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Calculate the volume or concentration required to dilute a stock solution. Support for Molarity, mM, µM, and custom units.
Make perfect lab solutions every time by understanding the core concepts of concentration.
The C₁V₁ = C₂V₂ formula relies on the fact that adding solvent (like water) does not change the total number of moles of solute present in the solution.
Buy or prepare concentrated "stock" solutions (C₁) to save space. When you need a working solution (C₂), simply measure out V₁ and add solvent until you reach V₂.
For extremely low concentrations, it\'s more accurate to perform a series of step-wise dilutions (e.g., 1:10, then 1:10 again to reach 1:100) rather than a single massive dilution.
Dilution reduces concentration by adding solvent while keeping total solute amount constant. In practical terms, you start with a concentrated stock (C1), transfer a measured volume (V1), and then add solvent until you reach a target final volume (V2) and concentration (C2).
This concept is critical in chemistry, microbiology, pharmacology, and environmental testing. Accurate dilution directly impacts assay reliability, calibration quality, dosing precision, and reproducibility across experiments and labs.
Primary use cases
Preparing working solutions, standards, and assay reagents.
Why precision matters
Small dilution errors can produce major concentration drift.
C1 × V1 = C2 × V2
The equation works because moles of solute are conserved during dilution. Only solvent volume changes, not the amount of dissolved solute transferred from stock.
Quick example:
Prepare 250 mL of 0.2 M from 1.0 M stock: V1 = (0.2 × 250) / 1.0 = 50 mL stock. Add solvent to reach 250 mL total, so solvent needed = 200 mL.
Need 100 mL of 1X buffer from 10X stock. Use C1=10, C2=1, V2=100 mL. V1=10 mL stock, then add 90 mL water.
For plate counts, perform 1:10 serial steps (1 mL sample + 9 mL diluent) to reach measurable colony ranges reliably.
Build a calibration curve by preparing known concentrations (e.g., 1, 2, 5, 10 ppm) from a single concentrated standard.
Compare common dilution goals and how stock volume changes with target concentration and final volume.
| Stock (C1) | Target (C2) | Final Volume (V2) | Stock Needed (V1) | Solvent to Add |
|---|---|---|---|---|
| 10X | 1X | 100 mL | 10 mL | 90 mL |
| 1.0 M | 0.2 M | 250 mL | 50 mL | 200 mL |
| 500 mM | 50 mM | 20 mL | 2 mL | 18 mL |
| 100 ppm | 5 ppm | 1 L | 50 mL | 950 mL |
Use this Markdown block for lab docs, SOPs, and quick team notes.
| Stock (C1) | Target (C2) | Final Volume (V2) | Stock Needed (V1) | Solvent to Add |
|---|---|---|---|---|
| 10X | 1X | 100 mL | 10 mL | 90 mL |
| 1.0 M | 0.2 M | 250 mL | 50 mL | 200 mL |
| 500 mM | 50 mM | 20 mL | 2 mL | 18 mL |
| 100 ppm | 5 ppm | 1 L | 50 mL | 950 mL |Mixing incompatible concentration units (e.g., mM with uM) without conversion.
Adding V2 solvent instead of bringing the mixture up to V2 total volume.
Assuming C1V1=C2V2 applies when mixing two active solutions rather than stock + pure solvent.
The dilution formula is C₁V₁ = C₂V₂ where C₁ is the initial concentration, V₁ is the initial volume, C₂ is the final concentration, and V₂ is the final volume. It states that the total amount of solute remains constant when you dilute a solution with more solvent.
If you have a 10x stock solution and you want 1000 mL of a 1x solution: Set C₁ to 10x, C₂ to 1x, and V₂ to 1000 mL. Keep V₁ blank. The calculator will tell you to use 100 mL of the 10x stock (and therefore add 900 mL of water).
Our calculator automatically handles unit conversions! Just make sure you select the correct units from the dropdown menus (e.g. mM vs µM). Internally, it converts concentrations to a base unit (like M) and volumes to a base unit (like L) to perform the math accurately.
This is an essential lab tool used when preparing working solutions from concentrated stock solutions, diluting samples for spectrophotometry, or scaling down biological assays in chemistry, biology, and pharmacology.
Yes! The equation works for molarity (M), normality (N), mass/volume percentages (%), parts per million (ppm), and practically any other concentration unit, provided you use the exact same unit on both sides of the equation.
A serial dilution is a stepwise dilution of a substance in solution. Usually, the dilution factor is kept constant at each step, resulting in geometric progression of the concentration (e.g., 1/10, 1/100, 1/1000). It is highly useful for creating standard curves.
Preparing and storing highly concentrated stock solutions saves physical laboratory space, increases shelf stability of sensitive reagents, and minimizes the weighing errors associated with measuring extremely tiny masses of dry powder.
When a protocol says to take 10 mL of stock and "bring it up to 100 mL," it means you add enough solvent (usually water) so the total, final volume (V2) equals 100 mL. You are adding 90 mL of solvent, not 100 mL.
Yes. In certain mixtures, particularly when mixing ethanol and water, the molecules pack together in such a way that adding 50 mL of ethanol to 50 mL of water results in slightly less than 100 mL total volume.
The C1V1 = C2V2 formula is strictly for diluting one solution with pure solvent. If mixing two active concentrations, you must use the mixture formula: (C1×V1) + (C2×V2) = C_final × (V1+V2).
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