One method for every dosage problem: let the units do the work.

01 / Method

The method in four steps.

Open RN's Nursing Skills defines dimensional analysis as converting a measurement into the unit you need by multiplying it by fractions equal to 1, such as 1 tablet / 325 mg, or 1 kg / 2.2 lb. Every problem follows the same steps:

02 / Oral doses

Tablets and liquids.

Mr. D. is the fictional 72-year-old with pneumonia from our clinical skills series. His medication orders give us the examples.

Example 1 · Tablets

Order: acetaminophen 650 mg by mouth. Supplied: 325 mg tablets.
tablets = (1 tablet / 325 mg) × (650 mg / 1) = 2 tablets

Example 2 · Liquid

Order: an oral liquid medication, 200 mg. Supplied: 100 mg per 5 mL.
mL = (5 mL / 100 mg) × (200 mg / 1) = 10 mL

In both, the first fraction puts the goal unit (tablet or mL) on top, and mg cancels out diagonally. If you'd written 325 mg / 1 tablet instead, you'd be left with mg² per tablet, an impossible unit that tells you the setup is upside down.

03 / Weight-based

Weight-based doses.

Many doses are ordered per kilogram of body weight. Convert pounds to kilograms first, using 1 kg = 2.2 lb, then calculate the dose, then the volume.

Example 3 · mg/kg

Order: a medication, 5 mg/kg. Weight: 176 lb. Supplied: 100 mg/mL.
Weight: (1 kg / 2.2 lb) × 176 lb = 80 kg
Dose: 5 mg/kg × 80 kg = 400 mg
Volume: (1 mL / 100 mg) × 400 mg = 4 mL

For weight-based orders, many facilities also require you to confirm the dose falls within the drug's safe dosage range before giving it, especially for children. Open RN covers this in its "Safe Dosage Range" section.

04 / IV rates

IV pump and gravity rates.

An infusion pump is programmed in mL/hr. A gravity infusion is regulated by counting drops per minute (gtt/min), using the tubing's drop factor: macrodrip tubing delivers 10, 15, or 20 drops per mL, and microdrip tubing 60 drops per mL. The drop factor is printed on the tubing package.

Example 4 · Pump

Order: 0.9% sodium chloride 1,000 mL IV over 8 hours.
mL/hr = 1,000 mL / 8 hr = 125 mL/hr

Example 5 · Short infusion

Order: IV antibiotic in 100 mL over 30 minutes, by pump.
mL/hr = (100 mL / 30 min) × (60 min / 1 hr) = 200 mL/hr

Example 6 · Gravity

Same order as Example 4, by gravity with 15 gtt/mL tubing.
gtt/min = (15 gtt / 1 mL) × (1,000 mL / 8 hr) × (1 hr / 60 min) = 31.25 → 31 gtt/min

Example 5 is where students most often slip: the time is in minutes, but the pump needs hours. The 60 min / 1 hr fraction handles it. Leave it out and you'd program 3.3 mL/hr, a 60-fold error.

05 / Timing

Completion time.

To know when an infusion will finish, divide the volume by the rate, then add the result to the start time.

Example 7 · Finish time

1,000 mL at 125 mL/hr, started at 0900.
hours = (1 hr / 125 mL) × 1,000 mL = 8 hr → 0900 + 8 hr = 1700

06 / Rounding

Rounding rules.

Round only at the end, and follow your program's and facility's rules. Open RN's conventions:

• Adult oral liquids over 1 mL: round to the tenth (17.276 mL → 17.3 mL).
• Doses under 1 mL: round to the hundredth (0.0467 mL → 0.05 mL).
• Drops per minute: round to a whole drop, since you can't count part of a drop (20.83 → 21 gtt/min).
• Leading zeros, never trailing zeros: write 0.5 mg, never .5 mg; write 5 mg, never 5.0 mg.

07 / Safety

Safety checks before you give anything.

• Does the answer make sense? An answer of 8 tablets, 0.02 mL, or 1,250 mL/hr for a routine order is a reason to stop and recalculate. It's very likely wrong.
• Did every unit cancel? If anything other than your goal unit is left, the setup is wrong.
• Read the concentration twice. Many errors come from misreading mg/mL vs. mg per 5 mL, or mg vs. mcg.
• Use independent double checks for high-alert medications and pediatric doses, as your facility's policy requires.
• When in doubt, ask the pharmacist or your instructor before you give the dose, not after.

Keep going

Medication safety is documentation too.