Dilution Factor Calculator
Solve C₁V₁ = C₂V₂ for whichever of the four values you do not know, or switch to Serial Dilution mode to build a complete stepwise dilution table with the stock volume, diluent to add, and running concentration for every tube. Concentration units (M, mM, µM, nM, g/L, mg/mL, %) and volume units (L, mL, µL) are selectable at each field so no manual conversion is needed.
Formula
Worked example
Single dilution: to make 100 mL of 1 mM from a 10 mM stock, V₁ = (1 mM × 100 mL) / 10 mM = 10 mL of stock topped up to 100 mL; dilution factor 10×. Serial dilution: starting at 1 M, a 1:10 series of 5 tubes gives 0.1 M, 10 mM, 1 mM, 0.1 mM, 10 µM in tube 5; cumulative factor 100,000×.
The dilution equation in plain terms
Diluting a solution adds solvent without changing the amount of dissolved solute, so the product of concentration and volume stays the same before and after: C₁V₁ = C₂V₂. Rearranging gives any of the four quantities when the other three are known. This calculator accepts any combination of concentration units (M, mM, µM, nM, g/L, mg/mL, or %) and volume units (L, mL, µL) so you do not have to convert manually before entering values. The ratio relationship means the units cancel, as long as both concentrations share one unit and both volumes share another.
Dilution factor and diluent volume
The dilution factor (DF) is the ratio of the final volume to the stock volume, V₂/V₁, and it equals C₁/C₂. A 10× dilution means the final solution is one tenth as concentrated as the stock. The convention "1:10" can mean one part stock to nine parts diluent (ten parts total, DF = 10) or, in some protocols, one part to ten (eleven total, DF = 11), so always confirm which convention a protocol uses. The diluent volume shown here is V₂ minus V₁, how much solvent to add to the stock to reach the target. Top up to a volumetric mark rather than measuring diluent separately for better accuracy, since volumes are not perfectly additive.
Serial dilutions: building a concentration series
A serial dilution repeats the same dilution step on the product of the previous step, producing a geometric concentration series. Each tube receives a fixed volume transferred from the one before, then diluent is added back to the original tube volume. With a 1:10 factor, five steps cover five orders of magnitude from 1 M down to 10 µM. Serial dilutions are standard in microbiology (counting colony-forming units), pharmacology (dose-response curves), immunology (antibody titrations) and any assay where a wide concentration range must be tested with a single stock. Switch to Serial Dilution mode above to get a full per-tube protocol table with transfer volume, diluent to add, tube concentration and cumulative dilution factor.
Unit conversions and practical tips
Common lab mistakes come from unit mismatches: mixing mM and µM without converting, or confusing mL and µL on a micropipette. Using the unit selectors on each field here eliminates those errors by converting everything to a common basis before calculation. When working with mass-based concentrations (g/L, mg/mL, %) the ratio C₁/C₂ is still dimensionally consistent and the solver works the same way. For very large dilution factors (>1000×), plan to use an intermediate dilution rather than a single step: a 1000× dilution in two 1:31.6 steps or a 1:10 followed by 1:100 is more accurate and reproducible than trying to pipette a very small volume into a large one.
Common dilution notations and factors
| Notation | Stock : Diluent | Total parts | Dilution factor | Strength |
|---|---|---|---|---|
| 1:1 | 1 : 1 | 2 | 2× | 50% |
| 1:4 | 1 : 3 | 4 | 4× | 25% |
| 1:10 | 1 : 9 | 10 | 10× | 10% |
| 1:100 | 1 : 99 | 100 | 100× | 1% |
| 1:1000 | 1 : 999 | 1000 | 1000× | 0.1% |
| 1:10,000 | 1 : 9,999 | 10,000 | 10,000× | 0.01% |
How notation, parts-stock-to-diluent, and dilution factors relate.
Frequently asked questions
What is the difference between a 1:10 dilution and a 10× dilution?
They describe the same result in most conventions. A 1:10 dilution means one part stock plus nine parts diluent for ten parts total, giving a final solution that is one tenth as concentrated, a dilution factor of 10×. Confusion arises when the notation is read as one part stock to ten parts diluent (eleven parts total, DF = 11), so always confirm which convention a protocol uses.
Which concentration and volume units should I use?
Any units work as long as both concentrations share one unit and both volumes share another. The calculator accepts M, mM, µM, nM, g/L, mg/mL, and % for concentration, and L, mL, µL for volume, converting each to a common basis before solving. If your stock is in mM and the final in µM, select those units and the conversion is automatic.
How does a serial dilution work and when should I use it?
In a serial dilution you transfer a fixed volume from one tube to the next and add diluent back to the original tube volume each time. The concentration decreases by the same factor at every step. Use it when you need a geometric concentration series for dose-response curves, antibody titrations, microorganism counting, or any assay that spans several orders of magnitude from a single stock.
Can this calculator handle concentration (making a solution more concentrated)?
Mathematically yes: if you enter a final concentration higher than the stock, the dilution factor falls below 1, which indicates concentration rather than dilution. In practice you cannot concentrate a solution by adding solvent; you would remove solvent or add solute. A factor below 1 usually means your inputs are reversed.
What volume should I transfer in a serial dilution?
Transfer volume equals the tube volume divided by the dilution factor. For a 1 mL tube with a 10× dilution factor, transfer 0.1 mL (100 µL) and add 0.9 mL (900 µL) of diluent. The schedule table in Serial Dilution mode calculates and shows both volumes for every step.
How do I make a very large dilution (1:10,000 or more)?
Very large single-step dilutions are difficult to pipette accurately because the stock volume is very small. Use two or more serial steps instead: for a 1:10,000 dilution, combine a 1:100 step followed by another 1:100 step. The serial dilution mode here can plan that automatically.