A dilution factor tells you how many times a sample has been diluted. If 1 mL of sample is made up to 10 mL, every component is ten times less concentrated and the dilution factor is 10, written 1:10, 1/10 or 10⁻¹. Microbiologists, analytical chemists and clinical labs use dilution factors constantly – to bring a sample into the range of an instrument, to make countable plates, or to report the concentration of the original sample.
There are two ways of writing the ratio and confusing them is the most common error. The stock-to-total ratio (S:T) compares the sample with the final volume; this is the dilution factor itself. The stock-to-diluent ratio (S:D) compares the sample with the solvent added, so S:T = 1:10 corresponds to S:D = 1:9. Recipes on product labels (1 part concentrate to 9 parts water) usually mean S:D, while lab protocols almost always mean S:T.
When one dilution is not enough, a serial dilution repeats the same step several times; the overall factor is the step factor raised to the number of steps, so three 1:10 steps give 1:1,000.
How to use the Dilution Factor Calculator
- I know
- Stock (sample) volume
- Diluent volume
- Final (total) volume
- Dilution factor (stock : total = 1 : DF)
- Number of identical serial dilution steps
- Stock concentration (optional)
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose which two quantities you know. The calculator fills in the third volume using V_total = V_stock + V_diluent, computes the dilution factor V_total / V_stock, writes both ratio forms and the exponent, multiplies the factor over the number of serial steps and, if you enter the stock concentration, gives the final concentration.
Worked example
10 mL of a 2 M stock is mixed with 90 mL of water. The total volume is 100 mL, so DF = 100 / 10 = 10, S:T = 1:10, S:D = 1:9 and the exponent form is 10⁻¹. The diluted solution is 2 / 10 = 0.2 M.
If you repeat the same step three times (10 mL of each dilution into 90 mL of water), the overall factor is 10³ = 1,000 and the final concentration is 2 / 1,000 = 0.002 M (2 mM).
S:T and S:D side by side
| Dilution factor | S:T | S:D | Example volumes |
|---|---|---|---|
| 2 | 1:2 | 1:1 | 50 mL + 50 mL |
| 5 | 1:5 | 1:4 | 20 mL + 80 mL |
| 10 | 1:10 | 1:9 | 10 mL + 90 mL |
| 20 | 1:20 | 1:19 | 5 mL + 95 mL |
| 100 | 1:100 | 1:99 | 1 mL + 99 mL |
| 1,000 | 1:1,000 | 1:999 | 0.1 mL + 99.9 mL |
Tips
- Use the final volume of the solution, not the volume of solvent added, for molarity.
- For dilutions, C₁V₁ = C₂V₂ only holds when both concentrations use the same unit.
- Add acid to water, never water to acid.
- Everything is calculated in your browser.
Common mistakes to avoid
- Mixing w/w, w/v and v/v percentages.
- Forgetting that pH is logarithmic – one unit is a tenfold change in [H⁺].
- Using pKa where Ka is asked for (or the other way round).
Inputs explained
| Field | What to enter |
|---|---|
| I know | Choose one: Stock volume and diluent volume, Stock volume and final (total) volume, Stock volume and the dilution factor, Final volume and the dilution factor |
| Stock (sample) volume | Units: mL, L, µL, cm³, m³, fl oz (US) … |
| Diluent volume | Units: mL, L, µL, cm³, m³, fl oz (US) … |
| Final (total) volume | Units: mL, L, µL, cm³, m³, fl oz (US) … |
| Dilution factor (stock : total = 1 : DF) | A number |
| Number of identical serial dilution steps | A number |
| Stock concentration (optional) | Units: mol/L (M), mmol/L (mM), µmol/L (µM), nmol/L (nM), mol/m³ |
What each result means
- Diluent volume per step = [Total volume per step] – [Stock volume per step]
- Dilution factor per step = [Total volume per step]÷[Stock volume per step]
- Stock : total ratio (S:T = 1 : x) = [Total volume per step]÷[Stock volume per step]
- Stock : diluent ratio (S:D = 1 : x) = ([Total volume per step] – [Stock volume per step])÷[Stock volume per step]
- Exponent form (10ˣ) = log10([Stock volume per step]÷[Total volume per step])
- Overall dilution factor after all steps = ([Total volume per step]÷[Stock volume per step])^[Number of identical serial dilution steps]
- Final concentration = [Stock concentration (optional)]÷([Total volume per step]÷[Stock volume per step])^[Number of identical serial dilution steps]
Formula
Dilution factor DF = V_total ÷ V_stock · S:T = 1 : DF · S:D = 1 : (DF − 1) · V_total = V_stock + V_diluent · serial: DF_total = DFⁿ · C_final = C_stock ÷ DF_totalWorked example
Inputs — I know: Stock volume and diluent volume; Stock (sample) volume: 10 mL; Diluent volume: 90 mL; Number of identical serial dilution steps: 1; Stock concentration (optional): 1 mol/L (M).
Results — Stock volume per step = 10 mL; Total volume per step = 100 mL; Diluent volume per step = 90 mL; Dilution factor per step = 10; Stock : total ratio (S:T = 1 : x) = 10; Stock : diluent ratio (S:D = 1 : x) = 9; Exponent form (10ˣ) = -1; Overall dilution factor after all steps = 10; Final concentration = 0.1 mol/L (M); Check = Valid dilution.
Key terms
- Stock (aliquot)
- The portion of the original sample that is diluted.
- Diluent
- The solvent added, often water or buffer.
- S:T ratio
- Stock to total volume; equals 1 : dilution factor.
- S:D ratio
- Stock to diluent volume; equals 1 : (dilution factor − 1).
- Serial dilution
- A sequence of dilutions where each step uses the previous dilution as its stock.
Frequently asked questions
What is a dilution factor?
The ratio of the final volume to the volume of sample: DF = V_total / V_stock. 1 mL made up to 10 mL has DF = 10 (1:10).
What does a 1:20 dilution mean?
In lab usage, 1 part sample in 20 parts total – 1 part sample plus 19 parts diluent. On many product labels "1:20" means 1 part to 20 parts water (21 parts total), so check which convention is meant.
How do I make a 1:10 dilution?
Mix 1 volume of stock with 9 volumes of diluent, e.g. 1 mL of sample + 9 mL of water, or 10 mL + 90 mL.
How do I calculate a serial dilution?
Multiply the factors of the steps. Three 1:10 steps give 10 × 10 × 10 = 1,000 (10⁻³); 1:2, 1:5 and 1:10 together give 100.
How do I get the original concentration back?
Multiply the measured concentration by the overall dilution factor. A reading of 0.25 mg/L after a 1:200 dilution means 50 mg/L in the original sample.
What is the difference between dilution factor and dilution ratio?
The dilution factor (S:T) counts the total volume; a dilution ratio as written on cleaning or drink labels often counts only the added water (S:D). A 1:9 S:D ratio is a dilution factor of 10.
Why write dilutions as powers of ten?
In microbiology plate counts, dilutions are often decimal steps written as 10⁻¹, 10⁻², 10⁻³…, which makes it easy to multiply colony counts back to the original sample.