How to Use This Dilution Calculator
- Single dilution: fill in three of M1, V1, M2, and V2 and leave the fourth blank. Each value has its own unit, so a 10.0 mL sample diluted to 1.00 L works without converting first.
- Serial dilution: enter the stock concentration, the volume moved at each step, the solvent already in each tube, and the number of steps.
- Significant figures: answers are rounded to the least precise value you typed. A trailing decimal point, as in 250., marks the zeros as significant.
Why M1V1 = M2V2 Works for Dilutions
Adding solvent spreads the same solute through a larger volume. Molarity times volume in liters is moles of solute, and that number does not change, so M1V1 before dilution equals M2V2 after it. The 2026 AP Chemistry exam used exactly this step: 3.00 mL of a solution diluted to 25.0 mL measured 0.055 M, so the original was (0.055 M)(25.0 mL) ÷ 3.00 mL = 0.46 M, worked in the 2026 AP Chemistry FRQ answers. The full method, with more worked problems, is in AP Chemistry dilution calculations, and making a solution from a solid instead is covered in molarity.
M1V1 = M2V2 is only for diluting one solution. When two solutions react, as in a titration, use the mole ratio from the balanced equation instead.
How a Serial Dilution Works
A serial dilution repeats the same dilution several times, each step starting from the solution made in the step before. Moving 1.00 mL into 9.00 mL of solvent gives 10.00 mL total, a 10-fold dilution, so a 1.00 M stock becomes 0.100 M, 0.0100 M, 1.00 × 10−3 M, and 1.00 × 10−4 M after four steps. The concentration after n steps is the stock divided by the step factor raised to the n. Serial dilutions are how labs make the standards for a calibration curve, the kind of graph used with the Beer-Lambert law.
How to Prepare a Dilution in the Lab
- Calculate V1, the volume of stock you need.
- Measure V1 with a volumetric pipet (or buret) and transfer it into a volumetric flask whose volume is V2.
- Add solvent until the bottom of the meniscus reaches the mark, then stopper and invert to mix.
Overshooting the mark leaves the solution more dilute than the calculation assumes, an error AP free-response questions like to ask about. To see how this kind of lab reasoning adds up across the exam, use the AP Chem Score Calculator.
Related Resources
- AP Chem Score Calculator
- All AP Chemistry Calculators
- AP Chemistry Dilution Calculations
- AP Chemistry Molarity
- AP Chemistry Beer-Lambert Law
- Significant Figures Calculator
- Unit 3 Review: Properties of Substances and Mixtures
Frequently Asked Questions
How do you use M1V1 = M2V2?
Enter the concentration and volume of the stock solution (M1 and V1) and of the diluted solution (M2 and V2), leaving out the one you want. Because the moles of solute stay the same when solvent is added, M1 times V1 equals M2 times V2. Diluting 250. mL of 6.00 M HCl to 1.50 M gives V2 = (6.00)(250.) / 1.50 = 1.00 x 10^3 mL, or 1.00 L.
Do the volumes have to be in liters?
No. M1V1 = M2V2 works with any volume unit as long as V1 and V2 use the same one. This calculator converts mixed units (for example, a stock volume in mL and a final volume in L) before solving.
What is a serial dilution?
A series of dilutions in which each new solution is made from the previous one, usually by the same factor each time. Transferring 1.00 mL into 9.00 mL of solvent dilutes by 10 at every step, so four steps take a 1.00 M stock to 1.00 x 10^-4 M.
What is a dilution factor?
The ratio of the final volume to the volume of stock used, V2 / V1, which equals the ratio of concentrations M1 / M2. A 10-fold dilution makes the solution one-tenth as concentrated.
How much water do I add to dilute a solution?
Measure the stock volume V1 into a volumetric flask of volume V2 and add water up to the mark. For dilute aqueous solutions the water added is close to V2 minus V1, but filling to the mark is what makes the final volume exact.
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