Dilution Molarity Calculator
Diluting a solution is one of the most common lab tasks in chemistry and biology: you have a concentrated stock and you need a weaker working solution. The math is governed by a single conservation law, the dilution equation M1V1 = M2V2, which says the amount of solute stays the same before and after you add solvent.
The calculator below solves the equation in every direction. Enter any three of the four values and it finds the fourth, then tells you exactly how much solvent to add and the dilution factor. Every result comes with the substitution steps shown, so you can check the working, not just trust a number.
Use the same volume units on both sides (mL with mL, L with L). Leave exactly one field blank: the calculator solves for it and fills it in.
Quick Answer
Key takeaways
- M1V1 = M2V2 is a mole count, not a recipe: the moles of solute before dilution equal the moles after, because only solvent is added.
- Leave exactly one field blank and the calculator solves for it, then fills the answer back into the field so a second run can start from it.
- Final volume and solvent to add are different numbers. In the worked example they are 100 mL and 95 mL, and confusing them is the most common bench error this page exists to prevent.
- Volume units only need to match each other. Millilitres on both sides cancel exactly like litres do, so no conversion is needed.
- Quick Answer
- Using the calculator at the bench, step by step
- The dilution equation, and why it has to be true
- Worked example: 100 mL of 0.5 M from a 10 M stock
- The same equation solved in all four directions
- Serial dilutions: when one step is not enough
- Is this a molarity problem, or a different dilution problem?
- What competing calculators miss
- Frequently Asked Questions
- Add This Calculator to Your Website
Using the calculator at the bench, step by step
Enter three values, leave the unknown blank, and read the solvent line before you touch a pipette. The bench procedure for the worked example runs like this.
Decide the unknown. Most bench questions ask for V1, the stock volume to pipette. Clear that field and enter M1, M2, and V2. Any of the four can be the unknown, but exactly one must be blank.
Calculate and read all three outputs. The headline gives the missing value (V1 = 5.0000), the detail line gives the solvent to add (95.00) and the dilution factor (20.00), and the steps box shows the substitution so a lab partner can check it.
Pipette the stock into the flask first. Put 5 mL of the 10 M stock into a 100 mL volumetric flask that already holds some solvent. For concentrated acids, the rule is absolute: add acid to water, never water to acid.
Bring to volume, do not add a measured 95 mL blindly. The 95 mL figure is the difference V2 minus V1. In a volumetric flask you dilute to the mark, which lands on the correct total even if the volumes are not perfectly additive.
Label with the factor. Write the final molarity and the 1:20 dilution factor on the bottle. The factor is what the next person needs to back-calculate or to repeat the preparation.
The dilution equation, and why it has to be true
Molarity is moles per litre, so molarity times volume in litres is simply moles. Dilution adds solvent and nothing else, which means the mole count cannot change.
That derivation is the whole theory. As OpenStax Chemistry 2e, Section 3.3 Molarity puts it, the two sides can be set equal because the molar amount of solute is unchanged, and the same relation is often written C1V1 = C2V2 for concentration units other than molarity. The Chemistry LibreTexts solution dilution chapter works the identical mole-conservation argument and lands on the same boxed equation. Two conditions hide inside it, and both matter in practice. Volumes are treated as additive, which is an excellent approximation for dilute aqueous work and a poorer one when concentrated acid meets water and the mixture contracts and heats. And nothing may react, precipitate, or evaporate along the way: the equation counts solute, so anything that removes solute from solution breaks it.
Worked example: 100 mL of 0.5 M from a 10 M stock
The calculator is pre-filled with this standard preparation: a 10 M NaOH stock on the shelf, and 100 mL of 0.5 M working solution needed.
| Quantity | Value | How it is reached |
|---|---|---|
| Stock volume V1 | 5.0000 mL | (0.5 x 100) / 10 |
| Solvent to add | 95.00 mL | V2 - V1 = 100 - 5 |
| Dilution factor | 20.00 (1:20.0) | V2 / V1 = 100 / 5 |
| Solute carried over | 0.05 mol | 10 M x 0.005 L = 0.5 M x 0.100 L |
Sanity-check the direction before trusting any dilution result: the final concentration (0.5 M) is below the stock (10 M), the stock volume (5 mL) is below the final volume (100 mL), and the dilution factor (20) equals the concentration ratio 10 / 0.5 as well as the volume ratio 100 / 5. When those three checks agree, the arithmetic is consistent. When one disagrees, a field was almost certainly filled in the wrong position.
The same equation solved in all four directions
Most bench work solves for V1, but the other three directions answer real questions too: identifying an unlabelled stock, predicting the strength of a dilution you already made, and working out how far a small stock aliquot will stretch.
| Solve for | Inputs entered | Calculator result | Bench meaning |
|---|---|---|---|
| V1 | M1 = 10, M2 = 0.5, V2 = 100 | V1 = 5.0000 | How much stock to pipette |
| M2 | M1 = 2, V1 = 100, V2 = 500 | M2 = 0.4000 M | Strength after diluting 100 to 500 |
| M1 | V1 = 250, M2 = 0.1, V2 = 1000 | M1 = 0.4000 M | Strength of the stock you started from |
| V2 | M1 = 6, V1 = 50, M2 = 0.3 | V2 = 1000.0000 | Final volume a 50 unit aliquot makes |
Every row also returns its own solvent volume and dilution factor: 400.00 and 5.00 for the M2 row, 750.00 and 4.00 for the M1 row, and 950.00 and 20.00 for the V2 row. The M1 direction deserves a caution. It reconstructs the stock strength from a dilution you performed, so any measuring error in that dilution lands directly in the inferred M1. For an unlabelled bottle that genuinely matters, titrate instead of back-calculating.
Serial dilutions: when one step is not enough
A single dilution step handles factors up to a few hundred comfortably. Beyond that, the stock volume becomes too small to pipette accurately, so labs chain steps: each dilution becomes the stock for the next.
The calculator handles one step at a time, which matches the bench reality. Run the worked example once and you have 100 mL of 0.5 M. Run it again with that solution as the stock (M1 = 0.5, M2 = 0.025, V2 = 100) and it returns the same 5 mL pipetting step. Two 1:20 steps multiply to a total dilution factor of 400, and 10 M divided by 400 is 0.025 M, which is the concentration after step two. The pattern generalizes: total factor is the product of the step factors, and equal steps keep every pipetting volume in the accurate range of the same pipette. Microbiology and pharmacology dose-response work lives on this pattern, usually in tenfold steps.
Is this a molarity problem, or a different dilution problem?
This page is deliberately narrow: concentrations in molarity, mol/L, on both sides. Nearby problems that sound similar are handled elsewhere on this site, and picking the right one saves a wrong answer.
If your concentrations are not in molarity at all, or the protocol is written as a ratio mix, the broader chemical dilution calculator covers C1V1 = C2V2 in general concentration units and ratio mixes. If you are preparing a solution from a weighed solid rather than from a stock, the starting point is mass percent, which the concentration calculator solves from solute and solution mass. If the question is how much solute volume a target concentration needs, the concentration volume calculator works that side of the preparation. And when a concentrated liquid reagent is labelled by percent and density rather than molarity, the mass-to-volume step runs through the density calculator before any dilution math begins. None of these is a diluted earnings or share problem: the word dilution in a lab means solvent added to a solution, full stop.
What competing calculators miss
The dilution keyword is well served, which makes the remaining gaps specific rather than general.
Miss 1: one-direction tools from authoritative names. The Sigma-Aldrich solution dilution calculator, the reference tool many labs trust, solves only for the volume of stock to add. That is the most common question, but the moment yours is "what did I actually make?" or "how far will this aliquot go?", the official tool cannot answer and this one can, in all four directions.
Miss 2: dilution buried inside general molarity suites. The big concentration suites solve dilution alongside mass, moles, and molar mass, with unit dropdowns on every field. That flexibility invites the classic error of mixing mL and L across the equation. Here there are no unit dropdowns at all, because matched units cancel: the constraint is explained once, in the hint under the fields, instead of being enforced by four menus.
Miss 3: final volume reported, solvent volume left as homework. Textbook treatments and several solver sites stop at the missing variable. The number a person at a bench actually measures second is the solvent, and it is not the final volume. This calculator prints both on separate lines of the same result, with the subtraction shown, every time.
Frequently Asked Questions
M1 x V1 = M2 x V2 states that the moles of solute are the same before and after dilution, because dilution only adds solvent. M1 and V1 describe the stock; M2 and V2 describe the final solution.
The two volumes must use the same unit as each other (both mL or both L), but the molarity units just need to be consistent too (M with M). You never need to convert mL to L as long as both sides match.
The ratio of final volume to initial volume, V2 / V1. A factor of 20 means the stock was diluted 1:20: one part stock brought up to twenty parts total.
Run the calculation once per step. Each step uses the previous step's final solution as its stock, so two 1:20 steps in a row give a total dilution factor of 20 x 20 = 400. Starting from the 10 M stock in the worked example, the first step makes 0.5 M and the second makes 0.025 M. The calculator handles one step at a time, which matches how serial dilutions are actually pipetted.
It assumes volumes are additive and no reaction occurs. Mixing concentrated acid with water, for example, produces less total volume than the sum of parts, and the simple equation becomes approximate. Always add acid to water, never the reverse.
Dilution starts from an existing stock solution and adds solvent. Preparing from solid starts with weighed solute dissolved and brought to volume; that needs a molarity-from-mass calculation instead.
No, and confusing them is the classic lab error. The final volume V2 is the total. The solvent to add is V2 minus the stock volume V1. This calculator reports both, labeled separately.
Add This Calculator to Your Website
References
- OpenStax, Rice University, "Chemistry 2e, Section 3.3 Molarity" - derivation of the dilution equation from mole conservation, including the general C1V1 = C2V2 form. OpenStax: Chemistry 2e, 3.3 Molarity. Accessed October 2026.
- Chemistry LibreTexts, "11.7: Solution Dilution" (CHEM 1010, North Central State College) - stock solutions, volumetric flask procedure, and the boxed M1V1 = M2V2 equation with worked examples. Chemistry LibreTexts: 11.7 Solution Dilution. Accessed October 2026.
- Chemistry LibreTexts, "10.8: Solution Dilution" (Chem 151, College of the Canyons) - the same mole-conservation derivation in a second textbook treatment, used to cross-check the rearrangements. Chemistry LibreTexts: 10.8 Solution Dilution. Accessed October 2026.
- BCcampus Open Publishing, "CHEM 1114: Introduction to Chemistry, Chapter 3.3 Molarity" (Langara College) - molarity definition and the dilution relation M1L1 = M2L2 with the unit-cancellation condition. BCcampus: CHEM 1114, 3.3 Molarity. Accessed October 2026.
- John Wiley and Sons, Chemistry All-in-One For Dummies, "How to Calculate Concentrations When Making Dilutions" - the stock solution workflow and the C1V1 = C2V2 form used with mixed concentration units. For Dummies: How to Calculate Concentrations When Making Dilutions. Accessed October 2026.