Stock Dilution Calculator (C₁V₁ = C₂V₂)
Calculates volume of concentrated stock (V₁) and volume of diluent needed to prepare a diluted solution of target concentration (C₂) and volume (V₂).
⚠️ Educational Calculation & Clinical Safety Safeguard: Target concentration C₂ must be strictly less than or equal to stock concentration C₁. Educational calculations do not replace clinician assessment, patient-specific laboratory monitoring, or institutional prescribing protocols.
Interactive Calculator
Allowed physiological/compounding range: 0.001 to 10000 % or mg/mL
Allowed physiological/compounding range: 0.0001 to 10000 % or mg/mL (same unit)
Allowed physiological/compounding range: 0.1 to 50000 mL
Calculated Output (mL stock (V₁) & mL diluent)
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Step-by-Step Mathematical Derivation & Explanation:
Validated Formula & Conversion Rules
V₁ = (C₂ × V₂) / C₁; Diluent to Add = V₂ − V₁Worked Clinical Example
Prepare 500 mL of 2% w/v solution from 20% w/v stock: V₁ = (2 × 500) / 20 = 50 mL stock + 450 mL diluent.
Rounding Rules, Clinical Interpretation, Assumptions & Known Limitations
- 1. Purpose: Calculates volume of concentrated stock (V₁) and volume of diluent needed to prepare a diluted solution of target concentration (C₂) and volume (V₂).
- 2. Required Inputs & Validated Units: Stock Concentration (C₁) (% or mg/mL, range 0.001–10000), Target Concentration (C₂) (% or mg/mL (same unit), range 0.0001–10000), Target Final Volume (V₂) (mL, range 0.1–50000)
- 3. Output Unit:
mL stock (V₁) & mL diluent - 4. Result Interpretation Notes: Solves C₁V₁ = C₂V₂ for concentrated stock volume (V₁) and required diluent volume (V₂ − V₁).
- 5. Rounding Guidance: Measure V₁ in an appropriately sized graduated cylinder or volumetric pipette.
- 6. Mathematical & Clinical Assumptions: Assumes additive volumes without significant volume contraction upon mixing.
- 7. Known Limitations & Contraindications to Formula Use: When diluting concentrated electrolytes (e.g., KCl) or vesicants, ensure thorough inversion mixing before infusion.
- 8. Supporting Compendial & Clinical References: Indian Pharmacopoeia (IP 2022), National Formulary of India (NFI), British National Formulary (BNF), and NCBI Bookshelf Clinical Pharmacology Compendia.