Six-point microbial dilution
A 10 mM tracer with 100 uL into 900 uL for six steps reaches 0.00001 mM and cumulative DF 1,000,000 while retaining 800 uL after a 100 uL assay draw and next transfer.
Chemistry and laboratory planning
Dilution Lab Table Calculator
Build a row-by-row constant-ratio serial dilution table with tube concentration, cumulative dilution factor, diluent demand, and usable residual volume.
Chemistry / laboratory workflow
Plan every transfer in a serial dilution run
This calculator turns one repeated transfer rule into a tube-by-tube protocol. Unlike a one-step dilution, it tracks cumulative concentration and verifies that assay withdrawal still leaves enough liquid for the next transfer.
Per-step dilution-
Final concentration-
Cumulative dilution-
Total fresh diluent-
Residual per tube-
LIVE CURRENT-VALUE ANALYSIS
Serial tube concentration trajectory
Each current tube is drawn on a logarithmic concentration scale, with cumulative factor and concentration labels generated from the exact table rows.
| Tube | Transfer in (uL) | Diluent (uL) | Mixed volume (uL) | Concentration (mM) | Cumulative DF | Residual after removals (uL) |
|---|
DETAILED CALCULATION PROCESS
Formula, units, current substitution, and reconciliation
1. Governing relation
f = Vtransfer / (Vtransfer + Vdiluent); ci = c0 f^i; DFi = f^(-i)
Each tube receives a fresh diluent volume and one transfer from the previous tube. The model assumes complete mixing before the next transfer and identical nominal volumes at every step.
2. Symbols and default basis
| Symbol | Meaning | Unit | Default basis |
|---|---|---|---|
| c0 | Starting concentration | mM | 10 |
| Vt | Transfer volume | uL | 100 |
| Vd | Fresh diluent | uL | 900 |
| f | Concentration fraction retained each step | dimensionless | 0.1 |
| i | Tube or dilution step | integer | 1 to 6 |
| DFi | Cumulative dilution factor | dimensionless | 10^i |
3. Unit normalization
- Transfer and diluent volumes are both in uL, so their ratio is dimensionless.
- The starting and all tube concentrations remain in mM.
- 10 nM equals 0.00001 mM; the table retains mM to preserve one consistent calculation unit.
4. Current numerical substitution
5. Independent reconciliation
HOW TO USE THIS CALCULATOR
Lay out a constant-ratio serial dilution tube by tube
- Choose a transfer volume that is reliable for the available pipette.
- Choose fresh diluent so the per-step factor spans the required range without excessive steps.
- Enter the number of receiving tubes and any assay withdrawal taken from each.
- Review every row, especially residual volume before executing the physical transfer sequence.
- Label tubes in advance and export the table with pipette, mixing, and timing records.
CHEMISTRY FOUNDATIONS
How transfer volume compounds into cumulative dilution
- Serial errors accumulate
- Every transfer and mixing error propagates into all downstream tubes.
- The ratio uses mixed volume
- The concentration fraction is transfer divided by transfer plus fresh diluent.
- Cumulative dilution is multiplicative
- Six tenfold steps produce 10^6, not a sixtyfold dilution.
- Mix before transfer
- Without complete mixing, the next aliquot does not represent the calculated concentration.
- Residual volume is a workflow constraint
- A mathematically valid ratio can still fail if transfers and assay withdrawals exhaust a tube.
DEEP ANALYSIS 1
Selecting the number of steps
Use fewer steps with larger factors to reduce handling, but avoid aliquots outside calibrated ranges. More steps improve operational scale at the cost of accumulated uncertainty.
DEEP ANALYSIS 2
Log scale is the honest visual
Serial concentrations often span orders of magnitude. The tube graphic uses log position so late tubes remain distinguishable rather than collapsing to zero.
DEEP ANALYSIS 3
Why downstream replicates are correlated
All tubes share upstream preparation errors. Replicates drawn from one chain are not independent preparation replicates.
RESULT INTERPRETATION
Read concentration and usable residual volume together
Final concentration is a nominal endpoint based on exact transfer ratios; it is not an assay of the last tube.
Residual volume is the post-transfer, post-assay amount available in each intermediate tube under the repeated workflow.
REAL USE CASES
A routine dilution series and a residual-volume failure
Twofold assay plate series
A 100 uL transfer into 100 uL diluent yields a twofold series. If 120 uL is also withdrawn before the next transfer, the protocol is invalid because only 100 uL would remain after transfer.
EVIDENCE AND DATA QUALITY
Keep the tube map, pipette record, and transfer order
Retain tube map, diluent lot, calibrated pipette IDs and ranges, tip-change policy, mixing method and cycle count, transfer order, timestamps, plate mapping, and any gravimetric verification.
LIMITS AND EXCLUSIONS
Where a constant-ratio serial protocol is insufficient
- Assumes the same transfer and diluent volumes at every step.
- Assumes complete mixing before each downstream transfer.
- Does not propagate pipette bias, imprecision, carryover, or evaporation.
- Does not model changing matrix composition or adsorption at low concentration.
- Supports 1 to 24 steps to keep the protocol and report inspectable.
TERMS USED HERE
Vocabulary for serial transfers, cumulative factor, and carryover
- Serial dilution
- Sequence in which each dilution supplies the next.
- Transfer volume
- Aliquot moved from one mixed tube to the next.
- Step factor
- Dilution factor produced by one transfer/diluent pair.
- Cumulative factor
- Product of all step factors through a given tube.
- Residual volume
- Liquid remaining after downstream transfer and assay withdrawal.
- Carryover
- Unintended material transferred by a tip or vessel between steps.
RELIABLE SOURCES
Solution concentration and laboratory-unit references
FREQUENTLY ASKED QUESTIONS
Why must the step count be an integer? and related questions
Why must the step count be an integer?
Each step corresponds to a physical receiving tube.
Can assay withdrawal be zero?
Yes; the residual then accounts only for the downstream transfer.
Why is the final value shown in mM?
All rows use one unit for consistent arithmetic; convert the final value for reporting if needed.
Can I use a different ratio in each tube?
Not on this page; a variable-ratio protocol needs a row-specific model.
Why does withdrawal have a limit?
The tube must retain the requested next transfer plus the assay portion without going negative.
Does the model include pipette uncertainty?
No. Use calibration and replicate data for an uncertainty analysis.
IMPORTANT BOUNDARY
A nominal transfer table, not a pipette uncertainty study
This nominal table is not a substitute for a validated dilution SOP, pipette qualification, contamination controls, uncertainty analysis, or assay-specific acceptance criteria.