Dilution Calculator (C₁V₁ = C₂V₂)
Calculate how much stock solution to dilute to make a desired concentration and volume. USP-aligned.
Calculate how much stock solution is needed to prepare a diluted solution using C₁V₁ = C₂V₂.
Formula
C₁ × V₁ = C₂ × V₂
C₁ = stock concentration, V₁ = stock volume needed, C₂ = final concentration, V₂ = final volume. Common in USP <797> sterile compounding.
Step-by-step method
- 1
Identify the stock concentration (C₁)
Read the strength of the stock solution from the label (e.g. 50 mg/mL or 10% w/v).
- 2
Identify the target concentration (C₂) and volume (V₂)
Note the prescribed final concentration and the volume needed.
- 3
Rearrange the equation
V₁ = (C₂ × V₂) ÷ C₁.
- 4
Calculate the diluent volume
Diluent = V₂ − V₁. Use the named diluent (sterile water for injection, 0.9% sodium chloride, D5W) per the package insert.
- 5
Confirm units match
C₁ and C₂ must be in the same units, and V₁ and V₂ in the same units, before substituting.
Worked example
Scenario: Make 100 mL of 5 mg/mL gentamicin from a 40 mg/mL stock vial.
Answer: V₁ = (5 × 100) ÷ 40 = 12.5 mL stock + 87.5 mL diluent.
Practice calculations for the NAPLEX
350+ exam-style calculation questions with detailed explanations, mapped to NABP NAPLEX competency Area 4 (Perform Calculations).