C1V1=C2V2 Dilution Calculator
Use the dilution equation (C1 × V1 = C2 × V2) to calculate stock concentration, desired concentration, and final volume. Perfect for preparing solutions in chemistry, biology, and microfluidics labs.
Parameters
Result
| Parameter | Value |
|---|---|
| C1 (stock) | 100.000 mM |
| C2 (desired) | 10.000 mM |
| V1 (stock volume) | 100.0 µL |
| V2 (final volume) | 1000.0 µL |
| Diluent to add | 900.0 µL |
| Dilution factor | 10.00× |
Understanding C1V1=C2V2 Dilutions
The dilution equation C1V1 = C2V2 is one of the most fundamental relationships in chemistry and biology. It describes how the concentration of a solution changes when it is diluted with solvent. This principle is used daily in labs to prepare buffers, standards, working solutions, and assay components.
The Equation
where C1 is the concentration of the stock solution, V1 is the volume of stock used, C2 is the final (desired) concentration, and V2is the total final volume. The relationship states that the number of moles of solute is conserved: the moles in the stock (C1 × V1) equals the moles in the final solution (C2 × V2).
Simple vs. Serial Dilutions
A simple dilution (1-step) directly mixes a stock solution with diluent to reach the target concentration. A serial dilution involves repeated 1-step dilutions, each using the previous product as the stock. Serial dilutions are often used to create standard curves, reduce concentration by orders of magnitude, or minimize measurement error when large dilution factors are needed. For example, a 10-fold serial dilution applied five times achieves a 100,000-fold reduction (10⁵×) while keeping individual steps manageable.
Practical Tips for Accuracy
- Use appropriate pipettes: Choose pipettes within the middle of their range (e.g., 20–200 µL for P200). Accuracy at the extremes is poor.
- Calibrate regularly: Verify pipette accuracy and precision quarterly or as per your SOP.
- Mix thoroughly: After adding stock and diluent, mix by inversion or gentle vortexing to ensure homogeneity.
- Account for diluent volume: Always mix the volume of stock into the final volume, not up to the final volume after adding stock.
- Temperature stability: Prepare dilutions at room temperature and allow time for thermal equilibration before use.
Microfluidics Relevance
In microfluidic systems, dilution equations remain valid but with added constraints. Small volumes (nanoliter to microliter scales) require ultra-precise pipetting; standard manual pipettes may introduce unacceptable errors. Solutions include electronic or air-displacement micropipettes, syringe pumps, or on-chip mixing networks. Evaporation becomes significant in open systems, and diffusion-driven mixing may not achieve complete homogeneity in the short timescales of some devices. For concentration-sensitive assays, validate dilution accuracy by measuring with spectrophotometry, HPLC, or the analytical method you plan to use for the final assay.
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