Weight-Based Pediatric Dose: mL Per Dose Calculation

Medication Dosage 7th-8th Grade
PROBLEM
Recommended dose for a child is 10 mg/kg/day in four equal doses. A child weighs 14 kg. Medication is supplied in 120 mg/5 mL. How many milliliters will be administered for each dose?

What This Problem Teaches

  • Weight-based dosing calculations using mg/kg formulations
  • Converting total daily doses into individual administration amounts
  • Dimensional analysis for medication concentration conversions
  • Unit safety and precision in clinical calculations
  • Connecting mathematical ratios to real-world medical practice

Visualizing the Calculation

Recommended dose for a child is 10 mg/kg/day in four equal doses. A child weighs 14 kg. Medication is supplied in 120...

This diagram shows the three-step conversion: weight to daily dose, daily dose to single dose, then mg to mL using the concentration.

Solution: The Step-by-Step Method

Step 1 — Calculate the total daily dose

The prescription calls for 10 mg per kilogram per day. The child weighs 14 kg.

Total daily dose = 10 mg/kg/day × 14 kg = 140 mg/day

Step 2 — Find the dose per administration

The daily dose is divided into four equal doses throughout the day.

Dose per administration = 140 mg/day ÷ 4 doses/day = 35 mg/dose

Step 3 — Convert mg to mL using the supplied concentration

The medication is supplied at 120 mg per 5 mL. We need to find how many mL contain 35 mg.

35 mg × (5 mL / 120 mg) = 35 × 5/120 = 175/120 = 1.458... mL

Step 4 — Round to appropriate precision

For clinical dosing, we round to two decimal places, which gives us 1.46 mL per dose.

Solution: Method 2 — Dimensional Analysis Chain

This method links all conversions in one continuous calculation, canceling units as we go.

Step 1 — Set up the conversion chain

Start with the child's weight and multiply by all the conversion factors in sequence:

14 kg × (10 mg/kg/day) × (1 day/4 doses) × (5 mL/120 mg)

Step 2 — Cancel units systematically

Watch how kg, day, and mg all cancel out, leaving only mL/dose:

= (14 × 10 × 1 × 5) / (1 × 4 × 120) mL/dose = 700 / 480 mL/dose

Step 3 — Simplify the fraction

Divide both numerator and denominator by their greatest common factor:

700/480 = 35/24 = 1.458... ≈ 1.46 mL/dose
1.46 mL will be administered for each dose

Verification

Let's check our answer by working backwards from the final dose to the original prescription:

Check the mg content per dose

1.46 mL × (120 mg / 5 mL) = 1.46 × 24 = 35.04 mg ✓

Check the total daily dose

35.04 mg/dose × 4 doses/day = 140.16 mg/day ✓

Check the weight-based dosing

140.16 mg/day ÷ 14 kg = 10.01 mg/kg/day ✓

Our answer checks out perfectly within rounding precision.

Watch Out For These

✗ Forgetting to divide by the number of doses

Calculating 140 mg total and converting directly to mL gives 5.83 mL — but that's the entire daily amount, not per dose. In clinical practice, this error could lead to dangerous overdosing.

✗ Inverting the concentration ratio

Using (120 mg / 5 mL) instead of (5 mL / 120 mg) gives 35 × 24 = 840 mL per dose — an impossibly large volume that should trigger immediate rechecking.

✗ Unit confusion (mg vs mcg)

Misreading milligrams as micrograms or vice versa creates thousand-fold errors. Always double-check that your prescription units match your calculation units.

How to Spot This Problem Type

You'll recognize weight-based dosing problems by these key phrases:

  • "mg/kg/day" or "mg per kilogram per day" — signals weight-based calculation
  • "divided into X doses" or "X times daily" — means you need to split the total
  • "supplied as" or "concentration is" — gives you the mg/mL conversion factor
  • "how many mL" — tells you the final unit needed

These problems appear frequently on nursing exams (NCLEX) and in pharmacy school curricula, where precise dosing calculations are critical for patient safety.

The Pattern Behind This

All weight-based dosing problems follow the same three-step structure:

Weight × (mg/kg) → Daily mg
Daily mg ÷ doses/day → mg per dose
mg per dose × (mL/mg) → mL per dose

This formula generalizes to any weight-based medication where you need to find the volume per administration. The middle step (dividing by frequency) is often forgotten but crucial — it's the difference between a single dose and a dangerous overdose.

Four "What-If?" Problems

1
Different Weight
A child weighs 22 kg. The recommended dose is still 10 mg/kg/day in four equal doses. The medication is supplied at 120 mg/5 mL. How many mL per dose?
Step 1 — Calculate total daily dose

Total daily dose = 22 kg × 10 mg/kg/day = 220 mg/day

Step 2 — Find dose per administration

Per dose = 220 mg/day ÷ 4 doses/day = 55 mg/dose

Step 3 — Convert to mL

Volume = 55 mg × (5 mL/120 mg) = 275/120 = 2.29 mL

Verification

Check: 2.29 mL × 4 doses × (120 mg/5 mL) = 219.8 mg/day ≈ 220 mg/day ✓

Answer: 2.29 mL per dose

2
Different Frequency
A child weighs 14 kg. The recommended dose is 10 mg/kg/day, but divided into three equal doses instead of four. The medication is supplied at 120 mg/5 mL. How many mL per dose?
Step 1 — Calculate total daily dose

Total daily dose = 14 kg × 10 mg/kg/day = 140 mg/day

Step 2 — Divide into three doses

Per dose = 140 mg/day ÷ 3 doses/day = 46.67 mg/dose

Step 3 — Convert to mL

Volume = 46.67 mg × (5 mL/120 mg) = 233.33/120 = 1.94 mL

Verification

Check: 1.94 mL × 3 doses × (120 mg/5 mL) = 139.7 mg/day ≈ 140 mg/day ✓

Answer: 1.94 mL per dose

3
Find the Weight
A child receives 2.5 mL of medication four times daily. The medication is 120 mg/5 mL, and the prescribed dose is 10 mg/kg/day. What is the child's weight?
Step 1 — Find mg per dose

mg per dose = 2.5 mL × (120 mg/5 mL) = 60 mg/dose

Step 2 — Find total daily mg

Daily dose = 60 mg/dose × 4 doses/day = 240 mg/day

Step 3 — Calculate weight

Weight = 240 mg/day ÷ 10 mg/kg/day = 24 kg

Verification

Check: 24 kg × 10 mg/kg/day = 240 mg/day ✓

Answer: The child weighs 24 kg

4
Different Concentration
A child weighs 14 kg. The dose is 10 mg/kg/day in four equal doses. The pharmacy supplies a different concentration: 80 mg/2 mL. How many mL per dose?
Step 1 — Calculate total daily dose

Total daily dose = 14 kg × 10 mg/kg/day = 140 mg/day

Step 2 — Find dose per administration

Per dose = 140 mg/day ÷ 4 doses/day = 35 mg/dose

Step 3 — Convert using new concentration

Volume = 35 mg × (2 mL/80 mg) = 70/80 = 0.875 mL

Verification

Check: 0.875 mL × 4 doses × (80 mg/2 mL) = 140 mg/day ✓

Answer: 0.88 mL per dose

Frequently Asked Questions

How do you calculate pediatric medication doses using weight? +

Multiply the child's weight by the per-kilogram dose to get the total daily amount, then divide by the number of doses per day. In this problem: 14 kg × 10 mg/kg = 140 mg daily, then 140 mg ÷ 4 doses = 35 mg per dose.

When do you use dimensional analysis for medication dosing? +

Use dimensional analysis whenever you need to convert between different units in dosing calculations. Here we convert from mg per dose to mL per dose using the medication concentration: 35 mg/dose × (5 mL/120 mg) = 1.46 mL per dose.

Why are pediatric doses calculated by weight instead of age? +

Children of the same age can vary significantly in body size, but medication dosing is based on how the body processes drugs, which correlates better with weight than age. Weight-based dosing (mg/kg) ensures each child receives a dose proportional to their body size.

NJ
Dr. Neven Jurkovic
Mathematics Professor • 15+ years teaching experience
NJ
Neven Jurkovic, PhD

Professor of Computer Science, Palo Alto College, Alamo Colleges District, San Antonio, TX

Developer of Algebrator

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This solution was prepared with AI assistance and reviewed by Dr. Jurkovic for mathematical accuracy and pedagogical clarity.

2026-07-03