How It Works
This calculator works in 4 steps.
Select the unknown variable
Choose C₁, V₁, C₂, or V₂ as the value to solve. The calculator locks the chosen field and treats the other 3 fields as inputs.
Enter 3 known values
Type the stock concentration, the target concentration, and one volume. Leave the unknown field empty.
Match concentration and volume units
Set C₁ and C₂ to the same unit, such as mM, and set V₁ and V₂ to the same unit, such as mL or µL. The calculator converts mixed prefixes before solving.
Read the result and diluent volume
The calculator rearranges C₁V₁ = C₂V₂, returns the missing value, and reports the diluent volume as V₂ − V₁ for the bench protocol.
The Formula
The C₁V₁ = C₂V₂ formula states that stock concentration multiplied by stock volume equals final concentration multiplied by final volume.
C₁ × V₁ = C₂ × V₂V₁ = (C₂ × V₂) / C₁C₂ = (C₁ × V₁) / V₂V_diluent = V₂ − V₁- C₁:
- Concentration of the stock solution
- V₁:
- Volume of stock transferred
- C₂:
- Concentration of the final solution
- V₂:
- Total volume of the final solution
To make 100 mL (3.38 US fl oz) of 1 mM solution from a 10 mM stock, V₁ = (1 mM × 100 mL) / 10 mM = 10 mL. Add 10 mL of stock to 90 mL of diluent.
Conversion Table
The C₁V₁ = C₂V₂ conversion table lists 6 common stock-to-working dilutions with the stock volume and diluent volume for each final volume.
| Stock (C₁) | Target (C₂) | Final volume (V₂) | Stock volume (V₁) | Diluent (V₂ − V₁) |
|---|---|---|---|---|
| 10 mM | 1 mM | 100 mL | 10 mL (10,000 µL) | 90 mL |
| 1 mM | 0.1 mM | 50 mL | 5 mL (5,000 µL) | 45 mL |
| 100 mM | 5 mM | 20 mL | 1 mL (1,000 µL) | 19 mL |
| 12 mM | 1 mM | 500 mL | 41.67 mL (41,667 µL) | 458.3 mL |
| 50 mM | 2.5 mM | 10 mL | 0.5 mL (500 µL) | 9.5 mL |
| 1,000 mM | 1 mM | 1 mL | 0.001 mL (1 µL) | 0.999 mL |
What Is the C₁V₁ = C₂V₂ Calculator?
The C₁V₁ = C₂V₂ Calculator is a four-variable dilution solver that returns any one missing value from stock concentration (C₁), stock volume (V₁), final concentration (C₂), and final volume (V₂). The calculator uses the conservation of solute amount: the moles or grams of solute in the stock aliquot equal the moles or grams of solute in the finished dilution.
The equation holds for any concentration unit that scales linearly with solute amount, including molarity (M), millimolar (mM), micromolar (µM), milligrams per milliliter (mg/mL), and percent weight per volume (% w/v). C₁ and C₂ share one unit, and V₁ and V₂ share one unit. The calculator assumes the diluent contains none of the solute and the final volume is measured after mixing.
Common Uses
There are 5 main uses of this calculator.
Working solution preparation
Lab staff convert a concentrated stock, such as 100 mM ATP, into a 1 mM working solution for an assay.
Buffer dilution
Technicians dilute 10× PBS or 50× TAE to 1× strength for routine bench work.
Calibration standards
Analysts prepare single-point standards from a certified reference solution at a stated concentration.
Reagent scale-up and scale-down
Researchers recalculate stock volume when the final volume changes from 50 mL to 2 L (0.53 US gal).
Chemistry teaching
Instructors use the 4-variable equation to teach solute conservation in general chemistry courses.