Three methods — each solves a different problem type
Proportion: X / known = wanted / known | Percent: g per 100 mL | Dilution: C&sub1;V&sub1; = C&sub2;V&sub2;
Cross-multiply works for simple ratios. C1V1=C2V2 works for all dilutions. Percent strength has ONE definition: grams per 100 mL (or g per 100 g). That's it.
Percent strength — the #1 tested concept
% w/v = grams of solute per 100 mL of solution
% w/w = grams per 100 g (creams, ointments)
1% = 1 g/100 mL = 10 mg/mL
2% = 2 g/100 mL = 20 mg/mL
0.9% NS = 0.9 g/100 mL = 9 mg/mL
Most common error: treating 1% as 1 mg (wrong by 1,000x)
% w/w = grams per 100 g (creams, ointments)
1% = 1 g/100 mL = 10 mg/mL
2% = 2 g/100 mL = 20 mg/mL
0.9% NS = 0.9 g/100 mL = 9 mg/mL
Most common error: treating 1% as 1 mg (wrong by 1,000x)
Dilution — C₁V₁ = C₂V₂
C&sub1; = starting concentration
V&sub1; = starting volume (what you need to find)
C&sub2; = desired concentration
V&sub2; = desired final volume
Example: Make 100 mL of D5W from D50W:
50 × V1 = 5 × 100 → V1 = 10 mL
V&sub1; = starting volume (what you need to find)
C&sub2; = desired concentration
V&sub2; = desired final volume
Example: Make 100 mL of D5W from D50W:
50 × V1 = 5 × 100 → V1 = 10 mL
Ratio strength
1:1,000 = 1 g per 1,000 mL = 1 mg/mL
1:10,000 = 1 g per 10,000 mL = 0.1 mg/mL
Epinephrine 1:1,000 = anaphylaxis dose (IM)
Epinephrine 1:10,000 = cardiac arrest (IV)
Convert ratio to %: 1/1,000 × 100 = 0.1%
1:10,000 = 1 g per 10,000 mL = 0.1 mg/mL
Epinephrine 1:1,000 = anaphylaxis dose (IM)
Epinephrine 1:10,000 = cardiac arrest (IV)
Convert ratio to %: 1/1,000 × 100 = 0.1%
Cross-multiply / proportion
If A/B = C/D, then A×D = B×C
Example: 250 mg/5 mL — how many mL for 375 mg?
250/5 = 375/x → 250x = 1,875 → x = 7.5 mL
Works for any two equivalent ratios.
Example: 250 mg/5 mL — how many mL for 375 mg?
250/5 = 375/x → 250x = 1,875 → x = 7.5 mL
Works for any two equivalent ratios.
⚠ Alligation (NHA/ExCPT only): Alligation was removed from the 2026 PTCB exam. This lesson includes 6 alligation questions for students taking the NHA ExCPT or working in compounding. If you are PTCB-focused, use your study time on percent strength and dilution instead. Questions are labeled [NHA ExCPT only] throughout.
★ PTCB tip: Percent strength and dilution (C1V1=C2V2) are the most PTCB-tested topics in this lesson. Expect 2–4 questions combining percent strength with dose calculation. Ratio strength (epinephrine concentrations) appears in safety/patient care questions. Practice recognizing percent as g/100 mL until it is automatic.
Six worked examples — from basic percent strength definition through advanced dilution calculations.
EasyRetail
Normal saline 0.9% NaCl. Patient asks: "How much salt is actually in this?"
How many mg of NaCl are in 100 mL of 0.9% NS?
Percent w/v definition:0.9% = 0.9 g per 100 mL
Convert to mg:0.9 g × 1,000 = 900 mg per 100 mL
✓ 900 mg (0.9 g) of NaCl per 100 mL — this is why NS tastes salty
MediumHospital
Prepare 100 mL of D5W from D50W (50% dextrose) and sterile water.
How many mL of D50W do you need? (C₁V₁ = C₂V₂)
Set up C₁V₁ = C₂V₂:50% × V&sub1; = 5% × 100 mL
Solve for V₁:V&sub1; = (5 × 100) / 50 = 10 mL
Add SWFI to make total 100 mL:100 − 10 = 90 mL SWFI
✓ 10 mL D50W + 90 mL SWFI = 100 mL of D5W
MediumHospital
Epinephrine 1:1,000 used for anaphylaxis. Dose: 0.3 mg IM.
How many mL?
1:1,000 = 1 g per 1,000 mL = 1 mg/mL:0.3 mg ÷ 1 mg/mL = 0.3 mL
✓ Draw up 0.3 mL from the 1:1,000 vial for anaphylaxis IM injection
Critical distinction: 1:1,000 (1 mg/mL) is IM for anaphylaxis. 1:10,000 (0.1 mg/mL) is IV for cardiac arrest. Using the wrong concentration gives a 10x dose error.
HardHospital
Prepare 250 mL of 0.45% NaCl using 0.9% NaCl and SWFI.
How many mL of 0.9% NaCl?
C₁V₁ = C₂V₂:0.9 × V&sub1; = 0.45 × 250
Solve:V&sub1; = 112.5 / 0.9 = 125 mL
✓ 125 mL of 0.9% NS + 125 mL SWFI = 250 mL of 0.45% NS
HardRetailNHA ExCPT only
[NHA ExCPT — not on 2026 PTCB] Mix 2.5% and 0.5% hydrocortisone cream to make 60 g of 1% cream.
How many grams of 2.5% cream? (Alligation method)
Alligation grid:2.5% ↘ (1-0.5) = 0.5 parts of 2.5%
1% (target)
0.5% ↗ (2.5-1) = 1.5 parts of 0.5%
Total parts:0.5 + 1.5 = 2 parts
Grams of 2.5%:(0.5/2) × 60 = 15 g
✓ 15 g of 2.5% + 45 g of 0.5% = 60 g of 1% hydrocortisone
HardRetail
Lidocaine 3% solution. Need to know mg content for a local anesthetic procedure using 20 mL.
How many mg of lidocaine in 20 mL of 3% solution?
3% = 3 g per 100 mL = 30 mg/mL:30 mg/mL × 20 mL = 600 mg
✓ 600 mg lidocaine. Maximum safe dose for a 70 kg adult: ~350 mg — verify with prescriber before preparing.
How this quiz works: Pick your question count and difficulty, then start. After answering, click Reveal explanation to see the full step-by-step solution — answers never show automatically. Score and type breakdown appear at the end.
ⓘ This lesson has 36 questions in the bank. A 10-question quiz draws a random subset. Run multiple sets to cycle through all questions.
ⓘ This lesson has 36 questions in the bank. A 10-question quiz draws a random subset. Run multiple sets to cycle through all questions.
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Shuffle every time you start
Timed mode
45-second countdown per question
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1
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Lesson 5 · Ratio, Proportion & Percent Strength · AlabamaPharmTech.com
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