Dilution Calculator (C1V1 = C2V2)

How to Use the Dilution Calculator

The Dilution Calculator solves the fundamental dilution equation C1V1 = C2V2 for any unknown variable. This equation is one of the most frequently used formulas in chemistry and biology laboratories, allowing scientists and students to determine how much stock solution and solvent are needed to prepare a diluted solution at a specific concentration and volume.

Understanding the Dilution Equation

The formula C1V1 = C2V2 expresses the conservation of solute during dilution. C1 represents the initial (stock) concentration, V1 is the volume of stock solution needed, C2 is the desired final concentration, and V2 is the desired final volume. Because no solute is added or removed during dilution, the amount of solute before dilution (C1 times V1) must equal the amount after dilution (C2 times V2). For example, to dilute a 5 M NaCl stock to make 500 mL of a 0.5 M solution: V1 = (0.5 M times 500 mL) / 5 M = 50 mL. You would take 50 mL of stock and add 450 mL of water.

How to Use the Calculator

Select which variable you want to solve for using the radio buttons at the top: C1, V1, C2, or V2. Enter the three known values in the input fields. Choose matching units for concentration (M, mM, %, g/L, mg/mL, or x) and volume (mL, L, or microliters). Leave the field for the unknown variable blank. Click Calculate Dilution to see the result, the formula with your values substituted in, and the volume of solvent you need to add.

Serial Dilutions

A serial dilution is a stepwise series of dilutions where each dilution uses the previous one as the stock solution. This technique is commonly used in microbiology for plating, in immunology for antibody titrations, and in pharmacology for dose-response curves. A typical 1:10 serial dilution takes 1 part solution and adds 9 parts solvent. After three steps of 1:10 dilution, the overall dilution factor is 1:1000. You can use this calculator for each individual step of a serial dilution by entering the concentration and volume from the previous step as C1 and adjusting C2 or V2 for the next step.

Practical Laboratory Examples

Preparing buffer solutions: A 10x PBS stock at 1.37 M NaCl needs to be diluted to 1x (0.137 M). Using C1V1 = C2V2 with C1 = 10x, C2 = 1x, and V2 = 1000 mL gives V1 = 100 mL. Take 100 mL of 10x stock and add 900 mL of water. For cell culture media, you might dilute a 100x antibiotic stock: to prepare 50 mL of media with 1x antibiotic, take 0.5 mL of stock and add it to 49.5 mL of media.

Important Considerations

Always use the same concentration units on both sides of the equation and the same volume units on both sides. The equation assumes ideal dilution behavior and no volume change upon mixing, which is a good approximation for dilute aqueous solutions. For highly concentrated solutions or organic solvents, volumes may not be strictly additive. The dilution equation does not apply when chemical reactions occur upon mixing or when you are mixing two solutions of different solutes.

Frequently Asked Questions

Q: When does the C1V1 = C2V2 equation apply?

A: The C1V1 = C2V2 dilution equation applies when you are diluting a solution by adding solvent (usually water) without any chemical reaction occurring. It works for any units of concentration and volume as long as you use the same units on both sides. The equation assumes the solute amount stays constant and only the total volume changes. It does not apply to mixing two solutions of different solutes or to reactions that change the solute.

Q: How do I perform a serial dilution?

A: A serial dilution is a series of stepwise dilutions where the diluted solution from one step becomes the stock for the next. For example, a 1:10 serial dilution takes 1 mL of solution and adds 9 mL of solvent to make 10 mL total. Repeating this three times gives dilution factors of 1/10, 1/100, and 1/1000. Use C1V1 = C2V2 at each step, where C1 and V1 are the concentration and volume taken from the previous dilution, and C2 and V2 are the new concentration and total volume.

Q: Do the units have to match when using C1V1 = C2V2?

A: Yes. The concentration units for C1 and C2 must be the same (both in M, mM, %, g/L, etc.), and the volume units for V1 and V2 must also match (both in mL, L, or microliters). If your units differ, convert them first before plugging values into the equation. The calculator handles this automatically when you select matching units from the dropdowns.