Alligation Alternate & Medial Pharmacy Calculator
Alligation Alternate is a fundamental mathematical technique used by pharmacists and chemists to calculate the relative amounts of two solutions of different concentrations needed to prepare a desi...
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📐 Formula
💡 Practical Example
Mix 70% stock (C1) and 20% stock (C2) to prepare 500 mL of 50% solution (Cd): Parts 70% = |50 - 20| = 30 parts Parts 20% = |70 - 50| = 20 parts Volume 70% = × 500 mL = 300 mL Volume 20% = × 500 mL = 200 mL
📖 About Alligation Alternate & Medial Pharmacy Calculator
Alligation Alternate is a fundamental mathematical technique used by pharmacists and chemists to calculate the relative amounts of two solutions of different concentrations needed to prepare a desired intermediate concentration.
To use the Alligation Alternate & Medial Pharmacy Calculator, enter your Higher Concentration Available (C1), Lower Concentration / Diluent Available (C2), Desired Target Concentration (Cd) and other values. The calculator instantly computes Parts of Higher Concentration (C1), Parts of Lower Concentration (C2) and more. Results update in real time as you change any input — no submit button needed.
How to Use This Calculator
Enter your Higher Concentration Available (C1) (e.g. 70 in %), Lower Concentration / Diluent Available (C2) (e.g. 20 in %), Desired Target Concentration (Cd) (e.g. 50 in %), and Desired Final Volume or Weight (e.g. 500 in mL / g). Results update instantly as you type — adjust any value to compare scenarios.
The Formula
Parts C1 (Higher) = |Target Concentration (Cd) - Lower Concentration (C2)|
Parts C2 (Lower) = |Higher Concentration (C1) - Target Concentration (Cd)|
Volume C1 = (Parts C1 ÷ Total Parts) × Desired Total Volume
Worked Example
Mix 70% stock (C1) and 20% stock (C2) to prepare 500 mL of 50% solution (Cd):
Parts 70% = |50 - 20| = 30 parts
Parts 20% = |70 - 50| = 20 parts
Volume 70% = 500 mL = 300 mL
Volume 20% = 500 mL = 200 mL
Understanding Your Result
Evaluate your result in the context of your specific use case and relevant industry standards or reference values. A single calculated result is a starting point — test two to three scenarios to understand how sensitive the outcome is to your key input assumptions. For high-stakes decisions, verify your result against a secondary source or subject-matter expert before acting.
💡 Mathematical Rigor & Applied Context
- This calculator applies exact mathematical definitions following conventions established by NIST and international standards bodies.
- Rounding errors accumulate across multi-step calculations. For precision-critical work, maintain extra significant figures through all intermediate steps.
- Many mathematical concepts have multiple valid formulations — if a result seems unexpected, verify which convention or definition applies to your context.
- Dimensional analysis (unit tracking) is the fastest way to catch formula errors. Every term in an equation must have consistent, compatible units.
- Numerical methods used in digital calculators introduce floating-point precision limits (~15 significant digits for IEEE 754 double precision).
- For statistical and probabilistic calculations, always specify whether you are working with population parameters or sample statistics — formulas differ.
- Visualizing a problem geometrically or testing with known boundary values (zero, infinity, negative) reveals hidden errors faster than algebraic checking.
- When in doubt, validate your result against a simplified hand calculation or a published worked example from a textbook or standards document.
Results are for informational and educational purposes only. Always verify critical decisions with a qualified professional.