Dilution Calculator
Use the dilution equation C1×V1 = C2×V2 to solve for any unknown variable. Enter three known values and select which variable to solve for. This calculator determines the final volume, concentration, or initial conditions needed for your dilution. See also our Molarity Calculator and Serial Dilution Calculator for related computations.
How to Calculate Dilutions
Dilution is one of the most common procedures in chemistry and biology laboratories. Whether you are preparing reagents for an experiment, making standard solutions for calibration curves, or adjusting the concentration of a stock solution, the dilution equation provides a simple and reliable method to determine the correct volumes and concentrations needed.
- Identify the known values: initial concentration (C1), initial volume (V1), final concentration (C2), or final volume (V2).
- Determine which variable you need to solve for — you need exactly three known values.
- Apply the dilution equation: C1 × V1 = C2 × V2.
- Rearrange to solve for the unknown variable.
- Ensure all volume units are consistent (both in mL or both in L).
- Calculate the dilution factor as C1/C2 (or V2/V1) to verify reasonableness.
The dilution equation works because the amount of solute (in moles) remains constant during dilution — you are only adding more solvent. The number of moles before dilution (C1 × V1) equals the number of moles after dilution (C2 × V2). This principle applies to any dilution where no chemical reaction occurs and the solute does not precipitate or evaporate.
Dilution Formula
C1 × V1 = C2 × V2
Solving for each variable:
V2 = (C1 × V1) / C2
C2 = (C1 × V1) / V2
V1 = (C2 × V2) / C1
C1 = (C2 × V2) / V1
Dilution Factor = C1 / C2 = V2 / V1
Where:
C1 = initial (stock) concentration
V1 = initial (stock) volume
C2 = final (diluted) concentration
V2 = final (total) volume
The dilution equation is derived from the conservation of moles: n₁ = n₂, where n = C × V. This equation assumes ideal behavior and is valid for dilute solutions. For concentrated solutions or solutions with significant volume changes upon mixing, more complex calculations involving densities and partial molar volumes may be required. The equation works with any consistent concentration units (M, mM, µM, %, ppm) as long as both C1 and C2 use the same units.
Example Calculation
Problem: You have a 1 M stock solution and need to prepare a 0.1 M solution. You want to use 100 mL of the stock. What final volume do you need?
Given:
• C1 = 1 M (stock concentration)
• V1 = 100 mL (stock volume)
• C2 = 0.1 M (desired final concentration)
• V2 = ? (final volume)
Solution:
V2 = (C1 × V1) / C2
V2 = (1 M × 100 mL) / 0.1 M
V2 = 1000 mL
Answer: The final volume should be 1000 mL. You need to add 900 mL of solvent to 100 mL of stock solution.
Dilution factor = 1 / 0.1 = 10× dilution
Verification: 1 M × 100 mL = 0.1 M × 1000 mL → 100 = 100 ✓
Common Dilution Reference Table
| Dilution Factor | Stock:Solvent Ratio | Final Concentration | Common Use |
|---|---|---|---|
| 1:2 (2×) | 1 part stock + 1 part solvent | 50% of original | Simple halving |
| 1:5 (5×) | 1 part stock + 4 parts solvent | 20% of original | Antibody dilutions |
| 1:10 (10×) | 1 part stock + 9 parts solvent | 10% of original | Buffer preparation |
| 1:20 (20×) | 1 part stock + 19 parts solvent | 5% of original | Serum dilutions |
| 1:100 (100×) | 1 part stock + 99 parts solvent | 1% of original | Bacterial plating |
| 1:1000 (1000×) | 1 part stock + 999 parts solvent | 0.1% of original | Drug dilutions |
| 1:10⁶ | Serial dilutions needed | 0.0001% of original | Microbiology CFU |
| 1:10⁹ | Serial dilutions needed | 10⁻⁷% of original | Homeopathy |
Frequently Asked Questions
What is the dilution equation?
The dilution equation C1V1 = C2V2 states that the product of concentration and volume before dilution equals the product after dilution. This works because the number of moles of solute remains constant — only the volume of solvent changes. It applies to any dilution where no chemical reaction occurs between solute and solvent.
What is a dilution factor?
The dilution factor is the ratio of the initial concentration to the final concentration (C1/C2), or equivalently, the ratio of final volume to initial volume (V2/V1). A 10× dilution means the solution was diluted to one-tenth its original concentration. Dilution factors are commonly expressed as ratios like 1:10, meaning 1 part sample to 9 parts diluent (10 parts total).
Can I use any units with C1V1 = C2V2?
Yes, as long as you use consistent units. Both concentrations must be in the same units (M, mM, %, ppm, etc.) and both volumes must be in the same units (mL, L, µL, etc.). The equation works because it is based on the conservation of solute amount, which is independent of the units used to express concentration and volume.
What is a serial dilution?
A serial dilution is a stepwise dilution of a substance where each step uses the diluted solution from the previous step as the new stock. For example, three consecutive 1:10 dilutions produce a final dilution of 1:1000. Serial dilutions are used when very large dilution factors are needed, as they are more accurate than attempting a single large dilution.
How do I dilute a concentrated acid safely?
Always add acid to water, never water to acid (remember: "Do as you oughta, add acid to water"). Adding water to concentrated acid can cause violent boiling and spattering due to the extreme heat of mixing. Slowly pour the acid into the water while stirring continuously. Use appropriate PPE including safety goggles, gloves, and a lab coat. Work in a fume hood when diluting volatile acids.
When does C1V1 = C2V2 not apply?
The dilution equation does not apply when: (1) a chemical reaction occurs between solute and solvent, (2) the solute precipitates out of solution, (3) volumes are not additive (as with mixing ethanol and water where total volume is less than the sum), (4) the solution is saturated and cannot hold more solvent without precipitation, or (5) gases are involved where pressure and temperature affect concentration.
Dilution in Laboratory Practice
Dilution is arguably the most frequently performed calculation in laboratory science. From preparing reagents for molecular biology experiments to formulating pharmaceutical compounds, the ability to accurately dilute solutions is a fundamental skill. Understanding the principles behind dilution helps prevent costly errors and ensures reproducible results.
In clinical laboratories, dilution is essential for bringing analyte concentrations into the measurable range of instruments. When a patient sample has an analyte concentration above the assay's linear range, the sample must be diluted and re-measured. The reported result is then multiplied by the dilution factor. Errors in dilution calculations can lead to incorrect diagnoses and inappropriate treatment decisions.
In microbiology, serial dilutions are used to enumerate bacteria in a sample. A typical protocol involves making 1:10 serial dilutions and plating each dilution on agar plates. After incubation, colonies are counted on plates with 30-300 colonies, and the original concentration is calculated by multiplying the count by the dilution factor. This technique is fundamental to food safety testing, water quality monitoring, and clinical microbiology.
Pharmaceutical compounding relies heavily on dilution calculations. Pharmacists must accurately dilute stock solutions to prepare patient-specific formulations. The concentration must be precise to ensure therapeutic efficacy without toxicity. Pediatric medications often require dilution of adult formulations, and errors can have serious consequences for vulnerable patients.
In molecular biology, dilution is used to prepare DNA and protein standards for quantification, to adjust primer concentrations for PCR, and to prepare serial dilutions for dose-response curves. Accurate pipetting technique is critical for small-volume dilutions, where even a 1 µL error can significantly affect the final concentration.