Use this when an aliquot of a stock solution is diluted to a stated final volume and an aliquot of that first mixture is diluted again. Enter the starting mg/mL and both measured aliquot and final volumes.

Formula: stage 1 mg/mL = stock × stage 1 aliquot ÷ stage 1 final volume; stage 2 mg/mL = stage 1 × stage 2 aliquot ÷ stage 2 final volume; overall factor = (final 1 ÷ aliquot 1) × (final 2 ÷ aliquot 2)

Worked example

A 10 mg/mL stock diluted 1 mL to 10 mL gives 1 mg/mL. Taking 2 mL of that mixture to a 20 mL final volume gives 0.1 mg/mL, an overall 100-fold dilution and 2 mg in the second vessel.

Final volumes are totals, not solvent added

Each stage final volume includes its aliquot. OpenStax derives C₁V₁ = C₂V₂ from conservation of solute during dilution. If the mixture is not homogeneous or analyte is lost, this arithmetic no longer describes the true sample.

Stage 2 starts from stage 1

The second aliquot is taken from the first diluted mixture, not directly from the original stock. Both steps use the same analyte and compatible mg/mL units. Volumes may be entered in mL throughout because each ratio cancels.

Laboratory math only

This calculator does not identify a substance, check sample stability, validate pipetting, recommend a clinical concentration or determine a dose. No entries are transmitted or stored.

Explore the related calculation

For a different starting point, try the single-stage mg/mL dilution calculator or return to the main calculator. Browse the complete tool directory for this site.

Reference and corrections

The definitions and assumptions above follow these sources; the examples and calculator arithmetic are original to this page.

openstax.org reference

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Two-step serial dilution calculator

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