5.3 Converting Between Metric & US Customary

5.3 Converting Between Metric & US Customary

Quick Answer: To move between metric and US customary units you need a short list of bridge factors: 1 kg ≈ 2.2 lb, 1 in = 2.54 cm (exact), 1 L ≈ 1.06 qt, 1 tsp ≈ 5 mL, and 1 tbsp ≈ 15 mL. You multiply by the factor in the direction that cancels the unit you have and leaves the unit you want. Nearly every weight-based dose in nursing starts with converting the patient's weight from pounds to kilograms using 1 kg = 2.2 lb.

The Core Bridge Factors

Note that 1 in = 2.54 cm is exact by international agreement; every other factor here is approximate. For NEX problems, use 2.2 lb/kg as the standard.

Worked Example 1: 154 lb = ___ kg

Set up so pounds cancel and kilograms remain:

154 lb × (1 kg / 2.2 lb) = 154 ÷ 2.2 = 70 kg.

Check: 70 kg × 2.2 = 154 lb. ✓

This is the classic nursing starting point: drug orders like gentamicin 5 mg/kg require the weight in kg.

Worked Example 2: A child is 39 in tall. How many cm?

39 in × (2.54 cm / 1 in) = 39 × 2.54 = 99.06 cm (≈ 99 cm).

Inches cancel, centimeters remain. For nursing charting you would round to the nearest whole cm or one decimal.

Worked Example 3: 1.5 tsp of cough syrup = ___ mL

1.5 tsp × (5 mL / 1 tsp) = 7.5 mL.

This is the household-to-metric link you teach families: "give 7.5 mL using the oral syringe."

Worked Example 4: A dose of 2 tbsp = ___ mL

2 tbsp × (15 mL / 1 tbsp) = 30 mL.

Useful when a home-measured dose must be drawn into a calibrated cup.

Worked Example 5: 3 qt = ___ L

3 qt × (1 L / 1.06 qt) = 3 ÷ 1.06 = 2.83 L (≈ 2.8 L).

Going from a larger US unit to a slightly smaller metric unit, the metric number is a bit bigger than 2.5 — reasonable because a liter is slightly bigger than a quart.

Setting Up the Conversion: Step by Step

1. Write the starting value with its unit. Example: 154 lb.
2. Write the conversion factor as a fraction with the unit you have on the bottom and the unit you want on the top. Example: (1 kg / 2.2 lb).
3. Multiply. Units cancel. The surviving unit is the answer's unit. 154 × (1 / 2.2) kg = 70 kg.
4. Check direction with a sanity estimate. 1 kg is about 2 lb, so 154 lb is roughly half of 154 = 77 kg. Our answer of 70 kg is close. A 2.2× error (154 kg) would fail this sanity check immediately.
5. Round only at the end. Carry at least one extra decimal through intermediate steps, then round the final answer to the precision the problem requests.

Nursing Context: Why Direction Matters

Weight-based dosing is the single most error-prone cross-system calculation in nursing. If you are supposed to divide pounds by 2.2 to get kilograms but instead multiply, you produce a weight that is roughly 2.2 × 2.2 = 4.84 times too large, and the resulting dose can be a fatal overdose. The sanity check above ("1 kg is about 2 lb, so kg number should be about half the lb number") is the fastest way to catch this. An adult who weighs 180 lb should be about 82 kg, not 396 kg.

Height is similarly charted in cm for BMI and growth charts. A patient who is 5 ft 6 in is 66 in; 66 × 2.54 = 167.6 cm. If you accidentally divide by 2.54 you get 26 cm, an obviously absurd height for an adult — the sanity check catches it.

Common Traps

1. Multiplying when you should divide (or vice versa). The factor 2.2 is symmetric: to go kg → lb you multiply by 2.2; to go lb → kg you divide by 2.2. Write the fraction so the unwanted unit cancels — do not rely on memory of "multiply" or "divide."
2. Unit mismatch in dosage. A dose ordered as mg/kg must use kilograms. If you leave the weight in pounds, you have effectively multiplied the dose by 2.2. Always convert weight first.
3. Rounding too early. Converting 154 lb → 70.0 kg, then using 70 kg in the next step, is fine. But converting 151 lb → 68.64 kg and rounding to 69 kg before multiplying by a dose of 5 mg/kg gives 345 mg instead of the more precise 343.2 mg. In pediatrics, even a few milligrams can matter. Carry one extra decimal until the last step.
4. Confusing 1 oz with 30 mL. 1 fl oz ≈ 29.57 mL, commonly rounded to 30 mL. That rounding is acceptable for intake/output records but not for high-strength medication; use the exact 29.57 when precision matters.
5. Using 2.2 as if it were exact. 1 kg = 2.20462 lb, but for NEX and almost all nursing math, 2.2 is the accepted factor. Just do not chain several 2.2 conversions and expect an exact textbook answer — rounding drift accumulates.
6. Mixing exact and approximate factors. 1 in = 2.54 cm is exact. 1 kg ≈ 2.2 lb is approximate. When a problem asks for a precise inch-to-cm result, use 2.54; for kg-lb, use 2.2 unless the problem states otherwise.

Putting It Together: A Full Nursing Problem

A pediatric order reads: "Administer amoxicillin 40 mg/kg/day in 2 divided doses." The child weighs 55 lb. How many mg per dose?

Step 1 — Convert weight: 55 lb ÷ 2.2 = 25 kg.

Step 2 — Total daily dose: 25 kg × 40 mg/kg = 1,000 mg/day.

Step 3 — Per dose (twice a day): 1,000 ÷ 2 = 500 mg per dose.

Notice how the cross-system conversion (lb → kg) is just the first link in a chain. Get it wrong and the entire dose is wrong. The unit-cancellation method protects each step: (lb) × (kg/lb) = kg, then kg × (mg/kg) = mg, then mg ÷ 2 = mg per dose.