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Mode{{ resultsReady ? modeLabel : '—' }} Factor{{ resultsReady ? `${formatNumber(computation.values.dilution_factor, 6)}×` : '—' }} Replicates{{ resultsReady ? computation.values.replicate_count : '—' }}
Use serial mode only when its intermediate transfers fit the approved protocol and equipment.
Stock and target must use the same physical concentration basis.
Use the value and unit from the stock label or approved protocol.
Use the requested final concentration from the same approved protocol.
Changing the unit preserves the same physical volume.
The neutral default is 1. Totals multiply externally introduced stock and diluent.
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The chart renderer is unavailable. Exact stage concentrations remain available in the preparation plan.

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Preparing a working solution from a concentrated stock preserves the amount of solute while adding diluent. The familiar C1V1 = C2V2 relationship determines how much stock belongs in the final volume. The equation is simple only when both concentrations describe the same physical basis and every unit is converted consistently.

A direct dilution transfers stock once into the final preparation. It is usually the clearest path when the required stock volume fits the calibrated equipment and the protocol allows the mix. A serial dilution splits a large overall factor across several stages, which can make each transfer more practical but adds vessels, mixing steps, and opportunities for accumulated error.

ApproachBest fitMain caution
DirectOne measurable stock transfer reaches the targetA tiny transfer may fall outside pipette accuracy
SerialA large dilution factor needs manageable intermediate stepsIncomplete mixing and transfer error propagate forward

Molar concentration and mass-per-volume concentration are separate bases. A value in mol/L cannot be converted to g/L without the solute's molar mass, and that conversion is not part of a dilution-only calculation. Stock and target must therefore remain on the same basis.

Final volume means the completed solution volume, not the amount of diluent poured first. In real laboratory work, mixing may not be perfectly additive, solubility or stability may limit the recipe, and calibrated equipment has a usable range and uncertainty. A calculated volume still needs review against the approved protocol, material identity, vessel capacity, and handling requirements.

These results are educational preparation plans. They do not establish sterility, compatibility, potency, safety, or suitability for clinical dosing.

How to Use This Tool:

Choose the preparation path only after checking that the concentration basis and available equipment match the written protocol.

  1. Select Direct preparation for one stock transfer or Serial preparation for an equal-factor sequence with intermediate tubes.
  2. Choose Molar concentration or Mass per volume, then enter stock and target values in supported units from that same basis.
  3. Enter the Final volume per replicate. For serial mode, choose 1 to 6 intermediate tubes and an inter-step transfer volume that fits the approved equipment and vessel capacity.
  4. Set the number of independent replicate preparations from 1 to 96. Totals multiply only the original stock and diluent introduced into each independent chain.
  5. Review every stage's transfer, diluent, final volume, and target concentration. If the last intermediate tube cannot supply the final transfer, increase the inter-step transfer or use fewer intermediate tubes.

Interpreting Results:

For a direct preparation, the stock volume is the amount to transfer and the diluent volume is the remainder needed to reach the final volume. For a serial preparation, read each row in order because the target from one stage becomes the source for the next.

  • Overall dilution factor is stock concentration divided by target concentration.
  • Per-stage factor is the same at every stage in serial mode.
  • Original stock total counts stock introduced at the first stage of each replicate, not intermediate solution carried forward.
  • A valid arithmetic plan is not evidence that each transfer lies within an instrument's calibrated range.

Technical Details:

Dilution conserves solute at each stage. Concentrations are normalized to mol/L or g/L, and volumes are normalized to liters before calculation. Display units can change without changing the physical quantity.

Formula Core:

For a direct preparation, stock concentration multiplied by stock volume equals target concentration multiplied by final volume.

C1V1=C2V2 V1=V2×C2C1 Vdiluent=V2-V1

A 10 mM stock diluted to 50 µM at a final volume of 20 mL has an overall factor of 200. Direct preparation requires 0.1 mL, or 100 µL, of stock and 19.9 mL of diluent.

Mechanism Core:

Serial mode divides the overall factor equally across the chosen number of stages. With k intermediate tubes, there are k + 1 stages.

Fstage = (CstockCtarget)1k+1

Every intermediate tube receives the entered transfer volume and enough diluent to make transfer volume multiplied by the stage factor. The final stage transfer equals final target volume divided by the stage factor. The last intermediate tube must contain at least that much solution, with a small numeric tolerance for floating-point arithmetic.

RuleSupported behavior
Concentration orderTarget must be less than or equal to stock; equal values are valid only in direct mode.
Serial depth1 to 6 intermediate tubes, producing 2 to 7 total stages.
Replicates1 to 96 independent preparation chains.
Volume unitsnL, µL, mL, and L are converted to liters.
Concentration unitsM, mM, µM, nM or matching mass-per-volume units are normalized within one basis.

Accuracy and Protocol Notes:

  • Confirm stock identity, concentration, solvent, purity, stability, and storage history.
  • Use calibrated equipment whose operating range contains every transfer volume.
  • Mix each intermediate thoroughly before taking the next transfer.
  • Check vessel capacity, dead volume, solubility, compatibility, sterility, and required uncertainty.
  • Follow the approved laboratory protocol and safety controls; do not use the result as a clinical dosing instruction.

Worked Examples:

Three direct replicates

A 5 g/L stock diluted to 0.5 g/L in 100 mL needs 10 mL stock and 90 mL diluent per replicate. Three independent preparations require 30 mL original stock and 270 mL total diluent.

Two-stage serial plan

The 10 mM to 50 µM, 20 mL case has a 200× overall factor. With one intermediate tube, two equal stages use a factor of about 14.142× each. A 100 µL first transfer makes about 1.414 mL of intermediate solution, and about 1.414 mL of that intermediate reaches 20 mL at the final target.

References: