Skip to main content

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.

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

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.