Understand the relationship
The reasoning behind the result
Dilution factors multiply
C₂ = C₀/(DF₁DF₂)
Each tube receives a sample of the immediately preceding well-mixed solution. A fivefold step followed by a twofold step therefore gives a tenfold dilution relative to the original stock. Adding the factors would describe a different and incorrect relationship.
The ledger shows both the factor introduced by a step and the cumulative factor. It avoids the ambiguity of a tube labelled only '1:10', which might mean relative to the stock or relative to the previous tube.
Concentration and retained volume answer different questions
Vretained,i = Vtransfer,i + Vdiluent,i − Vtransfer,i+1
Removing a well-mixed aliquot does not change the remaining mixture's concentration. It does reduce how much mixture remains for measurement. The last tube has no onward transfer in the entered series and retains its full prepared volume.
A planned onward transfer cannot exceed its source volume. The tool checks this dependency before returning a preparation ledger. It does not include unentered replicates, vessel dead volume or other withdrawals.
A numerical plan is not a mixing protocol
The calculation assumes each transfer represents its source mixture and that added diluent contains none of the measured material. It does not prescribe a mixing technique or assess adsorption, precipitation, evaporation, carryover or instrument limits.
Use a direct dilution when its required aliquot is practical; a serial design introduces more transfer operations and possible preparation error. This planner exposes those operations without claiming one plan has validated accuracy.
Follow the numbers
Three tenfold steps
- Start at 100 mg/mL. A 100 µL transfer plus 900 µL diluent has DF = 1,000/100 = 10.
- The three concentrations are 10, 1 and 0.1 mg/mL; cumulative factors are 10, 100 and 1,000.
- Each of the first two tubes supplies 100 µL onward and retains 900 µL. The final tube retains 1,000 µL.
The last concentration is 0.1 mg/mL. Earlier tubes retain less volume, but their concentrations remain unchanged by onward sampling.
Quick guide
How to use this calculator
- Enter the original concentration and its unit.
- Choose identical steps or supply a named step ledger.
- Check each cumulative factor and concentration, then inspect the retained volume after onward transfer.
- Account separately for any additional sampling, dead volume or disposal not entered in this series.
Calculation method
Calculation and interpretation
Follow the material from the original stock through each actual dilution tube.
DFᵢ = (transferᵢ + diluentᵢ)/transferᵢ; Cᵢ = C₀/ΠDFᵢ; retainedᵢ = preparedᵢ − next transfer
Worked example
Three tenfold steps
The last concentration is 0.1 mg/mL. Earlier tubes retain less volume, but their concentrations remain unchanged by onward sampling.
DFᵢ = (transferᵢ + diluentᵢ)/transferᵢ; Cᵢ = C₀/ΠDFᵢ; retainedᵢ = preparedᵢ − next transfer
Supported inputs
Precision and limits
Preparation arithmetic
Volumes are assumed additive and the stock uniformly mixed. The calculation does not choose a solvent, biological target, concentration, incubation condition or validated laboratory protocol. Check compatibility and the working range of the equipment separately.
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