Dilution Calculator
Enter 3 known values to calculate the 4th unknown variable using the $C_1V_1 = C_2V_2$ formula.
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menu_book The Complete Guide to Laboratory Dilutions
Dilution is the fundamental laboratory process of decreasing the concentration of a solute in a solution, typically by mixing it with an inert solvent (such as distilled water, PBS, or cell culture media). The core scientific principle behind dilution is the Conservation of Mass: adding more solvent increases the total volume and decreases the overall concentration, but the absolute number of solute molecules remains strictly constant.
The Universal Equation: $C_1V_1 = C_2V_2$
Whether you are preparing a drug treatment, diluting antibodies for Western blotting, or making standard curves for an ELISA, this formula is your primary tool. (Note: Often written as $M_1V_1 = M_2V_2$ when dealing with Molarity).
- C₁ (or M₁): Initial Concentration of the Stock Solution
- V₁: Volume of the Stock Solution required
- C₂ (or M₂): Desired Final Concentration
- V₂: Final Total Volume of the working solution
warning Critical Benchwork Tip: V₂ vs. Added Solvent
A very common mistake among junior researchers is confusing the Final Volume ($V_2$) with the amount of solvent (e.g., water) to add.
If you calculate that you need $V_1 = 10 \text{ mL}$ of stock to make a $V_2 = 100 \text{ mL}$ final solution, you DO NOT add 100 mL of water to the 10 mL of stock. You must add exactly 90 mL of solvent ($V_2 - V_1$) to reach the final 100 mL target. Our calculator automatically displays the precise amount of solvent to add to prevent this error.
Frequently Asked Questions (FAQ)
What is the difference between C₁V₁ = C₂V₂ and M₁V₁ = M₂V₂?
They are exactly the same formula. M stands for Molarity (a specific type of concentration), while C stands for Concentration (a more general term). You can use this formula for any unit of concentration (e.g., mg/mL, %, or X-fold) as long as you keep the units consistent on both sides of the equation.