Dilution Calculator
Solve C1V1 = C2V2 for any one value and see how much solvent to add.
What this tool does
The dilution equation is C1 × V1 = C2 × V2: the amount of solute stays the same when you add solvent. To make 100 mL of a 2 M solution from a 10 M stock you need V1 = 2 × 100 ÷ 10 = 20 mL of stock and 80 mL of solvent. Choose what to find above and enter the other three values.
Rearranges C1V1 = C2V2 for the unknown value.
Shows the dilution factor and the volume of solvent to add.
How to use it
- Choose which value to find.
- Enter the other three values in consistent units.
- Read the answer and the solvent to add.
- Copy or download the result.
Why use this calculator
Solves C1 × V1 = C2 × V2 for whichever of the four values you do not know, and always shows how much solvent to add. Diluting a stock solution is one of the most common lab tasks, and the arithmetic is easy to get wrong when units differ or the unknown changes. A calculator keeps the units and the dilution factor straight.
Why we built it
We built the dilution calculator to solve C1V1 = C2V2 for any unknown and to refuse an impossible answer. Work out stock strength with the molarity calculator and check acidity with the pH calculator.
Who this tool is for
- Chemistry and biology students
- Lab technicians preparing working solutions
- Anyone diluting a concentrate to a set strength
When to use it
- Preparing working solutions from a stock.
- Making chemical, medical lab or cleaning dilutions.
- Chemistry and biology homework.
- Checking a protocol.
How it works
Because the moles of solute do not change on dilution, C1 × V1 = C2 × V2. Solve for the unknown: V1 = C2V2 ÷ C1, C1 = C2V2 ÷ V1, C2 = C1V1 ÷ V2 and V2 = C1V1 ÷ C2. The solvent to add is V2 − V1, and the dilution factor is C1 ÷ C2. The two concentrations must share a unit and so must the two volumes.
Example: stock 10 M, final 2 M, final volume 100 mL. V1 = 2 × 100 ÷ 10 = 20 mL. Add 80 mL of solvent for a dilution factor of 5.
Add the stock to some solvent and mix, then top up to the final volume. Volumes are only approximately additive, particularly for concentrated solutions. Follow safe lab practice for the chemicals you handle.
A worked example
These are the values the calculator opens with, so you can see exactly what it does with them. Change any value on the page and the result updates; the figures below come from the same calculation.
| Input | Value |
|---|---|
| Find | Volume of stock needed (V1) |
| Stock concentration | 10 |
| Volume of stock | 20 |
| Final concentration | 2 |
| Final volume | 100 |
With those inputs, the calculator returns:
- Volume of stock (V1): 20
- Solvent to add (V2 − V1): 80
- Dilution factor (C1 ÷ C2): 5×
- C1: 10
- V1: 20
- C2: 2
- V2: 100
What you give it, and what you get back
| Item | Details |
|---|---|
| What to find | V1, C1, C2 or V2. |
| The other three values | Concentrations in one unit and volumes in one unit. |
| Output | The solved value, solvent to add, dilution factor and all four values. |
Issues you may run into
| What you see | Why it happens | What to do |
|---|---|---|
| The tool says it is a concentration | The stock volume would be larger than the final volume. | Check that C1 is higher than C2. |
| Different units | The tool does not convert units. | Use mL for both volumes, and the same unit for both concentrations. |
| Serial dilutions | Only one step is calculated. | Run the calculator once for each step. |
Assumptions and limitations
- A single dilution step.
- Assumes volumes are additive.
Frequently asked questions
What is the dilution formula?
C1V1 = C2V2, where C is concentration and V is volume, before (1) and after (2) dilution.
How much solvent do I add?
The final volume minus the stock volume: V2 − V1.
What is the dilution factor?
The stock concentration divided by the final concentration.
Can I use any concentration unit?
Yes, if C1 and C2 use the same unit, such as mol/L, mg/mL or %.
How do I do a serial dilution?
Repeat the calculation for each step, using the previous result as the new stock.
Is my information sent anywhere?
No. The calculation runs in your browser and nothing leaves the page.