Reagent Dilution Calculator: C1V1 = C2V2

A reagent dilution calculator works out how much concentrated starting solution and how much diluent are needed to prepare a target volume at a lower concentration. Enter the stock concentration, desired concentration, and final volume to get the stock volume and the additional diluent volume.

Formula

The standard dilution equation is C₁V₁ = C₂V₂. Rearranged to find the volume of stock solution, it is V₁ = C₂V₂ / C₁. The amount of diluent to add is Vd = V₂ − V₁.

• C₁ is the concentration of the stock solution, in mM.
• V₁ is the volume of stock solution to use, in mL.
• C₂ is the desired final concentration, in mM.
• V₂ is the desired final solution volume, in mL.
• Vd is the calculated volume of diluent, in mL.

Concentration units must match: for example, use mM for both C₁ and C₂, or convert one value first. Volume units must also match in the equation. This calculator uses mL for both volumes, so its output is in mL.

Worked Example

Using the defaults, the stock concentration is 100 mM, the target concentration is 10 mM, and the final volume is 50 mL.

1. Calculate stock volume: V₁ = (10 mM × 50 mL) / 100 mM = 5 mL.
2. Calculate diluent volume: Vd = 50 mL − 5 mL = 45 mL.

The calculator therefore returns 5.00 mL of stock solution and 45.00 mL of diluent. In practice, combine the stock with diluent and bring the mixture to the specified final volume if exact volume matters; adding liquid volumes does not always produce an exactly additive final volume.

How to Use a Reagent Dilution Calculator

Use the calculator when you know the concentration of a stock reagent and want to prepare a less concentrated solution. The first output is the amount of stock required; the second is the estimated diluent volume needed to reach the stated final volume.

1. Read the stock concentration from the reagent label or preparation record.
2. Choose the target concentration and final volume required for the procedure.
3. Enter the concentrations in the same units and the volume in mL.
4. Use the stock volume as the aliquot to transfer, then add diluent as appropriate for your protocol and bring the solution to its final volume.

The calculator does not determine which diluent is compatible with a reagent, whether a solution is stable, or whether a particular concentration is suitable for an experiment. Those choices depend on the reagent, intended use, and validated procedure.

Understanding Dilution and Concentration Units

A dilution lowers concentration by distributing the same amount of solute through a larger total volume. In the idealized equation, the amount of solute before and after dilution is conserved. For a simple aqueous solution, concentration may be given in molarity (M), millimolarity (mM), or another concentration unit. A stock labeled 1 M is 1,000 mM; convert before entering values if the two concentrations use different scales.

Mass concentration units, such as mg/mL, can also be used with C₁V₁ = C₂V₂ when both concentration entries use the same unit. The equation does not require mM specifically. It does require consistent concentration units and consistent volume units. A value in µL must be converted to mL if paired with a volume in mL: 1 mL = 1,000 µL.

A dilution factor is another way to describe the change in concentration: dilution factor = C₁ / C₂. In the example, 100 mM divided by 10 mM equals 10, so the final concentration is one-tenth of the stock concentration. This does not mean adding one part stock to ten parts diluent; a tenfold final dilution is one part stock in ten parts total solution.

Common Errors and Limits

• Mixing units: Entering 0.1 M as though it were 0.1 mM creates a thousandfold error. Convert to a shared unit first.
• Confusing final volume with diluent volume: V₂ is the final total volume, not the amount of diluent to add. The diluent estimate is V₂ − V₁.
• Using a target above the stock concentration: If C₂ is greater than C₁, the calculated stock volume exceeds the requested final volume and the diluent result is negative. Simple dilution cannot make a more concentrated solution; a stronger stock or a different preparation method is needed.
• Relying on excessive decimal places: A calculation may display hundredths of a milliliter, but the practical precision depends on the measuring equipment and the uncertainty of the stock concentration.
• Assuming volumes always add exactly: The equation is a useful concentration calculation, but some mixtures can change volume on mixing. For precision, prepare to the final-volume mark or follow the relevant procedure.

The equation assumes the solute amount is conserved and that the stock and final concentrations describe the same substance in compatible conditions. It does not account for chemical reaction, degradation, precipitation, evaporation, temperature effects, or interactions with the diluent. It also does not calculate how to make a stock from solid reagent; that requires the substance’s formula mass, desired amount, and a separate preparation calculation.

Practical Measurement and Safety

Choose measuring equipment suited to the volume and required precision. A small stock aliquot measured with equipment designed for much larger volumes may be inaccurate. Follow the applicable laboratory procedure, reagent label, and safety data for handling, protective equipment, storage, and disposal. Do not assume that water is an appropriate diluent: some reagents require a particular buffer or solvent, and some can react with water or become unstable in it.

Label prepared solutions with useful identification, including concentration, preparation date, and other details required by the local procedure. Keep the stock and diluted solution clearly distinguished. If a calculation produces a volume below the practical measuring range, consider a validated intermediate dilution rather than trying to measure an unreliable trace volume.

Frequently Asked Questions

What is the formula for reagent dilution?
Use C₁V₁ = C₂V₂. To find the stock volume, rearrange it to V₁ = C₂V₂ / C₁. Subtract that volume from the desired final volume to estimate the diluent amount.

How do I calculate how much diluent to add?
Subtract the stock volume from the final volume: Vd = V₂ − V₁. For accurate final volume, protocols commonly specify adding diluent until the mixture reaches the final volume rather than assuming the component volumes add perfectly.

Can I use mg/mL instead of molarity?
Yes. Use the same mass-per-volume unit for both stock and target concentrations. The dilution equation works with any consistent concentration unit.

What does a 1:10 dilution mean?
It generally means one part of the original solution in ten parts total volume, such as 1 mL stock brought to 10 mL final volume. That is different from mixing 1 part stock with 10 parts diluent, which makes 11 parts total.

Why is the calculated diluent volume negative?
A negative result usually means the target concentration is higher than the stock concentration. Diluting cannot increase concentration; use a more concentrated stock or prepare the solution by another suitable method.

Related

• PPB Dilution Calculator: Calculate a Final Concentration
• PPM Dilution Calculator: Formula and Examples
• Mass per Volume Dilution Calculator and Formula

in c1 | Stock concentration | mM | 100 | 0
in c2 | Target concentration | mM | 10 | 0
in v2 | Final volume | mL | 50 | 0
out v1 | Stock solution needed | mL | c2 * v2 / c1 | 2
out vd | Diluent to add | mL | v2 - v1 | 2