8.5 Calculations, Conversions, and Dosage Math

Conversions You Must Memorize

Calculation items are patient-safety items. Start by locking in the conversions; most dose errors are conversion errors.

Moving down the metric ladder (g to mg to mcg) you multiply by 1000; moving up you divide by 1000. Example: 0.25 g = 250 mg = 250,000 mcg.

Temperature Conversions

Use °C = (°F − 32) × 5/9 and °F = (°C × 9/5) + 32. Normal body temperature is roughly 37°C = 98.6°F.

• Worked example: convert 101.3°F to Celsius. (101.3 − 32) = 69.3; 69.3 × 5/9 = 38.5°C.
• Worked example: convert 39°C to Fahrenheit. (39 × 9/5) = 70.2; 70.2 + 32 = 102.2°F.

The Dose Formula: Desired over Have

The workhorse formula is (Desired / Have) × Quantity, where Desired is the ordered dose, Have is the strength on hand, and Quantity is the volume or tablet count that strength comes in.

• Tablet example: The order is 500 mg; tablets are 250 mg each. (500 / 250) × 1 tab = 2 tablets.
• Liquid example: The order is 375 mg; the bottle is 125 mg per 5 mL. (375 / 125) × 5 mL = 15 mL.
• Injection example: The order is 40 mg; the vial is 80 mg per 1 mL. (40 / 80) × 1 mL = 0.5 mL.

Always check the final unit: tablets, mL, or drops. If the math gives "2," know whether that is 2 tablets or 2 mL.

Weight-Based (mg/kg) Dosing — Convert First

The most common high-stakes trap: an order written in mg per kg with the patient's weight given in pounds. You must convert pounds to kilograms before multiplying.

Worked example: An order reads 10 mg/kg for a child who weighs 44 lb. First convert: 44 lb ÷ 2.2 = 20 kg. Then 20 kg × 10 mg/kg = 200 mg. If you forgot to convert and multiplied 44 × 10 = 440 mg, you would more than double the dose — exactly the error the exam punishes.

Second example: 5 mg/kg ordered for a 66-lb child. 66 ÷ 2.2 = 30 kg; 30 × 5 = 150 mg.

Dimensional Analysis and the Safety Check

Dimensional analysis lets you cancel units to confirm you set the problem up correctly. Write the order with units, multiply by conversion fractions arranged so unwanted units cancel, and the surviving unit should be your answer's unit. If your answer comes out in the wrong unit, the setup is wrong.

Finally, a calculation that is arithmetically perfect can still be unsafe. If the order is illegible, missing a unit or route, conflicts with a documented allergy, or yields a dose far outside a plausible range, the correct CCMA action is to clarify with the prescriber before administering — never administer a suspicious order just because the math "works." Do not round too early; carry decimals until the final step.

Flow Rates, Drops, and Tablet Splitting

Though most CCMA medication work is oral, topical, or injectable, the exam may show a basic flow-rate or drop calculation. For drops, use (volume in mL × drop factor) / time in minutes = drops per minute (gtt/min). Example: 1000 mL over 8 hours (480 minutes) with a 15 gtt/mL set gives (1000 × 15) / 480 ≈ 31 gtt/min. For an mL/hr rate, divide total volume by total hours: 1000 mL / 8 hr = 125 mL/hr. With tablets, you may divide a scored tablet in half (a 0.5-tablet answer is plausible), but you cannot meaningfully split an unscored or capsule form — an answer demanding a quarter of a capsule is a clarify-the-order signal.

Leading Zeros, Trailing Zeros, and Error-Prone Notation

Medication-safety items test notation as much as arithmetic. Always use a leading zero before a decimal less than one — write 0.5 mg, never ".5 mg," because a missed decimal point reads as 5 mg, a tenfold overdose. Never use a trailing zero — write 5 mg, never "5.0 mg," because a missed decimal reads as 50 mg. These are on the Institute for Safe Medication Practices (ISMP) error-prone list along with avoiding the abbreviations U (write "units"), IU, QD/QOD, and µg (write "mcg"). The CCMA should flag an order using these dangerous abbreviations rather than guessing the intent.

Notation Quick Rules

A Worked Multi-Step Problem

Put it together. Order: 15 mg/kg/day divided into 2 equal doses for a child weighing 33 lb; suspension is 250 mg per 5 mL. Step 1, convert weight: 33 ÷ 2.2 = 15 kg. Step 2, daily dose: 15 kg × 15 mg/kg = 225 mg/day. Step 3, per dose: 225 ÷ 2 = 112.5 mg per dose. Step 4, volume per dose: (112.5 / 250) × 5 mL = 2.25 mL per dose. Notice how an early-rounding habit (calling 112.5 "110") would distort the final volume — carry the decimals. Then apply the safety overlay: 2.25 mL of a children's suspension is plausible, the weight converted correctly, and the units cancel to mL, so the setup is sound.

Had the order omitted the strength or the frequency, the right move would be to clarify before drawing the dose.