Dilution Table Calculator: Mix Concentrations Clearly

A dilution table calculator works out how much stock solution and diluent are needed to prepare a target concentration at a chosen final volume. Enter the stock concentration, target concentration, and final volume; the calculator returns the stock volume and the amount of diluent to add.

Formula

The calculation uses the conservation-of-solute relationship C₁V₁ = C₂V₂. Rearranging gives V₁ = (C₂ × V₂) / C₁, and the diluent volume is V₂ − V₁.

• C₁ is the stock concentration, in mg/mL.
• V₁ is the volume of stock solution to use, in mL.
• C₂ is the target concentration, in mg/mL.
• V₂ is the desired final volume, in mL.
• Diluent volume is the additional liquid needed, in mL, assuming volumes are additive.

The concentration units must match, as must the volume units. The example calculator uses mg/mL and mL, but the same equation works with other consistent units, such as g/L and L.

Worked Example

Using the calculator’s defaults: stock concentration = 10 mg/mL, target concentration = 2 mg/mL, and final volume = 50 mL.

1. Stock volume = (2 mg/mL × 50 mL) ÷ 10 mg/mL = 10 mL.
2. Diluent volume = 50 mL − 10 mL = 40 mL.

Combine 10 mL of the 10 mg/mL stock with enough diluent to reach a final volume of 50 mL. Under the calculator’s additive-volume assumption, that is 40 mL of diluent. The results, rounded to two decimal places, are 10.00 mL of stock and 40.00 mL of diluent.

What a Dilution Table Shows

A dilution table lays out quantities for one or more target concentrations or final volumes. Rather than recalculating each mixture by hand, a table can show the stock volume and diluent volume for a series of targets. The calculator above handles one target at a time; repeat the calculation with each desired target to build a table.

For instance, keeping a 50 mL final volume and 10 mg/mL stock, target concentrations of 1, 2, and 5 mg/mL require respectively 5, 10, and 25 mL of stock. The corresponding diluent amounts are 45, 40, and 25 mL. These quantities follow the same equation and assume the final volume is the stated volume.

“Dilution” can also describe a dilution factor, which is a ratio rather than a volume. Here, dilution factor = stock concentration ÷ target concentration. In the example, 10 ÷ 2 = 5, so the stock is diluted fivefold. The factor alone does not tell you the batch size; the final-volume input is needed to calculate actual volumes.

How to Use the Calculator

1. Enter the concentration of the stock solution as supplied or measured.
2. Enter the concentration you want in the finished mixture.
3. Enter the intended final volume, not merely the amount of diluent.
4. Read the stock volume and diluent volume. Measure the stock, then add diluent until the mixture reaches the intended final volume when precision matters.

The stock concentration must be greater than or equal to the target concentration for a straightforward dilution. A target above the stock concentration would require concentrating the solution or using a stronger stock; adding diluent cannot achieve it. A target of zero corresponds mathematically to no stock, but in practice a zero-concentration mixture is simply diluent or solvent.

Choosing Units and Measuring Accurately

Concentration can be expressed in mass per volume, such as mg/mL or g/L, or in other forms such as mol/L or percent. Use the same concentration unit for stock and target. Convert one value first if the units differ: for example, 1 g/L equals 1 mg/mL. Do not enter a percentage as though it were a mass-per-volume value without confirming what that percentage means.

Volume units likewise need to match. One litre is 1,000 mL, and one US fluid ounce is approximately 29.57 mL. US fluid ounces measure volume; ounces by mass do not. For very small calculated volumes, the measurement tool may not provide adequate resolution. Making a larger batch or preparing an intermediate dilution can make measurement easier, but the resulting steps and uncertainties should be calculated separately.

Concentration labels may refer to different conventions, including mass/volume, mass/mass, or volume/volume. The simple equation is valid when both concentration values use the same definition and the quantities are compatible. It does not convert between these conventions automatically.

Assumptions and Common Mistakes

• Confusing final volume with diluent volume: V₂ is the total finished volume. In the example, 50 mL is the final mixture, not 50 mL of water plus stock.
• Mixing units: Using a stock value in g/L and a target in mg/mL without conversion can produce a thousandfold error.
• Rounding too early: Keep extra digits during intermediate calculations, then round to the precision your measuring equipment can reliably deliver.
• Assuming all volumes add exactly: The calculator subtracts stock volume from final volume. Some mixtures change volume when combined, so for precise preparation add diluent to the required final mark rather than relying on separate volumes to add perfectly.
• Using the wrong stock concentration: The calculation cannot correct for an inaccurate label, degradation, or a concentration defined on a different basis.

This is a mathematical mixing calculator, not a procedure for deciding whether a substance is suitable or safe to handle. Follow the relevant laboratory or product instructions for materials, equipment, and handling. The formula also does not account for chemical reactions, evaporation, density changes, or losses during transfer.

Frequently Asked Questions

What is the dilution formula?
The standard relationship is C₁V₁ = C₂V₂. To find the stock volume, calculate V₁ = C₂V₂ ÷ C₁; subtract that volume from the final volume to find the nominal diluent amount.

How do I calculate a 1:10 dilution?
A tenfold dilution has a final concentration one-tenth of the starting concentration. For a 10 mL final volume, use 1 mL of stock and make the mixture up to 10 mL total, conventionally about 9 mL of diluent if volumes are additive.

Does final volume include the stock solution?
Yes. Final volume is the volume of the complete mixture after stock and diluent are combined. It is not the amount of diluent alone.

Can I use different units for stock and target concentrations?
Not directly. Convert them to the same concentration unit first, then use matching volume units in the calculation.

How do I make a dilution table for several concentrations?
Choose a final volume, calculate the stock volume for each target using V₁ = C₂V₂ ÷ C₁, and calculate diluent as V₂ − V₁. Keep the stock and target concentration units consistent for every row.

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in stock | Stock concentration | mg/mL | 10 | 0
in target | Target concentration | mg/mL | 2 | 0
in volume | Final volume | mL | 50 | 0
out stockvol | Stock solution needed | mL | target * volume / stock | 2
out diluent | Diluent needed | mL | volume - stockvol | 2