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Alligation Calculator

Ready to calculate
Pharmacy Standard.
Alternate + Medial.
Mass + Volume.
100% Free.
No Data Stored.

How it Works

01Enter Two Stocks

Concentrations of high and low strength.

02Set Target

Target concentration between the two stocks.

03Cross-Subtraction

Classic alligation alternate parts.

04Mix Volumes

Returns volumes of each stock per final volume.

Last reviewed:

What is an Alligation Calculator?

The Alligation Calculator uses the alligation alternate method to determine the proportions of two stock solutions (or solid mixtures) needed to produce a desired intermediate concentration. Classic pharmacy compounding tool: e.g., mix 5% and 20% creams to make 10%, or combine 50% and 90% alcohol to get 70% disinfectant. The output is a parts ratio that scales to any final batch size.


Inputs: high stock %, low stock %, and target %. Output: parts of high + parts of low (and exact amounts in g, mL, or oz when batch size is given). Used by hospital pharmacy compounders, veterinary medication preparers, lab solution makers, and home brewers/distillers blending alcohol percentages.

How to Use the Calculator

Enter high stock concentration (%) — must exceed target.
Enter low stock concentration (%) — must be less than target (can be 0% for diluent).
Enter target concentration (%) — must lie between low and high.
Optional: enter total batch size in g, mL, or oz.
Calculate: Returns parts ratio + exact amounts of each stock.

The Math Behind It

Cross-subtraction (the "alligation grid"):

  • Parts of high stock = Target − Low stock
  • Parts of low stock = High stock − Target
  • Total parts = (Parts high) + (Parts low)

Then for batch size B: Amount high = B × Parts high / Total parts; Amount low = B × Parts low / Total parts. Works for any units (mass, volume) as long as both stocks use the same unit.

Real-World Example

Worked Example

Make 100 g of 10% hydrocortisone cream from 5% and 20% stocks:

  • Parts of 20% (high) = 10 − 5 = 5 parts
  • Parts of 5% (low) = 20 − 10 = 10 parts
  • Total = 15 parts → 5/15 = 33.3% from 20% stock; 10/15 = 66.7% from 5% stock
  • For 100 g: 33.3 g of 20% + 66.7 g of 5%
  • Verify: (33.3 × 0.20 + 66.7 × 0.05) / 100 = 0.10 = 10% ✓

Who Uses It

1
💊 Pharmacy Compounders: Mix two strengths of API to hit prescribed concentration.
2
🏥 Hospital Pharmacy: Custom IV admixtures and topical prep.
3
🐾 Veterinary Pharmacists: Compound species-specific concentrations.
4
🧪 Lab Technicians: Blend stock solutions to working concentrations.
5
🍷 Distillers / Brewers: Blend high and low ABV spirits to target proof.
6
🎓 Pharmacy Students: Practice classic alligation problems for board exams.

Technical Reference

The classic 4-square layout:

     High%   →   Target − Low% = parts High         ⬊ ⬈        Target%         ⬈ ⬋      Low%    →   High% − Target = parts Low

Common pharmacy applications:

  • Topical hydrocortisone: Combine 1% and 2.5% to get custom strength
  • Alcohol blending: 90% IPA + diluent for 70% disinfectant
  • Saline: 0.9% NaCl + 3% NaCl for hypertonic prep
  • Insulin diluent: Standard concentration adjusted for pediatric dosing
  • Veterinary doxycycline: Compound to species-appropriate concentrations

Key Takeaways

Alligation is faster than algebra for two-component blending — cross-subtract, get parts, scale to batch. Works for percent w/w, w/v, v/v, ABV, or any other concentration unit as long as both stocks share the unit. The target must lie strictly between high and low — you cannot extrapolate.

Frequently Asked Questions

Can I use alligation with three stocks?
Standard alligation is two-stock. Three-stock blending uses systems of equations — outside this calculator. Workaround: alligate two stocks to an intermediate, then alligate that with the third.
What if I want a target below the low stock?
Treat 0% (pure diluent) as the low stock. Alligation low = 0; the formula still works.
Does it work for v/v as well as w/w?
Yes — alligation is unit-agnostic as long as both stocks use the same unit. Volume blending of solutions ignores small volume contractions; for high-precision analytical work, prefer mass-based alligation.
What about temperature corrections for alcohol?
ABV measurements are temperature-dependent (legal definition is at 60°F / 15.6°C). For distillery blending, measure both stocks at the same reference temp before alligation. Volume contraction on alcohol-water mixing is significant (~3% at 50:50).
Why use alligation instead of C₁V₁ = C₂V₂?
C₁V₁ = C₂V₂ handles ONE stock + diluent (1 unknown). Alligation handles TWO stocks + diluent or two stocks at different concentrations (2 unknowns) — a different problem class.
Is alligation still taught in pharmacy school?
Yes — it's on the NAPLEX and required compounding curriculum. Most pharmacists eventually use a calculator or formulation software, but the conceptual understanding (and exam questions) remain alligation-based.

Author Spotlight

The ToolsACE Team - ToolsACE.io Team

The ToolsACE Team

Last reviewed May 2026

Our specialized research and development team at ToolsACE brings together decades of collective experience in financial engineering, data analytics, and high-performance software development.

Software Engineering Team

Disclaimer

Alligation assumes ideal mixing without volume contraction or chemical reaction. For analytical-grade compounding (especially alcohol blending), measure stocks at the same temperature and verify final concentration with hydrometer or assay. For prescription compounding, USP <795> and <797> standards apply — follow institutional SOPs.