Dilution Equation Calculator
Use the standard formula C1V1 = C2V2. Enter any 3 values, leave the unknown field blank, then click calculate.
Important: concentration units must be consistent (e.g., both in mg/mL), and volume units must match (e.g., both in mL).
What Is the Dilution Equation?
The dilution equation is one of the most widely used formulas in chemistry, biology, medicine, and laboratory workflows. It is written as C1V1 = C2V2 and helps you determine how to prepare a solution of a lower concentration from a more concentrated stock.
In plain language, the equation says: the amount of solute before dilution equals the amount of solute after dilution. You add solvent (such as water or buffer), but the total quantity of dissolved material stays the same.
Variable Definitions
- C1: concentration of the starting (stock) solution
- V1: volume of stock solution you need to use
- C2: target (final) concentration after dilution
- V2: final total volume after adding diluent
How to Use This Calculator Correctly
This calculator is designed to solve for one missing variable. For accurate results:
- Enter exactly three known values.
- Leave only one field blank.
- Use positive numbers (no zero or negatives).
- Keep units consistent within concentration and volume categories.
If the final volume is larger than your stock volume, the difference (V2 - V1) is the amount of diluent to add.
Worked Examples
Example 1: Find Stock Volume (V1)
You have a 100 mg/mL stock and want 500 mL of 10 mg/mL solution.
Rearrange the equation:
V1 = (C2 × V2) / C1 = (10 × 500) / 100 = 50 mL
So you need 50 mL stock, then add diluent up to 500 mL total.
Example 2: Find Final Concentration (C2)
If you dilute 25 mL of a 2 M solution to a final volume of 200 mL:
C2 = (C1 × V1) / V2 = (2 × 25) / 200 = 0.25 M
Example 3: Find Final Volume (V2)
You use 4 mL of a 5% solution and want a final concentration of 1%:
V2 = (C1 × V1) / C2 = (5 × 4) / 1 = 20 mL
This means add enough solvent to bring the total to 20 mL.
Common Mistakes to Avoid
- Mixing unit systems: mL in one term and L in another without conversion.
- Using percentages incorrectly: 10% and 5% can be used directly if both are percent units of the same type.
- Forgetting that V2 is total volume: it includes stock + added solvent.
- Rounding too early: keep extra decimal places until the final step.
Lab and Practical Tips
- Label prepared solutions with concentration, date, and initials.
- Use calibrated pipettes and volumetric flasks for better accuracy.
- Prepare slightly more volume than required to account for handling loss.
- For serial dilutions, compute each step carefully and document every transfer.
Frequently Asked Questions
Can I use this for serial dilutions?
Yes. Use the calculator step-by-step for each dilution stage. The output of one step becomes the input for the next.
Can concentrations be in different units?
They can, but you must convert them before calculation. For example, convert mg/mL and g/L into matching units first.
What if all four values are already known?
This tool is intended to solve one unknown value. If all fields are filled, clear one field to calculate and verify your setup.
Bottom Line
The dilution equation is simple but incredibly powerful. Whether you are preparing buffers, reagents, standards, or dosing solutions, using C1V1 = C2V2 correctly helps you save time, reduce errors, and improve reproducibility.