Every dosage calculation rests on one idea: a quantity can be rewritten in another unit by multiplying it by a conversion factor that equals 1. Because 1 g and 1,000 mg are the same amount, the fraction "1,000 mg / 1 g" equals 1. Multiplying 0.5 g by that fraction changes the unit without changing the amount: 0.5 g × 1,000 mg/1 g = 500 mg. The grams cancel (one on top, one on the bottom), leaving milligrams.

This is the core of dimensional analysis: write the starting quantity, then line up conversion factors so that each unwanted unit appears once on top and once on the bottom and cancels. Only the unit you want is left.

The metric system is the standard for medication dosing in both the United States and the Philippines. Units change by factors of 10, so conversions are decimal-point moves.

Direction rule:

• Larger unit → smaller unit: multiply (the number gets bigger). g → mg: × 1,000 (move the decimal 3 places right).
• Smaller unit → larger unit: divide (the number gets smaller). mcg → mg: ÷ 1,000 (move the decimal 3 places left).
• Sanity check: when you move to a smaller unit, you must end up with more of them.

When conversions are needed: the order and the label are in different units (order in g, tablet in mg), the weight is in pounds but the dose is per kilogram, a rate is per hour but a drip is per minute, or a client describes intake in cups or ounces.

Core conversion table (memorize)

Units that cannot be converted to mass by a general rule

• Units (insulin, heparin) and international units (vitamin D, vitamin A) are measures of biologic activity. There is no fixed "units to mg" factor; each drug is different. Write the word "units" in full.
• Milliequivalents (mEq) describe chemical combining power (potassium chloride, sodium bicarbonate). For monovalent ions such as potassium, 1 mEq = 1 mmol.
• Percent and ratio strengths are concentrations (covered in Topic 11).

Drugs commonly ordered in micrograms — where a mg/mcg slip causes a thousandfold error: levothyroxine, digoxin (often written in mg on orders and mcg on labels), fentanyl, cyanocobalamin, clonidine, and many infusions (norepinephrine, dopamine, nitroglycerin in mcg/min or mcg/kg/min).

Worked examples

Example 1 — mg to mcg. Order: digoxin 0.125 mg. The label reads 125 mcg per tablet. Are they the same?

• Set-up: 0.125 mg × 1,000 mcg/1 mg
• Units: mg cancels, mcg remains
• Answer: 125 mcg — the order equals 1 tablet.
• Recheck: larger to smaller unit, so the number should grow: 0.125 → 125. Correct.

Example 2 — mcg to mg. Levothyroxine 88 mcg. Express in mg.

• Set-up: 88 mcg × 1 mg/1,000 mcg
• Units: mcg cancels
• Answer: 0.088 mg (leading zero required).
• Recheck: 0.088 × 1,000 = 88. Correct.

Example 3 — pounds to kilograms. An adult weighs 154 lb; a child weighs 25 lb.

• Set-up: 154 lb × 1 kg/2.2 lb = 70 kg
• Set-up: 25 lb × 1 kg/2.2 lb = 11.363… kg
• Rounding: body weight is commonly rounded to tenths → 70 kg and 11.4 kg (follow facility policy; some pediatric units keep two decimals).
• Recheck: 70 × 2.2 = 154; 11.4 × 2.2 = 25.08 ≈ 25. Correct.

Example 4 — grams to mg to tablets (two-step dimensional analysis). Order: 0.3 g. Tablets are 150 mg.

• Set-up: 0.3 g × 1,000 mg/1 g × 1 tablet/150 mg
• Units: g and mg cancel, tablets remain
• Math: 0.3 × 1,000 = 300; 300 ÷ 150 = 2
• Answer: 2 tablets. Recheck: 2 × 150 mg = 300 mg = 0.3 g. Correct.

Example 5 — household to metric for intake and output. A client drank one 8-oz cup of juice and 2 tablespoons of liquid medicine.

• Juice: 8 oz × 30 mL/1 oz = 240 mL
• Medicine: 2 tbsp × 15 mL/1 tbsp = 30 mL
• Answer: 270 mL oral intake. Recheck: 240 + 30 = 270. Correct.

Example 6 — temperature. A child's temperature is 38.5 °C. Convert to °F. A second client reads 102.2 °F; convert to °C.

• 38.5 × 1.8 = 69.3; 69.3 + 32 = 101.3 °F
• 102.2 − 32 = 70.2; 70.2 ÷ 1.8 = 39 °C
• Recheck: 39 × 1.8 + 32 = 70.2 + 32 = 102.2. Correct.

In a calculation topic, the "adverse effect" is the harm caused by a wrong unit.

• Tenfold errors — a misplaced decimal point (0.5 mg read as 5 mg). Most common in children and in drugs with narrow margins (digoxin, opioids, insulin, heparin, chemotherapy).
• Thousandfold errors — mg confused with mcg. A client ordered 50 mcg fentanyl who receives 50 mg would receive a lethal dose; the reverse gives no effect.
• Weight-unit errors — a weight in pounds entered as kilograms makes every weight-based dose 2.2 times too high. Always record weight in kg only.
• Household-measure errors — kitchen teaspoons vary widely in volume, and "tsp" and "tbsp" are confused (a threefold error).
• "Units" errors — a handwritten "U" read as 0 or 4 (10U read as 100). Insulin and heparin errors are among the most harmful.

Do not use (Joint Commission "Do Not Use" list and ISMP error-prone list)

Cautions

• Do not convert units of activity (units, international units) to mg without a drug-specific factor from the label.
• Temperature conversion needs both a multiplier and an offset; checking with a quick reverse calculation catches slips.
• Keep the same unit throughout a problem; convert before entering a formula, not halfway through.
• Round only the final answer, not intermediate steps, unless the step is a body weight rounded per policy.

Listed in priority order.

1. Confirm the client's weight in kg, measured (not estimated or stated) whenever possible; recheck if the weight changes substantially or looks inconsistent with the chart.
2. Read the order and the label side by side — drug, strength, unit, and form. Circle or say aloud the unit on each.
3. Convert to the unit on the label before calculating (order 0.5 g; tablets 250 mg → work in mg).
4. Set up with units written at every step and cancel them visibly; the unit left over must be the unit you need (tablets, mL, mL/h, gtt/min).
5. Estimate first, then calculate. If you expect "about 2 tablets" and get 20, stop and recheck.
6. Recalculate independently and use an independent double check for high-alert drugs (insulin, heparin, opioids, concentrated electrolytes, pediatric doses) per policy.
7. Document in metric units with leading zeros and no trailing zeros.

• Measure liquid medicines with the oral syringe or dosing cup marked in mL that comes with the product — never a kitchen spoon.
• Know the dose in mL, not "a spoonful," and match the device to the product (devices are not interchangeable between brands or concentrations).
• Keep a written list of each medication with its strength and unit (for example, "levothyroxine 88 mcg").
• Parents should know the child's current weight in kg, because many pediatric doses depend on it.
• When a thermometer reads in °F or °C, record which scale was used before reporting a fever.

What goes wrong — patterns to recognize

• Answer too large or too small to be plausible (for example, 15 tablets or 0.01 tablet) usually means a missed conversion.
• mg vs mcg in opioids, digoxin, levothyroxine, and vasoactive infusions → thousandfold overdose or underdose.
• lb entered as kg → 2.2-fold overdose of weight-based drugs (antibiotics, anticoagulants, chemotherapy, sedatives).
• Decimal slip in pediatric doses → tenfold overdose.

If an error reaches the client: assess the client first (vital signs, level of consciousness, drug-specific signs), notify the prescriber, give the antidote if ordered (for example, naloxone for opioid overdose, protamine for heparin, dextrose for insulin-induced hypoglycemia), then report through the facility's error-reporting system. Reporting supports system fixes, not blame.

• Larger unit → smaller unit: multiply; smaller → larger: divide
• 1 g = 1,000 mg; 1 mg = 1,000 mcg; 1 L = 1,000 mL; 1 kg = 2.2 lb (kg = lb ÷ 2.2)
• Convert to the label's unit before calculating
• Leading zero always (0.5 mg); trailing zero never (5 mg, not 5.0 mg)
• Write "units" in full; write mcg, not µg; write mL, not cc
• Household measures (5 mL tsp, 15 mL tbsp, 30 mL oz, 240 mL cup) are for intake records and teaching, not for dosing
• Units and international units are activity measures — no general conversion to mg
• °F = °C × 1.8 + 32; °C = (°F − 32) ÷ 1.8
• A pound weight recorded as kg makes weight-based doses 2.2 times too high
• Round only the final answer; if the answer is implausible, recheck the conversion first