Can I use alligation for more than two stocks?

The standard alligation alternate method works with exactly two stocks. For three or more stocks, use the alligation medial method or set up simultaneous equations. This calculator handles the two-stock case.

What if I need 0% as one of my stocks (i.e. pure diluent)?

If one stock is pure diluent (0% concentration), use the C1V1 = C2V2 dilution calculator instead — alligation with 0% simplifies to a standard dilution.

How precise is the alligation result?

Alligation gives exact ratios. The precision of the final preparation depends on the accuracy of your weighing or measuring equipment, and the thoroughness of mixing.

Alligation Calculator — Free Pharmacy Calculator

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You need a 2.5% cream but you only have 1% and 5% in stock. How many parts of each do you mix?

Alligation Calculator

Compounding

Higher concentration (%)

Lower concentration (%)

Desired concentration (%)

Total volume needed (mL)

Optional — leave blank for ratio only

Parts of high = Desired % − Lower % Parts of low = Higher % − Desired % Example: Mix 10% with 2% to make 5%:
Parts of 10% = 5−2 = 3 · Parts of 2% = 10−5 = 5 · Ratio = 3:5
For 200 mL: 75 mL of 10% + 125 mL of 2%

Reference: Pharmacy Board of Australia · AMH Compounding Guidelines

⚕️ Clinical safety: 🇦🇺 Verify with facility drug formulary and senior clinician · Meets AHPRA/ACSQHC standards

1 What this calculator does

Calculates the ratio of two different-concentration solutions or preparations to mix in order to reach a target concentration between them. Uses the alligation medial (or alternate) method — the standard pharmacy technique for mixing two strengths.

2 Formula & professional reasoning

Parts of high-concentration stock = Target% − Low%
Parts of low-concentration stock = High% − Target%
Total parts = (Target − Low) + (High − Target)
Fraction of high stock = parts high ÷ total parts

Alligation is the method for finding proportions when you cannot achieve a concentration by simple dilution (which only adds diluent). When you must mix two stocks of different strengths, the alligation alternate method gives the exact ratio required. The target concentration must be between the two stock concentrations — it is impossible to achieve a concentration outside this range by simple mixing.

3 Worked examples

⚠️ Illustrative example only — not clinical or professional instruction.

Basic

Mix two creams to reach 2.5%

Given: Low: 1% · High: 5% · Target: 2.5%

Working: Parts of 5%: 2.5 − 1 = 1.5 · Parts of 1%: 5 − 2.5 = 2.5 · Total: 4 parts

Answer: 1.5 parts of 5% + 2.5 parts of 1%

💡 To make 100 g: 37.5 g of 5% cream + 62.5 g of 1% cream.

Standard

Alcohol solutions for preparation

Given: Low: 70% alcohol · High: 95% alcohol · Target: 80%

Working: Parts of 95%: 80 − 70 = 10 · Parts of 70%: 95 − 80 = 15 · Total: 25 parts

Answer: 10 parts 95% + 15 parts 70%

💡 To make 1000 mL: 400 mL of 95% ethanol + 600 mL of 70% ethanol.

Advanced

Verify with C1V1 + C2V2 check

Given: Check: 37.5 g at 5% + 62.5 g at 1% = target 2.5% in 100 g

Working: (37.5 × 0.05) + (62.5 × 0.01) = 1.875 + 0.625 = 2.5 g active · 2.5/100 = 2.5% ✓

Answer: Verified: 2.5%

💡 Always verify alligation results with the mass balance check: (C1 × V1) + (C2 × V2) = C_target × V_total.

4 Sanity check

Target must be between the two concentrations

Low% < Target% < High%

If target is outside this range, alligation cannot achieve it by mixing these two stocks.

Always verify with mass balance

(C1 × V1) + (C2 × V2) = Ctarget × Vtotal

Cross-multiplication verification should agree to within rounding error.

Ratio can be scaled

1.5 parts + 2.5 parts can become 15 g + 25 g or 150 mL + 250 mL

Multiply all parts by the same factor to reach your required total quantity.

Homogeneity after mixing

Mix thoroughly to ensure uniform concentration throughout

Creams and ointments especially — use geometric dilution technique for potent drugs.

5 Common errors

Error	Cause	Consequence	Fix
Target outside the range of the two stock concentrations	Incorrect stock selection	Impossible calculation — alligation cannot work here	Target must be strictly between the two stock concentrations. If not possible, source a different stock strength.
Mixing up high and low parts assignment	Reversing the formula	Wrong ratio — final concentration opposite of intended	Parts of HIGH stock = Target − Low · Parts of LOW stock = High − Target. Always subtract from the diagonal.
Not verifying with mass balance	Trusting the calculation without checking	Dispensing error reaches patient	Always check: (C_high × V_high) + (C_low × V_low) must equal C_target × V_total
Not mixing thoroughly	Assuming the two components blend automatically	Concentration gradient in final product — patient receives inconsistent dose	Use geometric dilution for potent compounds. Mix cream/ointment bases in a mortar with trituration.

6 Reference & regulatory links

🇦🇺 Australia

🇺🇸 United States

7 Professional workflow

Common tools used alongside this one:

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Pharmacy Markup & Margin

After calculating the preparation, use Pharmacy Markup to price the compounded product

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Input	Result
1% + 5% → 2.5%	2.5 parts 1% + 1.5 parts 5%
70% + 95% → 80%	15 parts 70% + 10 parts 95%