity is not always the same as working volume. Leave room for mixing, circulation, foam, or other operational needs as applicable, and enter the actual intended final volume rather than the tank’s nominal capacity.

Units, Measurement, and Common Mistakes

The calculation is only as reliable as its input measurements. Read concentration units carefully: mg/L, g/L, percent by mass, and percent by volume are not interchangeable without conversion and, in some cases, additional information such as density. Do not enter a percentage as though it were mg/L.

• Mixing volume units: Convert gallons to litres or vice versa before calculating. One US gallon is about 3.785 L; one Imperial gallon is about 4.546 L. They are different units.
• Confusing added water with final volume: The input is the total volume after mixing. If you add the calculated stock volume to the full entered volume of water, you exceed the intended final volume and dilute more than planned.
• Rounding too early: Keep extra digits during intermediate calculations, then round the measured quantities to a practical precision. A displayed value such as 0.01 L equals 10 mL, but equipment may not measure that accurately.
• Assuming volume is perfectly additive: The simple formula treats final volume as the stated total. Some mixtures contract, expand, or react on mixing. For precision work, follow an applicable procedure that accounts for final-volume adjustment.

Limits and Practical Checks

The stock concentration must be greater than zero, and a target concentration greater than the stock cannot be reached by dilution alone. A target equal to the stock requires no dilution; a zero target mathematically requires no stock, though it may not be a meaningful mixing instruction. The calculator’s nonnegative inputs do not replace checking that the entered values are sensible for the intended use.

For a target below the stock concentration, the calculated stock volume should not exceed the final volume, and the diluent result should not be negative. Verify that the tank and measuring tools use compatible units, that the stock is properly mixed if it can settle, and that the finished solution is mixed uniformly before taking a sample. Follow relevant handling instructions for the actual substance; the equation itself does not address compatibility, hazards, or required protective measures.

Frequently Asked Questions

How do I calculate dilution for a tank?
Use C₁V₁ = C₂V₂. Multiply the target concentration by the desired final volume, then divide by the stock concentration to get the stock volume. Subtract that amount from the final volume to find the diluent volume.

Do I add the stock to the tank’s full water volume?
No, not when you want the entered final volume. Measure the stock, then add diluent until the combined mixture reaches that total volume. Adding stock to a full tank changes the final volume.

Can I use gallons instead of litres?
Yes, as long as all volume inputs use the same gallon definition and concentration units are consistent. Do not mix US and Imperial gallons or combine gallons and litres without converting.

Can dilution make a solution more concentrated?
No. Adding diluent can only lower concentration or leave it unchanged. To reach a concentration above the stock strength, a stronger stock or a different preparation method is needed.

Does mg/L always equal ppm?
No. They are approximately equivalent for many dilute water-based solutions, but ppm is a ratio by mass while mg/L is mass per volume. Density and the definition used for ppm matter in other mixtures.

Related

• Dilution Ratio Calculator: Mix Concentrate and Water
• ug/mL to ng/mL Dilution Calculator and Formula
• Dilution Calculator Percentage: Formula and Examples

in stock | Stock concentration | mg/L | 1000 | 0
in target | Target concentration | mg/L | 100 | 0
in volume | Final tank volume | L | 100 | 0
out stockvol | Stock solution needed | L | target * volume / stock | 2
out diluent | Diluent to add | L | volume - stockvol | 2