Last updated: July 3, 2026
Serial Dilution Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Quick Answer
A serial dilution repeats the same dilution step through a sequence. The per-step dilution factor is (sample volume + diluent volume) / sample volume. The cumulative dilution factor after n equal steps is DF^n, and final concentration is initial concentration divided by that cumulative factor.
For a serial dilution, calculate the dilution factor for one step, raise it to the number of steps, and divide the starting concentration by that total factor. One millilitre plus nine millilitres repeated three times gives a total dilution factor of one thousand.
Key Takeaways
- Per-step dilution factor equals (sample volume + diluent volume) divided by sample volume.
- Total serial dilution factor equals the per-step factor raised to the number of steps.
- Final concentration equals initial concentration divided by the cumulative dilution factor.
- A 1:10 dilution means one part sample in ten total parts, commonly 1 plus 9.
- Mix every tube thoroughly before transferring to the next step.
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
DF_step = (V_sample + V_diluent) / V_sample; DF_total = DF_step^n; C_final = C_initial / DF_total
Where:
- DF_step=Dilution factor per serial step(dimensionless)
- DF_total=Cumulative dilution factor after n steps(dimensionless)
- V_sample=Sample transferred into the next tube(mL or L)
- V_diluent=Diluent added in each tube(mL or L)
- n=Number of serial dilution steps(steps)
- C_i=Initial concentration(any concentration unit)
- C_f=Final concentration(same as C_i)
Worked Examples
Three ten-fold serial dilutions
Transfer 1 mL sample into 9 mL diluent and repeat for three tubes.
- 1Calculate the per-step final volume: 1 mL + 9 mL = 10 mL.
- 2Divide by the transferred sample volume: DF_step = 10 ÷ 1 = 10.
- 3Raise to the number of steps: DF_total = 10^3 = 1000.
Final concentration after four 1:10 steps
Start with 100 µg/mL and make four ten-fold serial dilutions.
- 1Each step is a 1:10 dilution, so DF_step = 10.
- 2Four steps give DF_total = 10^4 = 10000.
- 3Divide the starting concentration: 100 µg/mL ÷ 10000 = 0.01 µg/mL.
Five two-fold serial dilutions
Mix equal volumes of sample and diluent at each step.
- 1Each tube has 1 mL sample plus 1 mL diluent, for 2 mL total.
- 2The per-step dilution factor is 2 ÷ 1 = 2.
- 3After five steps, DF_total = 2^5 = 32.
Introduction
A serial dilution is a stepwise dilution series in which each tube is prepared from the previous tube rather than directly from the original stock. This calculator finds the per-step dilution factor, the cumulative dilution factor, and optional final concentration. Use it with the dilution factor calculator for a single tube and the molarity calculator when your stock is mole-based. The concentration relationship follows standard IUPAC concentration terminology and common laboratory dilution practice described by LibreTexts Chemistry.
What is a serial dilution?
A serial dilution repeats the same dilution operation through a chain of tubes, wells, flasks, or vials. After mixing one tube, a measured sample from it is transferred into fresh diluent to make the next tube. This produces evenly spaced concentration levels for calibration curves, microbiology counts, dose-response experiments, and analytical method checks.
Each step uses the previous tube as its sample.
A 1:10 serial dilution repeated three times gives 1:10, 1:100, and 1:1000 tubes.
The dilution factor grows exponentially with the number of steps.
Mix thoroughly before transferring to the next tube.
Serial dilution formula
The per-step dilution factor is the total volume in the receiving tube divided by the sample volume transferred: DF_step = (sample volume + diluent volume) / sample volume. If the same step is repeated n times, multiply the factors, which is the same as DF_total = DF_step^n. Final concentration is then C_final = C_initial / DF_total.
A 1:10 dilution means one part sample in ten total parts, typically 1 part sample plus 9 parts diluent.
How to calculate serial dilutions step by step
Start with the volume transferred between tubes and the diluent volume in each receiving tube. Calculate the per-step dilution factor from those volumes, raise it to the number of repeated steps, and divide the initial concentration by the cumulative factor when a concentration is needed.
Record sample volume, such as 1 mL.
Record diluent volume, such as 9 mL.
Compute DF_step = (1 + 9) / 1 = 10.
For 4 steps, compute DF_total = 10^4 = 10000.
If the stock is 100 µg/mL, final concentration is 100 / 10000 = 0.01 µg/mL.
Common serial dilution series
Ten-fold and two-fold series are the most common because they are simple to pipette and easy to interpret. The table shows cumulative factors for typical series. For concentration units such as percent solutions, pair this tool with the percent solution calculator.
| Per-step setup | Step DF | After 3 steps | After 5 steps |
|---|---|---|---|
| 1 mL + 9 mL | 10 | 1000 | 100000 |
| 0.1 mL + 0.9 mL | 10 | 1000 | 100000 |
| 1 mL + 1 mL | 2 | 8 | 32 |
| 2 mL + 8 mL | 5 | 125 | 3125 |
Fold dilution notation and 1 in 10 wording
Laboratory protocols may describe a ten-fold dilution as 1:10, 1 in 10, or 10× dilution. These phrases usually mean one volume of sample brought to ten total volumes, not one volume plus ten volumes. In a serial series, the first tube is 1:10, the second is 1:100, and so on when each step is ten-fold.
Write tube labels as both step DF and cumulative DF, for example: Tube 3, 1:10 step, 1:1000 total.
Accuracy and common mistakes
Serial dilution accuracy depends on pipetting, mixing, carryover, and correct notation. Small pipetting errors compound across steps, so use calibrated pipettes, choose volumes large enough for the instrument range, change tips as needed, and vortex or invert each tube before the next transfer. For regulated analytical work, follow method-specific quality practices and reference materials from organizations such as NIST and BIPM.
Do not use diluent volume alone as the denominator.
Do not transfer from an unmixed tube.
Use the same volume units for sample and diluent.
Remember that total dilution factors multiply, not add.
Quick Reference Card
Serial Dilution — Quick Reference
Quick reference • Serial Dilution Calculator
DF_step = (sample + diluent) / sample; DF_total = DF_step^n; C_final = C_initial / DF_totalValid range: Sample volume > 0; diluent volume ≥ 0; steps ≥ 0; initial concentration optional and > 0
Common Values
⚠ Watch Out
- •A 1:10 dilution is one part sample in ten total parts, not one plus ten unless stated.
- •Use the same units for sample and diluent volumes.
- •Total dilution factors multiply across steps; they do not add.
- •Mix thoroughly before removing the aliquot for the next tube.
- •Very small transfers can create large relative pipetting errors.
Pro Tips
- →Pre-label tubes with both step and cumulative dilution factors.
- →Use pipette volumes near the middle of the calibrated range when possible.
- →Change tips between tubes to reduce carryover.
- →Prepare replicate series when quantitation depends on the final tube.
- →Keep concentration units unchanged when dividing by dilution factor.
FAQs
How do I calculate the total dilution factor in a serial dilution?
Calculate the dilution factor for one step, then raise it to the number of steps if every step is the same. For 1 mL sample plus 9 mL diluent, DF_step is 10; after 3 steps, total DF is 10^3 = 1000.
What does a 1:10 serial dilution mean?
A 1:10 dilution means one part sample in ten total parts, commonly prepared as 1 part sample plus 9 parts diluent. Repeating this step creates 1:100, 1:1000, and further cumulative dilutions.
How do I calculate final concentration after serial dilution?
Divide the initial concentration by the cumulative dilution factor. A 100 µg/mL stock after four 1:10 steps has total DF = 10000, so final concentration is 0.01 µg/mL.
Do serial dilution factors add or multiply?
They multiply. Three consecutive 1:10 steps give 10 × 10 × 10 = 1000, not 30.
Can I use litres instead of millilitres?
Yes. The sample and diluent volumes can be in any matching volume unit because the units cancel in the dilution factor.
Why are serial dilutions used instead of one large dilution?
Serial dilutions make very large dilution factors practical with accurate pipetting volumes. They are also useful for preparing evenly spaced standards and countable microbiology plates.