🧪 Dilution Calculator (C1V1 = C2V2)
By Shihab Mia · Updated 2026-08-03
This calculator performs the standard C1V1 = C2V2 dilution math for reference and lab-planning purposes only. It is not a substitute for a validated laboratory or clinical dilution protocol, and results should be checked against your institution or manufacturer standard operating procedures before use.
Uses C1V1 = C2V2. Keep concentration and volume units consistent across all four values. This is a general math reference tool for educational and lab-planning purposes, not a substitute for a validated laboratory or clinical protocol.
This dilution calculator solves the C1V1 = C2V2 equation for whichever value you are missing, initial concentration, initial volume, final concentration, or final volume, once you supply the other three. It then turns that answer into a lab-ready instruction: exactly how much diluent to add to your stock solution to hit the target concentration. Whether you are diluting a reagent for an assay, a stock buffer, or a concentrate, the underlying dilution math is always the same. Use this dilution calculator any time you need to double-check dilution math before you pipette, mix, or scale a solution.
What is the Dilution Calculator?
Dilution is the process of lowering the concentration of a solute in a solution, usually by adding more solvent (the diluent) without changing the total amount of solute present. Because the amount of solute stays constant, the product of concentration and volume before dilution equals the product of concentration and volume after dilution. That relationship is written as C1V1 = C2V2, where C1 and V1 are the concentration and volume of the starting (stock) solution, and C2 and V2 are the concentration and volume after dilution. A dilution calculator like this one applies exactly that equation, so it is one of the most-used tools in chemistry, molecular biology, pharmacy and food science, because almost every working solution starts life as a more concentrated stock.
This dilution calculator lets you solve for any one of the four terms as long as you know the other three. Most people use it to find V2, the final volume a stock needs to be brought up to in order to reach a target concentration, or C2, the concentration you end up with after diluting a known volume of stock into a known final volume. It also works in reverse: if you know how concentrated your final solution needs to be and how much of it you must end up with, you can solve for C1 to figure out what strength of stock solution to prepare, or for V1 to figure out how much of an existing stock to measure out.
Once V1 and V2 are both known, the volume of diluent to add is simply V2 minus V1, since the stock volume is already part of the final volume, you are not adding a full V2 worth of solvent on top of it. This is a common source of dilution errors: a '1 to 10 dilution' typically means 1 part stock plus 9 parts diluent to make 10 total parts, not 1 part stock plus 10 parts diluent. Getting the diluent volume right, rather than the total volume, is exactly what this tool is built to make foolproof.
Because this dilution calculator is unit-agnostic, you can work in whatever concentration and volume units your protocol uses, molar, millimolar, percent, milligrams per milliliter, milliliters, liters or microliters, as long as you keep the same unit for concentration on both sides and the same unit for volume on both sides. The tool defaults to millimolar (mM) and milliliters (mL) as example units for a typical dilution, but you can relabel them to match your own workflow without changing how the math works.
When to use it
- Diluting a concentrated stock reagent, dye, or buffer down to a working concentration for an experiment.
- Working out how much diluent to add to a stock solution to reach a target final volume and concentration.
- Planning a serial dilution series and checking the concentration at each step.
- Figuring out what stock concentration to prepare in advance so that a known volume, diluted to a known final volume, lands on the target concentration.
- Scaling a concentrate, such as a cleaning solution, juice concentrate, or fertilizer mix, to a usable strength.
- Double-checking a dilution calculation by hand before pipetting, to catch unit or arithmetic mistakes early.
How to use the Dilution Calculator
- Choose which value you need to solve for: final volume, final concentration, initial volume, or initial concentration.
- Enter the other three known values for concentration and volume. The field you are solving for is locked and fills in automatically.
- Set the concentration unit and volume unit labels if you want something other than the default mM and mL, just keep each unit consistent across both sides of the dilution.
- Read the solved value plus the diluent volume to add, and use the copy button to grab the result for your notes.
Formula & method
Worked examples
You have 5 mL of a 10 mM stock solution and need to dilute it down to 2 mM. How much final volume do you end up with, and how much diluent do you add?
- Identify the knowns: C1 = 10 mM, V1 = 5 mL, C2 = 2 mM. You are solving for V2.
- Apply the formula: V2 = C1V1 / C2
- V2 = (10 mM x 5 mL) / 2 mM = 50 / 2 = 25 mL
- Diluent to add = V2 - V1 = 25 mL - 5 mL = 20 mL
Result: Bring the 5 mL of 10 mM stock up to 25 mL total (by adding 20 mL of diluent) to get a 2 mM solution.
You need 200 mL of a 5 mM working solution, and your protocol calls for using 10 mL of stock to make it. What concentration should the stock be?
- Identify the knowns: C2 = 5 mM, V2 = 200 mL, V1 = 10 mL. You are solving for C1.
- Apply the formula: C1 = C2V2 / V1
- C1 = (5 mM x 200 mL) / 10 mL = 1000 / 10 = 100 mM
Result: Prepare a 100 mM stock solution; 10 mL of it, diluted up to 200 mL, will give you the 5 mM working solution.
Common dilution ratios and the resulting concentration, starting from a 100 mM stock
| Dilution ratio (stock : total) | Dilution factor | Resulting concentration |
|---|---|---|
| 1 : 2 | 2x | 50 mM |
| 1 : 5 | 5x | 20 mM |
| 1 : 10 | 10x | 10 mM |
| 1 : 100 | 100x | 1 mM |
A 10-fold serial dilution series starting from a 1 M stock
| Step | Action | Resulting concentration |
|---|---|---|
| Stock | As prepared | 1 M |
| Dilution 1 | 1 part stock + 9 parts diluent | 100 mM |
| Dilution 2 | 1 part of dilution 1 + 9 parts diluent | 10 mM |
| Dilution 3 | 1 part of dilution 2 + 9 parts diluent | 1 mM |
| Dilution 4 | 1 part of dilution 3 + 9 parts diluent | 0.1 mM |
Common mistakes to avoid
- Adding a full V2 of diluent instead of V2 minus V1. The final volume V2 already includes the stock you started with. If you add a whole new V2 worth of diluent on top of your stock volume, the solution ends up far more dilute than intended. The diluent volume to add is always V2 - V1, not V2.
- Misreading what a "1 to 10 dilution" means. A 1:10 dilution normally means 1 part stock combined with enough diluent to make 10 total parts, which is 1 part stock plus 9 parts diluent, not 1 part stock plus 10 parts diluent. Confusing the ratio notation with the diluent volume is one of the most common dilution mistakes.
- Mixing units on either side of the equation. C1V1 = C2V2 only works cleanly if both concentrations share the same unit and both volumes share the same unit. Mixing milligrams per milliliter with molarity, or milliliters with liters, without converting first, will silently produce a wrong dilution.
- Assuming volumes are perfectly additive for very concentrated solutions. For typical dilute aqueous solutions, mixing V1 of stock with (V2 - V1) of diluent gives a final volume close enough to V2 for lab purposes. For very concentrated solutions, viscous liquids, or mixes with large density differences, actual mixed volume can deviate slightly, so precise work may call for weighing or using volumetric glassware to hit V2 exactly.
Glossary
- Dilution
- Reducing the concentration of a solute in a solution, typically by adding more solvent (diluent) without adding more solute.
- Diluent
- The solvent added to a stock solution during dilution, such as water, saline, or buffer, to lower its concentration.
- Stock solution
- A concentrated solution prepared in advance and later diluted to working concentrations as needed.
- Dilution factor
- The ratio of final volume to initial volume (V2 / V1), showing how many times the original solution has been diluted.
- Serial dilution
- A series of sequential dilutions, each one made from the previous dilution rather than from the original stock, commonly used to create a range of concentrations.
- Molarity (M, mM)
- A common way to express concentration, in moles of solute per liter of solution (M) or millimoles per liter (mM).
Frequently asked questions
What is the dilution formula?
The standard dilution formula is C1V1 = C2V2, where C1 and V1 are the concentration and volume of the starting stock solution, and C2 and V2 are the concentration and volume after dilution. Because the total amount of solute does not change during a simple dilution, this dilution calculator uses that equation to solve for any one of the four values if you know the other three.
How do I calculate how much diluent to add?
Once you know the initial volume (V1) and the final volume (V2) needed to reach your target concentration, the diluent to add is simply V2 - V1. This calculator works that out automatically after solving the dilution equation.
What does a 1:10 dilution mean?
A 1:10 dilution means 1 part of the original solution combined with enough diluent to make a total of 10 parts, which works out to 1 part stock plus 9 parts diluent. The concentration is reduced to one tenth of the original.
Can I use this dilution calculator with any units?
Yes. This dilution calculator is unit-agnostic, so you can use molarity, percent, milligrams per milliliter, or any other concentration unit, and milliliters, liters, or microliters for volume. Just keep the same concentration unit on both sides and the same volume unit on both sides, and relabel the unit fields if you are not using the default mM and mL.
How do you dilute a stock to a lower molarity?
Decide on the target concentration (C2) and the final volume you need (V2), then solve C1V1 = C2V2 for V1, which tells you how much stock to measure out. Bring that volume of stock up to the full final volume V2 with diluent, adding V2 - V1 of diluent.
What is the difference between a single dilution and a serial dilution?
A single dilution takes one stock solution straight to one final concentration in one step. A serial dilution repeats the process, using each diluted solution as the "stock" for the next dilution step, which is an efficient way to produce a range of evenly spaced concentrations, such as the 10-fold dilution series shown in the reference table above.