A dilution adds solvent to a solution without adding any more solute. The amount of solute stays fixed while the volume grows, and since concentration is just solute divided by volume, the concentration falls in exact proportion to how much the volume rises. That conservation is the entire basis of the dilution equation:
C1 × V1 = C2 × V2
C1 and V1 are the concentration and volume of the stock you start from; C2 and V2 are the concentration and final volume after diluting. Each side of the equation equals an amount of solute (concentration × volume), and since you never added or removed solute, the two sides stay equal. Enter any three values and the calculator solves the fourth. The only judgment you make is which variable you are solving for, usually V1 (the volume of stock to measure). Concentrations can be molar (M, mM, µM), percent (w/v), or mass-per-volume (mg/mL); volumes can be µL, mL, or L, as long as the two concentrations share a unit and the two volumes share a unit.
Spotted a wrong result, broken field, or typo? Tell us below and we’ll fix it fast.Report an issue
Rearranging C1 V1 = C2 V2 for each unknown
Which form you use depends on what you already know:
- V1 = C2V2 ÷ C1: how much stock to measure for a target dilution (the everyday case).
- C2 = C1V1 ÷ V2: the concentration you land at if you dilute a fixed aliquot into a fixed volume.
- V2 = C1V1 ÷ C2: the final volume to dilute a known aliquot into to reach a target concentration.
- C1 = C2V2 ÷ V1: back-calculate an unknown stock strength from a dilution you already made.
The equation does not care which units you use, only that each side is consistent: both concentrations in one unit, both volumes in another. That is why molarity, percent, and mg/mL all obey the same formula. The calculator converts within the molar family (M, mM, µM) for you, but a percent value and a molar value cannot be compared without the solute’s molar mass.
Dilution factor and 1:N ratios
The dilution factor (DF) is how many times more dilute the solution became: DF = C1 ÷ C2 = V2 ÷ V1. A tenfold dilution has DF 10. In lab shorthand a “1:10 dilution” means one part stock made up to ten parts total (1 part stock + 9 parts solvent), which is DF 10. Watch the ambiguity: read as a stock-to-solvent ratio, “1:10” would be 1 part stock to 10 parts solvent, eleven parts total, DF 11. When it matters, say “one in ten” or give the factor outright.
Molarity dilutions (M, mM, µM)
To make 50 mL of 1 mM from a 10 mM stock, solve for V1: V1 = (1 mM × 50 mL) ÷ 10 mM = 5 mL of stock, brought to the mark with about 45 mL of solvent. The dilution factor is 10, matching the tenfold drop from 10 mM to 1 mM. Because the molar units cancel, you can enter the stock in mM and the target in µM and the calculator reconciles them.
Percent and w/v dilutions
Percent solutions follow the same rule, %1 V1 = %2 V2. To make 500 mL of 7% from a 70% stock: V1 = (7 × 500) ÷ 70 = 50 mL of stock plus solvent to 500 mL. One caveat the equation hides: at high concentration, mixing is not perfectly additive (concentrated acids and alcohols contract and give off heat), so add the stock first and bring up to the final volume in graduated glassware rather than assuming 50 mL + 450 mL lands exactly on 500 mL.
Mass-per-volume (mg/mL) dilutions
From a 2 mg/mL stock, making 10 mL of 0.5 mg/mL needs V1 = (0.5 × 10) ÷ 2 = 2.5 mL of stock plus 7.5 mL of diluent (DF 4). Mass-per-volume is the natural unit for proteins, antibiotics, and reagents quoted in mg/mL, and it dilutes linearly as long as the solute stays fully dissolved at the working concentration.
Serial dilutions for very low concentrations
When a single step would force an impractical measurement, dilute in stages, because each step multiplies: three tenfold steps give an overall factor of 10 × 10 × 10 = 1000. Going from 1 M to 1 mM in one shot means pipetting 10 µL into roughly 10 mL, where a 1 µL slip is a 10% error. Three 1:10 steps keep every transfer in the comfortable 1 mL range and reach the same 1 mM with far less error. Mix each stage thoroughly before drawing the next aliquot, or the error compounds down the series.
Dilution ratio reference
| Dilution | Dilution factor | Stock fraction | To make 10 mL |
|---|---|---|---|
| 1:2 | 2 | 50% | 5 mL stock + 5 mL solvent |
| 1:5 | 5 | 20% | 2 mL stock + 8 mL solvent |
| 1:10 | 10 | 10% | 1 mL stock + 9 mL solvent |
| 1:100 | 100 | 1% | 0.1 mL stock + 9.9 mL solvent |
| 1:1000 | 1000 | 0.1% | 10 µL stock + 9.99 mL solvent |
When C1 V1 = C2 V2 stops being accurate
The equation assumes solute is conserved and the solution behaves ideally. That holds for routine aqueous dilutions but loosens when:
- volumes are not additive (concentrated acids, alcohols, high-salt solutions), so the final volume must be measured, not added;
- density shifts, which matters when converting between w/w%, w/v%, and molarity;
- temperature changes the volume between preparation and use.
Prepare to the mark in a volumetric flask, let exothermic mixtures return to room temperature before topping up, and confirm critical solutions with a second method. This is calculation support, not a substitute for your lab’s validated protocol or the reagent’s safety data sheet; when diluting a strong acid, always add acid to water, never the reverse.
Sources
- LibreTexts: Preparing Solutions and Dilutions
- IUPAC Gold Book: concentration and molarity
- Khan Academy: Dilution and concentration
- American Chemical Society: Laboratory Safety
Dilution FAQ
How do you calculate a dilution?
Pick the unknown and rearrange C1V1 = C2V2. For the usual question, how much stock to take, use V1 = C2V2 ÷ C1. Keep both concentrations in one unit and both volumes in another.
What is a dilution factor?
The ratio of starting to final concentration: DF = C1 ÷ C2 = V2 ÷ V1. A “1:10” dilution is DF 10, one part stock made up to ten parts total.
How do you do a serial dilution?
Repeat a fixed-factor step and multiply the factors: five 1:10 steps give 1:100,000. Mix between steps so error does not carry forward.
What does C1V1 = C2V2 mean?
Concentration times volume is the amount of solute. Diluting changes the volume but not that amount, so the product is the same before and after.
Does it handle percent and ppm?
Yes. Any concentration unit works as long as both sides use the same one; percent and ppm slot into the formula exactly like molarity.