2.2 Toxicologic Calculations: Doses, Concentrations, and Conversions
Key Takeaways
- Every liquid concentration can be converted with one relationship: a 1% solution contains 10 mg of active ingredient per milliliter, so percent times 10 equals mg/mL.
- Weight-based dose is total milligrams of active ingredient divided by weight in kilograms; pounds are converted by dividing by 2.2, and a teaspoon is 5 mL while a tablespoon is 15 mL.
- Working backward from a toxic threshold answers the common caller question: threshold dose in mg/kg multiplied by weight, divided by the product strength, gives the number of tablets or milliliters needed to reach danger.
- Combination products require a separate calculation for every active ingredient, and elemental content must be used for iron, calcium, and fluoride rather than salt weight.
- Estimating the maximum possible amount, then rounding against the patient, keeps a calculation error on the safe side of the disposition.
A dose is the difference between reassurance and an ambulance. The CSPI blueprint devotes a full content area to calculations, and the arithmetic is always the same: convert the product into milligrams of active ingredient, divide by kilograms of patient, and compare the result with a published threshold.
The Conversions Worth Memorizing
| Conversion | Relationship | Example |
|---|---|---|
| Percent to mg/mL | 1% = 10 mg/mL | 2.5% permethrin = 25 mg/mL |
| Percent to mg/g | 1% = 10 mg/g | 5% benzocaine gel = 50 mg/g |
| Household volume | 1 teaspoon = 5 mL; 1 tablespoon = 15 mL; 1 fluid ounce = 30 mL | "Two teaspoons" = 10 mL |
| Weight | 1 kg = 2.2 lb | 33 lb = 15 kg |
| Child swallow | Young child about 5 mL; older child 10 mL; adult 15 mL | Unwitnessed "sip" of a 22 kg child = 10 mL |
| Parts per million | 1 ppm = 1 mg/L (dilute aqueous) | 0.5 ppm fluoride water is 0.5 mg/L |
| Metric prefixes | 1 g = 1,000 mg; 1 mg = 1,000 mcg | 0.25 mg digoxin = 250 mcg |
Elemental Content
Some products must be expressed as the element, not the salt.
| Product | Elemental Fraction | 1 Tablet or 1 mL Contains |
|---|---|---|
| Ferrous sulfate 325 mg | 20% iron | 65 mg elemental iron |
| Ferrous gluconate 325 mg | 12% iron | 39 mg elemental iron |
| Ferrous fumarate 325 mg | 33% iron | 107 mg elemental iron |
| Carbonyl iron | About 100% iron | Label states elemental iron |
| Sodium fluoride 1.1 mg tablet | 45% fluoride | 0.5 mg fluoride ion |
Pattern 1: Solid Dose, Known Count
Case. A 3-year-old weighing 15 kg is found with an open bottle of ibuprofen 200 mg tablets. The bottle held 40 tablets; 22 remain and none are on the floor.
- Maximum missing: 40 - 22 = 18 tablets.
- Total drug: 18 x 200 mg = 3,600 mg.
- Weight-based dose: 3,600 mg / 15 kg = 240 mg/kg.
- Interpretation: above the 100 mg/kg symptomatic threshold and in the range where gastrointestinal effects, drowsiness, and monitoring of kidney function are expected, so this child is referred.
Pattern 2: Liquid or Gel Dose from a Concentration
Case. A 10 kg toddler mouths a 2% chlorhexidine skin cleanser and the caller estimates one teaspoon.
- Concentration: 2% = 20 mg/mL.
- Volume: 1 teaspoon = 5 mL.
- Total: 20 mg/mL x 5 mL = 100 mg.
- Dose: 100 mg / 10 kg = 10 mg/kg.
Case. A 22 kg child drinks an unknown amount of children's acetaminophen suspension, 160 mg per 5 mL. The 4-ounce (120 mL) bottle is empty and was full yesterday except for two doses of 10 mL each.
- Volume missing: 120 - 20 = 100 mL.
- Concentration: 160 mg / 5 mL = 32 mg/mL.
- Total: 32 mg/mL x 100 mL = 3,200 mg.
- Dose: 3,200 mg / 22 kg = 145 mg/kg, just under the 150 mg/kg acute threshold, which still warrants a 4-hour serum concentration because the volume estimate is soft.
Rounding rule: when an estimate is uncertain, round the amount up and the weight down. The calculation should err toward referral, never away from it.
Pattern 3: Back-Calculating to a Toxic Threshold
Callers rarely know the amount; they know the container. So invert the arithmetic: how much would it take to matter?
Case. A 12 kg toddler may have chewed adult ibuprofen 200 mg tablets. The symptomatic threshold is about 100 mg/kg.
- Needed: (100 mg/kg x 12 kg) / 200 mg = 6 tablets.
- If the bottle is intact except for one or two tablets, the exposure is below the threshold, which supports home observation for an asymptomatic child.
Case. A 14 kg child may have swallowed a 0.1 mg clonidine tablet. Here the threshold is not a mg/kg number but a rule: a single tablet can cause coma, bradycardia, and apnea in a toddler. The correct calculation is recognition, not arithmetic - every credible exposure goes to the hospital.
Case. Oil of wintergreen is 98% methyl salicylate, and 1 mL is roughly equivalent to 1.4 g of aspirin.
- One teaspoon (5 mL) is about 7,000 mg of salicylate.
- In a 14 kg child that is 500 mg/kg, far above the 150 mg/kg threshold for serious salicylate toxicity. A single swallow is a medical emergency.
Pattern 4: Combination Products
Every active ingredient needs its own calculation, and the most dangerous ingredient sets the disposition.
Case. A 52 kg adolescent swallows 48 caplets of a cold product containing acetaminophen 325 mg, dextromethorphan 10 mg, phenylephrine 5 mg, and guaifenesin 200 mg.
| Ingredient | Total | mg/kg | Interpretation |
|---|---|---|---|
| Acetaminophen | 15,600 mg | 300 | Far above 150 mg/kg; 4-hour level and acetylcysteine |
| Dextromethorphan | 480 mg | 9.2 | Dissociative effects, agitation, serotonergic risk |
| Phenylephrine | 240 mg | 4.6 | Hypertension with reflex bradycardia |
| Guaifenesin | 9,600 mg | 185 | Vomiting; low intrinsic toxicity |
The acetaminophen number drives management, and the intentional nature of the ingestion makes hospital referral mandatory regardless of dose.
Pattern 5: Infusions and Rates
Bedside consultations often require rate arithmetic.
Case. High-dose insulin for calcium channel blocker shock in a 70 kg patient: a 1 unit/kg bolus is 70 units, and 1 unit/kg/hour is 70 units/hour.
Case. Acetylcysteine bag two: 50 mg/kg over 4 hours in an 80 kg patient = 4,000 mg over 4 hours = 1,000 mg/hour.
Case. Sodium bicarbonate infusion: 150 mEq in 1 L of 5% dextrose in water, run at 1.5 to 2 times maintenance. For a 70 kg adult, maintenance is about 110 mL/hour, so the infusion runs at roughly 165 to 220 mL/hour.
Sanity Checks Before You Quote a Number
- Does the unit make sense? A pediatric dose in grams per kilogram is almost always an error of 1,000.
- Is the weight real? Convert pounds to kilograms once, out loud, and confirm it with the caller.
- Did you use elemental content? Iron, fluoride, and calcium are reported as the element.
- Did you use the maximum credible amount? Not the caller's best guess.
- Does the answer match the clinical picture? A calculated non-toxic dose in a symptomatic patient means the calculation, the product, or the history is wrong.
A 15 kg child may have swallowed a mouthful of a 4% lidocaine topical solution. The caller estimates 5 mL. How much lidocaine did the child receive, and how is that expressed per kilogram?
A 10 kg toddler is reported to have chewed part of a 325 mg ferrous sulfate tablet. Assuming one whole tablet was swallowed, what is the elemental iron dose, and what does it imply?
A caller asks how many of her 500 mg acetaminophen tablets it would take to be dangerous for her 20 kg child. Using the 150 mg/kg acute threshold, what is the answer?
A 44 lb child drank an unknown amount of a 1% permethrin lice treatment. The bottle contained 60 mL and roughly half is missing. What is the approximate weight-based dose?