🚧 Under construction — VoTechWorks is being built. A free tech program — complimentary, as our commitment to get America working.
voTechWorksGrade 13 · a vocational technology learning center, by urbanicity
newSchoolWorks.com › VoTechWorks › Health & Personal Services › Pharmacy Technician › Pharmacy Calculations and Order Entry › Lesson 7
HLT-PHAR41-03 · Lesson 7 · 15 clock hours · theory

Concentrations: percent strength, ratio strength and mg/mL

Objective. Convert between w/v, w/w and v/v percent, ratio strength and mg/mL, and calculate how much drug is in a given volume.

⚠ Pending professional review

This lesson, its worked examples and its practice questions has not yet been verified by a licensed pharmacist or by a certification or approval body. It is a study draft and may contain errors. Do not use it to make decisions about any patient or medication. Always follow your instructor, your supervising professional, and current official references and regulations.

VoTechWorks program approval and accreditation are still in progress. Credentials are issued only by the certifying bodies named in each program, after their own exams.

What Is Concentration?

Concentration describes how much drug (solute) is dissolved or dispersed in a given amount of product (solution or mixture). Pharmacy labels express concentration in several formats—percent strength, ratio strength, and mg/mL—and you must move fluently among all three. A calculation error in concentration can cause a patient to receive too little drug (treatment failure) or too much drug (toxicity), so accuracy is non-negotiable.

Percent Strength

Percent strength always means "parts per 100 parts of the final product." Three sub-types exist based on the physical states of solute and product:

Weight-in-volume (w/v): grams of solute per 100 mL of solution. This is the most common type in pharmacy. A 1% w/v solution contains 1 g of drug in every 100 mL of solution.

Weight-in-weight (w/w): grams of solute per 100 g of product. Used for ointments, creams, and other solid or semi-solid preparations. A 2.5% w/w ointment contains 2.5 g of drug in every 100 g of ointment.

Volume-in-volume (v/v): milliliters of solute per 100 mL of solution. Used when both solute and solvent are liquids, such as alcohol solutions. A 70% v/v isopropyl alcohol solution contains 70 mL of isopropyl alcohol in every 100 mL of solution.

When a label simply states a percent without further notation (for example, "dextrose 5%"), w/v is assumed for liquid preparations and w/w is assumed for solid or semi-solid preparations.

Ratio Strength

Ratio strength expresses concentration as 1 part of solute in a stated number of parts of product, written as 1:X. The units follow the same convention as percent strength:

Epinephrine injection is a classic example. A 1:1000 epinephrine solution contains 1 g of epinephrine per 1,000 mL, and a 1:10,000 solution contains 1 g per 10,000 mL. Never confuse these two strengths; the error has caused patient deaths.

Converting ratio strength to percent: divide 1 by the second number (X), then multiply by 100.

> 1:1000 → (1 ÷ 1000) × 100 = 0.1%

> 1:10,000 → (1 ÷ 10,000) × 100 = 0.01%

Converting percent to ratio strength: divide 1 by the decimal equivalent of the percent.

> 0.1% → 0.1 ÷ 100 = 0.001; 1 ÷ 0.001 = 1000, so 1:1000

mg/mL

Milligrams per milliliter is the most clinically useful expression because it directly states the mass of drug in a unit volume that can be drawn into a syringe. Many IV solutions, injectable drugs, and oral liquids are labeled this way.

Converting w/v percent to mg/mL:

1. Recall that 1% w/v = 1 g/100 mL.

2. Convert grams to milligrams: 1 g = 1,000 mg.

3. Therefore, 1% w/v = 1,000 mg/100 mL = 10 mg/mL.

The shortcut: multiply the percent by 10 to get mg/mL (for w/v solutions).

> 0.9% NaCl → 0.9 × 10 = 9 mg/mL

> 5% dextrose → 5 × 10 = 50 mg/mL

Converting mg/mL to percent: divide by 10.

> 4 mg/mL → 4 ÷ 10 = 0.4% w/v

Calculating Amount of Drug in a Given Volume

Once you know the concentration in consistent units, multiply by the volume to find the total amount of drug.

Formula: Amount of drug = Concentration × Volume

Keep units consistent before multiplying. If concentration is in g/mL and volume is in mL, the answer is in grams. If concentration is in mg/mL and volume is in mL, the answer is in milligrams.

Putting It All Together

When you read a pharmacy label, identify the concentration format, convert to the unit you need, then perform your calculation. Always label every number with its unit and double-check your conversion factor. A useful memory anchor:

| Starting unit | Multiply/divide | Result |

|---|---|---|

| % w/v | × 10 | mg/mL |

| mg/mL | ÷ 10 | % w/v |

| Ratio 1:X | ÷ X × 100 | % |

| % | ÷ 100 × X (set X) | Ratio 1:X |

Mastering these conversions protects patients and prepares you for every concentration-related task you will encounter on the job and on the PTCE.

Key terms7

Percent strength (w/v)Grams of solute dissolved in 100 mL of solution; the standard way to express the concentration of most liquid drug products.
Percent strength (w/w)Grams of solute in 100 g of product; used for ointments, creams, powders, and other solid or semi-solid preparations.
Percent strength (v/v)Milliliters of liquid solute in 100 mL of solution; used when both the active ingredient and the vehicle are liquids.
Ratio strengthConcentration expressed as 1 part of drug per X parts of product (written 1:X); commonly used for very dilute solutions such as epinephrine injections.
mg/mLMilligrams of drug per milliliter of solution; a clinical concentration unit that directly indicates how much drug is in a measurable volume.
SoluteThe drug or active ingredient that is dissolved or dispersed in the product.
Solvent (vehicle)The liquid in which the solute is dissolved to form a solution.

Worked examples4

1. A vial is labeled '2% lidocaine injection.' How many mg of lidocaine are in 20 mL?
  1. Identify the concentration type: 2% w/v means 2 g per 100 mL.
  2. Convert percent to mg/mL: 2% × 10 = 20 mg/mL.
  3. Calculate amount in 20 mL: 20 mg/mL × 20 mL = 400 mg.
Answer: 400 mg of lidocaine in 20 mL.
2. Epinephrine 1:1000 injection is available. Express this concentration as a percent and as mg/mL.
  1. Convert ratio to percent: (1 ÷ 1000) × 100 = 0.1%.
  2. Convert percent to mg/mL: 0.1% × 10 = 1 mg/mL.
  3. Verify with ratio definition: 1 g per 1,000 mL = 1,000 mg per 1,000 mL = 1 mg/mL. ✓
Answer: 0.1% and 1 mg/mL.
3. A pharmacist asks you to prepare 250 mL of a 0.45% NaCl solution from a 0.9% NaCl stock solution. How many mL of stock solution are needed?
  1. Determine the total amount of NaCl needed in the final 250 mL: 0.45% × 10 = 4.5 mg/mL; 4.5 mg/mL × 250 mL = 1,125 mg = 1.125 g.
  2. Determine the concentration of the stock: 0.9% × 10 = 9 mg/mL.
  3. Calculate volume of stock needed: 1,125 mg ÷ 9 mg/mL = 125 mL.
  4. The remaining 250 − 125 = 125 mL would be supplied by sterile water for injection to reach the final volume.
Answer: 125 mL of 0.9% NaCl stock solution.
4. A hydrocortisone cream is labeled 2.5% w/w. How many grams of hydrocortisone are in a 30 g tube?
  1. Interpret the label: 2.5% w/w means 2.5 g of hydrocortisone per 100 g of cream.
  2. Set up a proportion: 2.5 g / 100 g = x g / 30 g.
  3. Solve for x: x = (2.5 × 30) ÷ 100 = 75 ÷ 100 = 0.75 g.
Answer: 0.75 g (750 mg) of hydrocortisone in a 30 g tube.

The math in this lesson2

Learners convert 2% w/v lidocaine to 20 mg/mL to find 400 mg in 20 mL and convert ratio strengths to percent.
7.RP.3N-Q.1
Brush up in the math halls at newSchoolWorks.com:
In class: Concentration conversion drills · Label-strength reading · Epinephrine ratio-strength case
Materials: Calculation workbook
Check: Quiz ≥ 90%

Practice check12

Answer each question, then check it. Nothing is recorded; this is your own practice.

Order Entry and Processing
1. How many grams of drug are in 100 mL of a 2% (w/v) solution?
Order Entry and Processing
2. How many grams of drug are in 500 mL of a 0.9% (w/v) solution?
Order Entry and Processing
3. How many grams of drug are in 250 mL of a 10% (w/v) solution?
Order Entry and Processing
4. How many grams of drug are in 1000 mL of a 5% (w/v) solution?
Order Entry and Processing
5. A solution is labeled '5% dextrose injection.' What does this concentration mean?
Order Entry and Processing
6. Which of the following is the correct mg/mL equivalent of a 0.9% w/v sodium chloride solution?
Order Entry and Processing
7. How many milligrams of drug are contained in 15 mL of a 4% w/v solution?
Patient Safety and Quality Assurance
8. Epinephrine 1:10,000 injection is ordered for a patient. What is this concentration expressed as mg/mL?
Order Entry and Processing
9. A prescription calls for 60 g of a 1% w/w hydrocortisone ointment. How many grams of hydrocortisone active ingredient are needed?
Order Entry and Processing
10. A solution has a concentration of 25 mg/mL. Which ratio strength correctly represents this concentration?
Patient Safety and Quality Assurance
11. A technician confuses epinephrine 1:1,000 with epinephrine 1:10,000. These two concentrations differ by a factor of:
Order Entry and Processing
12. A label reads '50 mg/mL.' What is the equivalent percent w/v concentration?
Record this lesson on my transcript. Sign in with your key and enrollment email to record lessons (enroll free if you have no key). This page stays open to read and practise.
← Previous lessonTop-200 drugsNext lesson →