Solution Dilution Calculator

Determine how to dilute a stock solution to any target concentration and volume.

Supports 9 molar concentration units and 22 volume units with full bidirectional solving.

Updated September 11, 2026

CreatorFrank Zhao

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What is solution dilution?

Solution dilution is the process of reducing the concentration of a solute in a solution, typically by adding more solvent. In chemistry labs, biology research, clinical testing, and industrial manufacturing, you almost never use a stock solution at its original concentration — you dilute it to the exact strength your protocol requires.

This calculator solves the fundamental dilution equation $\mathrm{C_1} \times \mathrm{V_1} = \mathrm{C_2} \times \mathrm{V_2}$ , where you can enter any three known values and immediately find the fourth. It supports 9 molar concentration units (from $\\mathrm{yM}$ to $\\mathrm{M}$ ) and 22 volume units, so you can mix metric, imperial, and laboratory-specific units without manual conversion.

Who uses this? Lab technicians preparing buffer solutions, pharmacists compounding medications, students running titration experiments, quality-control engineers verifying reagent concentrations, and anyone who needs to figure out how much stock solution to measure out.

How to use this calculator

Enter the concentration of your stock solution (C₁) with its unit.

Enter the concentration you want to achieve (C₂) with its unit.

Enter the final volume of diluted solution you need (V₂).

The calculator instantly computes the volume of stock solution required (V₁). You can also leave any other field blank to solve for it instead.

Worked example

You have a $1\ \mathrm{M}$ stock solution of hydrochloric acid. You need $500\ \mathrm{mL}$ of a $20\ \mathrm{mM}$ working solution. How much stock do you measure?

Computation:

\mathrm{V_1} = \frac{\mathrm{C_2} \times \mathrm{V_2}}{\mathrm{C_1}}

=

\frac{20 \times 10^{-3} \times 0.5}{1}

=

0.01\ \mathrm{L} = 10\ \mathrm{mL}

Measure $10\ \mathrm{mL}$ of the stock solution, then add solvent (typically deionized water) until the total volume reaches $500\ \mathrm{mL}$ . The calculator also supports entering the answer in mL, cups, fl oz, or any of the 22 available volume units — it automatically converts between them.

Formula explanation

The dilution equation expresses conservation of solute amount: the moles of solute in the initial solution equal the moles in the final diluted solution.

\mathrm{C_1} \times \mathrm{V_1} = \mathrm{C_2} \times \mathrm{V_2}

Symbol	Meaning	Default unit
$\mathrm{C_1}$	Initial (stock) concentration	mol/L (M)
$\mathrm{V_1}$	Volume of stock solution needed	liters (L)
$\mathrm{C_2}$	Final (diluted) concentration	mol/L (M)
$\mathrm{V_2}$	Total volume of diluted solution	liters (L)

All four rearrangements:

\mathrm{V_2} = \frac{\mathrm{C_1} \times \mathrm{V_1}}{\mathrm{C_2}}

\mathrm{C_2} = \frac{\mathrm{C_1} \times \mathrm{V_1}}{\mathrm{V_2}}

\mathrm{V_1} = \frac{\mathrm{C_2} \times \mathrm{V_2}}{\mathrm{C_1}}

\mathrm{C_1} = \frac{\mathrm{C_2} \times \mathrm{V_2}}{\mathrm{V_1}}

The calculator uses high-precision decimal arithmetic internally, so even extreme dilution ratios (e.g., nanomolar to attomolar) are computed without rounding errors propagating through intermediate steps.

Real-world examples

Preparing a buffer for cell culture

A biology lab needs 250 mL of 1X PBS from a 10X stock.

$\mathrm{C_1} = 10\times$ , $\mathrm{C_2} = 1\times$ , $\mathrm{V_2} = 250\ \mathrm{mL}$

\mathrm{V_1} = \frac{1 \times 250}{10} = 25\ \mathrm{mL}

→ stock + 225 mL water

Clinical reagent preparation

A clinical lab has a 5 mM glucose standard and needs 10 mL of a 0.25 mM working solution.

$\mathrm{C_1} = 5\ \mathrm{mM}$ , $\mathrm{C_2} = 0.25\ \mathrm{mM}$ , $\mathrm{V_2} = 10\ \mathrm{mL}$

\mathrm{V_1} = \frac{0.25 \times 10}{5} = 0.5\ \mathrm{mL}

→ stock + 9.5 mL diluent

Cross-unit dilution — finding the stock concentration

You measured 2 tsp of a stock dye solution and diluted it to 1 US gal. The final concentration reads 0.5 mM. What was the original stock concentration?

$\mathrm{V_1} = 2\ \mathrm{tsp} = 0.01\ \mathrm{L}$ , $\mathrm{V_2} = 1\ \mathrm{US\ gal} = 3.785\ \mathrm{L}$ , $\mathrm{C_2} = 0.5\ \mathrm{mM}$

\mathrm{C_1} = \frac{0.5 \times 3.785}{0.01} \approx 189.3\ \mathrm{mM}

→ stock concentration

Tips & best practices

Watch your unit mixing

The calculator handles unit conversion automatically — you can enter C₁ in mM and C₂ in μM, or V₁ in mL and V₂ in US gal. But always double-check that the result unit matches what your lab protocol expects.

Add solvent, not the other way around

When performing the dilution, always add the stock solution to the container first, then fill to the target volume with solvent. Adding stock to solvent can cause local concentration spikes and heat generation.

Volume is not always additive

This equation assumes the final volume equals the volume you specify. In practice, mixing some solutions causes slight volume contraction or expansion. For high-precision work, always bring to final volume in a volumetric flask.

Use the right precision for your glassware

If your pipette measures to 0.1 mL, there is no benefit to calculating V₁ to six decimal places. Match the calculator output to your actual measurement capability.

Limitations

•The equation assumes ideal mixing — that the final volume equals the value you specify and that no chemical reaction, evaporation, or significant heat effect changes the solution volume during dilution.
•All input values must be strictly positive. A concentration or volume of zero makes the equation mathematically undefined.
•This calculator handles molar concentration dilution only. It does not account for mass-to-mole conversions — use a molarity calculator if you need to convert between mass concentration and molarity first.
•For multi-step serial dilutions (e.g., 1:10 repeated 5 times), use the serial dilution calculator instead — it tracks cumulative dilution factors and volumes at each step.

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