Dilution Calculator for C₁V₁ = C₂V₂
This dilution calculator works out the volumes and concentrations you need to prepare a diluted solution, using the standard equation C₁V₁ = C₂V₂. Enter the values you know, and it solves for the one you don't — perfect for lab benchwork, classroom problems, and quick stock-to-working-solution math.
The Simple Dilution tab solves for any single variable (C₁, V₁, C₂, or V₂) and draws a beaker diagram of the result. The Serial Dilution tab builds a full step-by-step dilution series with transfer and diluent volumes for each tube.
Understanding the C₁V₁ = C₂V₂ Formula
The dilution equation says the amount of solute stays the same before and after you add diluent — only the concentration changes. The four variables are:
C₁ — Initial concentration
The concentration of your stock solution before dilution.
V₁ — Initial volume
The volume of stock solution you need to take.
C₂ — Final concentration
The concentration you want the diluted solution to have.
V₂ — Final volume
The total volume of diluted solution you want to make.
The relationship holds as long as C₁ and C₂ use the same unit type — for example both in molarity or both in percentage. The calculator checks this for you and warns when the units are incompatible.
How to Use the Dilution Calculator
Simple Dilution
Choose what to solve for
Under Solve for, click one of the four buttons — C₁, V₁, C₂, or V₂. That field is left blank for the calculator to fill in.
Enter the three known values
Type the other three values and pick a unit for each. Concentration supports M, mM, µM, nM, % (w/v), % (v/v), ppm, and ppb; volume supports L, mL, and µL.
Calculate
Click Calculate or press Enter in any field. The unknown value appears with its unit, along with the full C₁ × V₁ = C₂ × V₂ line and a beaker diagram of the stock and diluted solutions.
Serial Dilution
Open the Serial Dilution tab
Switch to Serial Dilution and enter the initial concentration of your stock solution with its unit.
Set factor, steps, and volume
Set the dilution factor (1 : N, for example 1 : 10 for a 10-fold dilution), the number of steps (1 to 20), and the total volume per tube.
Read the series
Click Calculate to see a pipeline of test tubes plus a table giving the concentration, transfer volume, and diluent volume for every step.
Features
Solve for Any Variable
Find C₁, V₁, C₂, or V₂ from the C₁V₁ = C₂V₂ equation — just pick the unknown and enter the other three.
Many Concentration Units
Work in M, mM, µM, nM, % (w/v), % (v/v), ppm, or ppb, with conversions handled automatically.
Flexible Volume Units
Enter and read volumes in litres, millilitres, or microlitres without doing the math yourself.
Beaker Diagram
Each simple dilution shows stock and diluted beakers whose fill and opacity reflect the relative concentrations.
Serial Dilution Builder
Generate a multi-step series from your starting concentration, dilution factor, and number of steps.
Step-by-Step Table
See the concentration, transfer volume, and diluent volume for every tube, alongside a tube pipeline diagram.
Unit Compatibility Check
The calculator warns you if C₁ and C₂ use mismatched unit types, so results stay correct.
Calculation History
Your recent simple dilutions are saved locally and listed below the result, with a button to clear them.
Enter to Calculate
Press Enter in any input field to run the calculation instead of reaching for the button.
Frequently Asked Questions
What does C₁V₁ = C₂V₂ mean?
It states that the amount of solute stays constant during dilution. The initial concentration times the initial volume (C₁ × V₁) equals the final concentration times the final volume (C₂ × V₂). It is the most common formula for preparing diluted solutions from a stock.
How do I use the dilution calculator?
On the Simple Dilution tab, pick which variable to solve for (C₁, V₁, C₂, or V₂), enter the three values you know with their units, and click Calculate or press Enter. The calculator fills in the missing value and draws a beaker diagram of the dilution.
How do I calculate the dilution factor?
The dilution factor is how many times the concentration is reduced. A 1 : 10 factor means a 10-fold dilution. In the Serial Dilution tab you set this factor directly; each step then transfers a volume equal to the total tube volume divided by the factor, with the rest made up of diluent.
Why must C₂ be lower than C₁?
Dilution can only reduce concentration, so the final concentration C₂ is always lower than the stock concentration C₁. If you ask the calculator to solve for a volume that would require concentrating the solution instead, it flags the result as invalid.
What is a serial dilution?
A serial dilution is a chain of sequential dilutions where each tube uses the previous one as its source. A 1 : 10 serial dilution lowers the concentration 10-fold at every step. It is widely used to build a range of concentrations for dose-response curves, microbial counts, and standard curves.
Can I mix mol/L and mg/mL or ppm units?
C₁ and C₂ must use the same unit type — for example both molarity (M, mM, µM, nM) or both a percentage. Mixing different types such as M with ppm would give the wrong answer, so the calculator shows a warning instead of a result when the units are incompatible.
Is my data saved or sent anywhere?
No. Every calculation runs in your browser, and your simple-dilution history is stored only in this browser's local storage. Nothing is sent to a server, and you can clear the history at any time with the delete button.
No comments yet. Be the first to comment!