Ratio and Proportion for Dosage Calculations
Ratio and proportion compares what you know about the product with what you need, then solves for the missing amount.
In this lesson
- How H / Q = D / X is built
- Cross multiplying and solving for X
- Tablet, liquid and unit-conversion examples
- How this compares with the other methods
What you're solving for
X: the quantity of product that holds the ordered dose, in the same unit as Q.
The setup
H over Q equals D over X
- H / Q
- The known ratio from the label: dose available per quantity, such as 160 mg per 5 mL.
- D / X
- The ratio you need: the ordered dose per unknown quantity.
A proportion says two ratios are equivalent. The product always holds the same amount of drug per mL (or per tablet), so the ordered dose must sit in the same ratio. The dose units on both sides must match — mg with mg, not mg with g — and the quantity units must match too.
To solve, cross multiply (H × X = D × Q) and divide both sides by H.
Worked examples
Example 1: Tablets
Ordered: 20 mg. On hand: 10 mg tablets. How many tablets?
Step 1: Set up the proportion (known : desired)
10 mg / 1 tablet = 20 mg / X
Step 2: Cross multiply
10 mg × X = 20 mg × 1 tablet
Step 3: Solve for X
X = (20 mg × 1 tablet) ÷ 10 mg
X = 2 tablets
Answer: 2 tablets
Example 2: Liquid
Ordered: 240 mg. On hand: 160 mg / 5 mL. How many mL?
Step 1: Set up the proportion (known : desired)
160 mg / 5 mL = 240 mg / X
Step 2: Cross multiply
160 mg × X = 240 mg × 5 mL
Step 3: Solve for X
X = (240 mg × 5 mL) ÷ 160 mg
X = 7.5 mL
Answer: 7.5 mL
Example 3: Convert first
Ordered: 1 g. On hand: 500 mg / 10 mL. How many mL?
Change 1 g to mg so both dose terms use mg.
Step 1: Make the units match
1 g = 1,000 mg
Step 2: Set up the proportion (known : desired)
500 mg / 10 mL = 1,000 mg / X
Step 3: Cross multiply
500 mg × X = 1,000 mg × 10 mL
Step 4: Solve for X
X = (1,000 mg × 10 mL) ÷ 500 mg
X = 20 mL
Answer: 20 mL
Common mistakes
Mismatched ratio order
- What goes wrong
- 160 mg / 5 mL = X / 240 mg
- Why it fails
- The right side is flipped (quantity over dose), so the ratios aren't comparable.
- Correct approach
- 160 mg / 5 mL = 240 mg / X
Different dose units on each side
- What goes wrong
- 500 mg / 10 mL = 1 g / X
- Why it fails
- mg and g can't be compared directly.
- Correct approach
- 500 mg / 10 mL = 1,000 mg / X
Quick self-check
On hand 40 mg / 1 mL; ordered 60 mg. Write the proportion and solve.
Show the answer
40 mg / 1 mL = 60 mg / X → 40 × X = 60 × 1 → X = 1.5 mL
Compare methods
Rearranged, H / Q = D / X becomes X = D ÷ H × Q — the Desired Over Have formula. The dimensional analysis chain multiplies the same numbers. Use whichever your course asks for.
Calculate and practice
Related lessons
- Desired Over Have (D ÷ H × Q) — The D ÷ H × Q formula for tablets, capsules and liquids.
- Dimensional Analysis for Dosage Calculations — Chain conversion factors so unwanted units cancel.
- Liquid Medication Calculations — Read a concentration correctly and calculate the mL.
Sources
- Dose Calculation Ratio and Proportion Method — NCBI StatPearls
- Pharmacology for Nurses — 2.4 Dosage Calculations — OpenStax
Explanations are original Dosage Calcs wording. See all sources and the methodology.
Educational Use & Safety
Educational content only. These lessons teach medication math using fictional values and do not determine an appropriate medication, dose, infusion rate, or treatment for an actual patient.
Educational Use & Safety