Solution Dilution Calculator (C1V1 = C2V2)
Enter any three of the four dilution variables and this calculator solves for the fourth using C1V1 = C2V2. Choose your solve target, pick concentration and volume units, and get the answer with full step-by-step working. Useful for preparing buffer solutions, serial dilutions, drug dosing in cell culture, and any bench chemistry task that requires diluting a stock solution.
Formula
Worked example
Stock: 1 mM, want 100 uM in 50 mL. V1 = (100 uM x 50 mL) / 1000 uM = 5 mL. Take 5 mL of stock and add 45 mL of solvent to reach 50 mL total. Dilution factor = 1000 / 100 = 10 (a 1:10 dilution).
What is the dilution equation and why does it work?
The equation C1V1 = C2V2 (also written M1V1 = M2V2 for molarity) states that the total moles of solute are conserved when you dilute a solution. Concentration times volume gives moles: if you take V1 millilitres of a stock at concentration C1, dissolve it into more solvent so the total volume is V2, the number of moles has not changed, so C2 = C1 x V1 / V2. This simple conservation law applies equally to molar concentrations (M, mM, uM, nM, pM, fM), percent concentrations (w/v, v/v), and even ratios or arbitrary units as long as C1 and C2 share the same unit. The key constraint is that C2 can never be greater than C1: you can only dilute down, not concentrate up.
How to use this calculator
Select which of the four variables you want to solve for from the "Solve for" dropdown, then enter the other three values. Choose matching concentration units (C1 and C2 must use the same unit) and volume units (V1 and V2 must use the same unit). The result updates instantly and includes the dilution factor, the dilution ratio (1:N), the percentage of the final volume that comes from your stock, and the volume of solvent to add. The step-by-step panel shows exactly how the arithmetic was performed so you can check your working at a glance. Use the chart to see how concentration falls as you add more diluent - useful for planning serial dilutions.
Serial dilutions and when to use them
When the required dilution factor is large (100-fold or more), a single pipetting step introduces significant relative error because the stock volume is tiny compared to the total volume. For example, a 1:1000 dilution requires taking only 1 uL from a 1 mL final volume - within the dead volume and accuracy limit of most pipettes. A better approach is to perform two or three serial dilutions: a 1:10 followed by another 1:10 (and again) gives 1:1000 overall, but each individual step involves volumes that are easy to measure accurately. To chain dilutions, apply C1V1 = C2V2 at each stage: the output concentration of stage 1 becomes the input concentration for stage 2.
Common dilution examples in the lab
Buffer preparation: if you make a 10x PBS stock (e.g. 1.37 M NaCl) and want 500 mL of 1x working solution, take 50 mL of stock and add 450 mL of water. Cell culture media: a 100x antibiotic stock added at 1% (v/v) to culture media is a 1:100 dilution; take 1 mL of stock per 99 mL of media. Drug dosing: a 10 mM DMSO stock of a compound diluted to 10 uM in assay buffer requires a 1000-fold dilution; perform it in two steps (1:100 intermediate, then 1:10 final) for accuracy. Bradford assay standard curve: a 1 mg/mL BSA stock is serially diluted to give 0.125, 0.25, 0.5, and 1 mg/mL standards by successive twofold dilutions.
Common dilution factors and preparation steps
| Dilution factor | Ratio | Stock fraction | Preparation method |
|---|---|---|---|
| 2 | 1:2 | 50% | Mix 1 part stock with 1 part solvent |
| 5 | 1:5 | 20% | Mix 1 part stock with 4 parts solvent |
| 10 | 1:10 | 10% | Mix 1 part stock with 9 parts solvent |
| 100 | 1:100 | 1% | One-step (1+99) or serial: 1:10 then 1:10 |
| 1000 | 1:1000 | 0.1% | Serial: 1:10 three times, or 1:100 then 1:10 |
| 10000 | 1:10,000 | 0.01% | Serial: 1:100 twice, or 1:10 four times |
For each dilution factor, the stock fraction and a recommended preparation method.
Frequently asked questions
What is the C1V1 = C2V2 equation?
C1V1 = C2V2 is the dilution equation. It states that the amount of solute (moles or mass) is the same before and after you dilute a solution: the starting concentration (C1) times the starting volume (V1) equals the final concentration (C2) times the final volume (V2). You can rearrange it to solve for whichever variable is unknown. C1 and C2 must be in the same concentration unit; V1 and V2 must be in the same volume unit.
Can C2 be greater than C1?
No. Dilution only reduces concentration by adding more solvent. C2 must always be less than or equal to C1. If you need to increase concentration, you must use a different process such as evaporation, lyophilisation (freeze-drying), or preparing a fresh stock at a higher concentration.
What is the dilution factor?
The dilution factor (DF) is the ratio C1 / C2, or equivalently V2 / V1. It tells you how many times the solution has been diluted. A dilution factor of 10 (written 1:10) means the final concentration is one-tenth of the original. To get the final concentration from the dilution factor, divide the stock concentration by DF.
What is a serial dilution?
A serial dilution is a sequence of successive dilutions, each using the previous solution as the new stock. For example, three 1:10 dilutions in series give a total of 1:1000 (10 x 10 x 10). Serial dilutions are preferred when the required dilution factor is large (100 or more) because individual steps involve volumes that are easier to measure accurately than a single very small stock aliquot.
Does C1V1 = C2V2 work for percent concentrations?
Yes, as long as C1 and C2 are both in the same percent unit (both % w/v or both % v/v). The equation is unit-agnostic: it requires only that both concentrations are expressed in the same way. It does not apply directly when mixing two solutions of the same solute to reach a target concentration; for that you need the mixing equation: (C1 x V1 + C2 x V2) / (V1 + V2) = Cfinal.
How do I account for the solute volume when making a dilution?
For most aqueous dilutions at low concentrations, the volume of solute added is negligible and the equation C1V1 = C2V2 is exact. At high concentrations or when working with solutes that have significant density (such as glycerol or concentrated acids), the contribution of the solute to the total volume matters. In those cases, prepare by adding the calculated stock volume to a small amount of solvent in a volumetric flask, then bring to the final mark with more solvent.
Why does my result seem too small to pipette accurately?
If the required stock volume (V1) is very small relative to V2 - for example, 0.5 uL into 1 mL - pipetting error will be proportionally large. Consider making an intermediate dilution first, or using a more concentrated stock solution so that the required V1 becomes a more practical volume (ideally at least 2-5% of V2 for good accuracy).