Free tool
Mix a higher-strength and a lower-strength product to make a strength in between. Enter the three percentages and the final quantity to get the parts and the exact amount of each to use.
Built for pharmacy technician (PTCE) exam prepUse 0 for a diluent such as water or a plain base.
Enter the strengths and final quantity to see the amounts.
Alligation looks tricky until the steps are automatic - Encodr uses spaced repetition to keep PTCE calculations like this one ready for exam day.
Get started freeWrite the higher strength top left, the lower strength bottom left, and the desired strength in
the middle. Subtract across the diagonals, always taking the positive difference:
parts of higher = desired − lower and parts of lower = higher − desired.
Add the parts for the total, then amount of each = final quantity × (its parts ÷ total parts).
The desired strength has to fall strictly between the two you're mixing - you can't mix 40% and
70% into 80%.
Worked example: make 300 g of 50% from 70% and 40%. Parts of 70% = 50 − 40 = 10; parts of 40% = 70 − 50 = 20; total 30 parts. So use 300 × 10/30 = 100 g of the 70% and 300 × 20/30 = 200 g of the 40%. Check: (100 × 70% + 200 × 40%) ÷ 300 = 150 ÷ 300 = 50%. A dilution works the same way with 0% as the lower strength: 500 mL of 5% from a 20% stock and water is 5 parts stock to 15 parts water, so 125 mL of stock and 375 mL of water.
This assumes percentages of the same type (all w/w or all v/v) and that volumes add, which is the standard exam assumption. More pharmacy tech prep: the PTCB exam deck and the exam pass score calculator.
How to use alligation to mix two strengths into a third: the grid, turning parts into volumes, diluting with water, and how to check the answer.
The calculation types behind the PTCE outline (conversions, doses, days supply, percent strength, dilutions, alligation, IV rates) with worked examples.
The PTCE passing scaled score is 1,400 on a 1,000 to 1,600 range. What a scaled score means, how many questions count, and the PTCB retake rules.
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