← Common Core coursesBMS 1110 · Applied Mathematics and Medical Biostatistics
BMS 1110 · Common Core (Tronc commun)Section 2.3 · Measurement, ratios and conversions
Section 8 of 30

Pounds, kilograms and body weight

Convert a body weight between pounds and kilograms, explain why an order written in mg/kg demands kilograms, and record the measured weight that makes the dose safe.

New to this course? How each section works
  1. Learn gives you one short idea at a time. Each idea starts with a single sentence, then explains it, gives an example, and asks you a small question you can answer straight away.
  2. Explore shows a diagram of the same ideas. Click the numbered parts to read what each one is.
  3. Check asks a few questions. Answer them all correctly to finish the section and unlock the next one.
  4. “Go deeper” is optional. It adds mechanism and extra detail for when you are ready — nothing you need for the checks is hidden there.
Why this matters

A weight-based order is a promise: the prescriber has said “give this many milligrams for every kilogram the patient weighs”. That promise can only be kept if the nurse knows the weight in kilograms. Many patients, families and older charts still speak in pounds, so a beginner who cannot convert pounds to kilograms — or who converts and then uses the wrong number — will give a dose that is wrong by a large factor while every step of the arithmetic looks perfectly reasonable.

What you need to know first

You need division and multiplication of whole numbers and decimals, which you met in Units 1 and 2. If dividing by 2.2 feels awkward, that is expected — the tutorials below do it one small step at a time and show you how to check the answer by going back the other way.

Words to know (5)
Pound (lb)
A unit of mass still used for body weight on many scales and in many patients’ own descriptions. One pound is a little less than half a kilogram. A patient says “I weigh 154 pounds.” The 154 is a number of pounds, written 154 lb.
Kilogram (kg)
The metric base unit of mass and the unit that medication orders written per kilogram expect. A kilogram is the heavier unit, so the kilogram number for a patient is always smaller than the pound number. A 70 kg adult weighs 154 lb on a pound scale. Same body, two numbers.
Body weight
The mass of the patient, measured on a scale. It is one physical quantity, even though it can be reported in more than one unit. The body weight is what the scale shows; the unit is only the name we give the number.
Conversion factor
The number that links two units of the same quantity. Here the factor is 2.2, because one kilogram contains about 2.2 pounds. It is a rounded value, not a definition. Using the factor: 44 lb ÷ 2.2 = 20 kg, and back again 20 kg × 2.2 = 44 lb.
Weight-based order (mg/kg)
A prescription that gives the dose for every kilogram of the patient’s weight. The unit “per kg” is a built-in demand that the weight be expressed in kilograms. “Give 15 mg/kg” means a 20 kg child receives 15 × 20 = 300 mg.
One idea at a timeIdea 1 / 5

In one sentence A pound and a kilogram both name the same physical property — body weight — but they are different sizes, so the same patient has one number in pounds and a smaller number in kilograms.

One body weight, two unit names

Body weight is a single quantity: the mass of the patient sitting on the scale. The unit is simply the name we attach to the number. A pound, written lb, is the unit many hospital scales, many older charts and most patients still use in everyday speech. A kilogram, written kg, is the metric base unit and the unit the rest of the hospital uses for medication. Because these two units are different sizes, the same patient produces two different numbers. One kilogram is heavier than one pound, so the kilogram number is always the smaller of the two. Nothing about the patient has changed between the two readings; only the counting unit has changed. This matters clinically because a weight-based order names its unit, and the number you substitute must be measured in that same unit.

For example

A ward scale set to pounds prints 154 lb for a patient. The same patient on a metric scale reads 70 kg. Measure once, and be sure which name the scale is using.

Pause and check yourself

A patient weighs 44 lb. Will the kilogram number be larger or smaller than 44, and why?

Show the answer

Smaller. A kilogram is heavier than a pound, so we need fewer of them to describe the same weight. 44 lb ÷ 2.2 = 20 kg, and 20 is smaller than 44.

Read detailed explanations
What 2.2 really stands for, and the discrepancy it hides

The factor 2.2 is a rounded value, and knowing where it comes from turns it from a chant into a measurement. The international avoirdupois pound is defined as exactly 0.45359237 kg, so one kilogram equals 1 ÷ 0.45359237 ≈ 2.20462262 lb. Using 2.2 therefore introduces a small systematic discrepancy: 70 kg × 2.2 = 154.0 lb, while the exact computation gives about 154.32 lb, roughly 0.2 % low. That tiny bias propagates into every milligram scaled from the weight. For ordinary adult body-weight dosing the discrepancy sits far inside clinical tolerance, which is precisely why the supplied notes can offer 2.2 as a convenient working estimate. It is not, however, a definition, and no clinician should treat the final decimal as meaningful. Laboratory metrology separates accuracy — closeness to the true value — from precision, the repeatability of a reading. A conversion factor carries its own uncertainty, and a scale carries another. When the drug has a narrow therapeutic index, or the patient is a small infant whose absolute dose is measured in fractions of a milligram, a percentage bias that is negligible in an adult can become clinically relevant. Some practitioners therefore use 2.205 or divide by the reciprocal 0.454 to reduce that bias. The reverse factor deserves the same care: one pound is approximately 0.454 kg. Whichever figure you adopt, state it, use it consistently, and never let a stated precision outrun the measurement behind it.

Weighing the patient: the number on the chart is a measurement, not a memory

Because the dose is proportional to the weight, the credibility of the weight is the credibility of the dose. A usable weight comes from a calibrated instrument and a defined procedure. Standing, chair and bed scales each carry their own technique: the patient centred on the platform, feet bare, heavy outer clothing removed, the reading taken at eye level, and the instrument zeroed beforehand. Body mass genuinely fluctuates: one litre of retained fluid adds about one kilogram, so peripheral oedema, ascites and intravenous infusions all inflate the reading, while amputations, plaster casts and dehydration deflate it. Some patients exceed the capacity of an ordinary floor scale, and a bed or chair scale has to be used instead. Documentation must carry the unit, the date and, where it exists, the instrument; a pound reading entered without a unit is not a weight at all. The defensible rule is blunt: for any mg/kg order, weigh the patient, write kilograms, and if a pound reading is all you have, convert it and mark the conversion on the chart.

The silent error: how a wrong unit stays plausible

A wrong weight unit does not announce itself, and that is what makes it dangerous. Suppose a nurse multiplies 6 mg/kg by 154, the pounds figure, and obtains 924 mg. Every keystroke is correct; the product is a plausible-looking quantity; nothing visibly fails. Contrast that with a misplaced decimal in a dilution, which usually produces an absurd volume and provokes immediate suspicion. The reason the unit error hides is that the notation mg/kg encodes a silent instruction: “for each kilogram”. The multiplication is valid only when the second factor genuinely is a number of kilograms, and dimensional analysis is the instrument that makes the hidden instruction visible, because pounds refuse to cancel with the kilograms in the denominator and the surviving unit betrays the mistake. Three separate failures can masquerade as one good number on a chart: the wrong unit, a measurement of the wrong age, and an unmeasured round-number guess. Independent double-checking — two nurses calculating separately and comparing — catches all three only if each checker starts from the source measurement rather than from the other’s arithmetic. A useful cross-check is a clinical benchmark: does the answer fall inside the range you would expect for this drug and this patient? Many medications behave proportionally, so doubling the weight doubles the dose; others do not, and a loading dose may scale with weight while maintenance dosing depends on clearance and volume of distribution instead. Recognising that difference stops a nurse from assuming that every dose must move with the weight. The safest habit remains cheap and unglamorous: convert, write the unit, reverse the conversion, and compare with a reference range before the syringe moves.

Explore the diagram

Look at the whole drawing first. Then select one numbered part and connect it to the idea you just read.

Pounds, kilograms and body weight

A four-panel teaching plate for weight conversion. The first panel shows one body weight carrying two unit names; the second maps the conversion in both directions with the rule kg = lb ÷ 2.2 and its reverse; the third walks the 44 lb → 20 kg → 300 mg chain that a mg/kg order requires; the fourth states the warning about stated and remembered weights.

New to diagrams? Read this first
  1. Look at the whole drawing once without clicking anything. Ask yourself only: what kind of picture is this (a comparison, a route, a sequence, a table)?
  2. Press Play, or use the arrows, to move through the numbered parts in order. The drawing stays still; only the highlight moves.
  3. Click a number, or its name in the list below, to read what that part is and why it matters. Use “Hide labels” when you want to test your memory.
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01 / 4One weight, two unit names

Pounds, kilograms and body weightA four-panel teaching plate for weight conversion. The first panel shows one body weight carrying two unit names; the second maps the conversion in both directions with the rule kg = lb ÷ 2.2 and its reverse; the third walks the 44 lb → 20 kg → 300 mg chain that a mg/kg order requires; the fourth states the warning about stated and remembered weights.One body weight, two unit namesScale set to pounds → reads 154 lbScale set to kilograms → reads 70 kgSame patient, same body; only the unit changed.1 kg ≈ 2.2 lb — a rounded factor, not a definition.Convert in both directionsweight in lbpoundsweight in kgkilograms÷ 2.2× 2.2kg = lb ÷ 2.2 and lb = kg × 2.2.44 lb ÷ 2.2 = 20 kg 154 lb ÷ 2.2 = 70 kgCheck by reversing: 20 kg × 2.2 = 44 lb.A mg/kg order only accepts kilogramsOrder: 15 mg/kg Measured weight: 44 lb44 lbpounds÷ 2.2the factor20 kgkilogramsdose = 15 mg/kg × 20 kg = 300 mgkg cancels kg → the answer is left in mg.Never dose from a stated or remembered weight“About 150 pounds” is not a measurement.Dose from the weight measured on the scale.Wrong unit → wrong dose, with no arithmetic warning.

If the drawing is wider than this panel, scroll it sideways. Labels stay readable; the numbered explanations below show the same ideas.

One weight, two unit names

A pound and a kilogram name the same physical property, body weight, in units of different size. The patient on the scale has one mass; the number attached to it depends on the unit the scale is set to. Because a kilogram is heavier than a pound, the kilogram number is always the smaller of the two: the 154 lb reading is the same body as the 70 kg reading. The unit is a name for the number, never a second patient.

Schematic teaching plate, not drawn to scale. The equal-size boxes show the order of the moves, not the relative size of the units; remember that one kilogram is heavier than one pound, so the kilogram number is always the smaller number.

Key points to remember

  • A pound and a kilogram name the same body weight in different-sized units; the kilogram number is always the smaller one.
  • weight in kilograms = weight in pounds ÷ 2.2, and weight in pounds = weight in kilograms × 2.2.
  • 2.2 is a rounded conversion factor, not a definition: the multiplication is a routine estimate, good for body weight and never exact.
  • A mg/kg order needs kilograms because kg must cancel with kg; substituting pounds leaves a meaningless unit and a dose wrong by a large factor.
  • Round a converted weight once, at the end of the conversion, and dose only from a weight that was measured and documented with its unit and date.
Go deeper

Worked example

From pounds on the chart to milligrams in the syringe. An order reads “6 mg/kg”. The scale in the room is set to pounds and shows 154 lb. The nurse wants the dose in milligrams, and wants to be sure the conversion is right before drawing anything up.

  1. Read the unit of the order first. “6 mg/kg” is written per kilogram, so the weight must reach the calculation in kilograms.
  2. Convert the measured weight. 154 lb ÷ 2.2 = 70 kg. Division is used because kilograms are the heavier unit.
  3. Check the conversion by reversing it. 70 kg × 2.2 = 154 lb, which matches the scale exactly, so the conversion stands.
  4. Apply the order to the kilogram weight. Dose = 6 mg/kg × 70 kg = 420 mg. The kilograms cancel and milligrams remain.
  5. Sense-check the size of the answer. 6 mg for each of 70 kilograms is 6 × 70 = 420 mg, and that dose is consistent with the order; had the pounds figure been used as if it were kilograms, the answer would have been 924 mg.

The routine is always the same four moves: read the unit on the order, convert the measured weight into that unit, check the conversion by reversing it, then multiply. The conversion factor 2.2 is a rounded estimate, so the final dose is a carefully bounded estimate too — good enough for body weight, and never a licence to skip the check.

Tutorial 1 — 44 lb into a mg/kg order

A child on the paediatric ward is ordered 15 mg/kg of a liquid medicine. The only weight on the chart is 44 lb, recorded by a scale that was set to pounds. Work out the child’s weight in kilograms and then the dose in milligrams, checking the conversion on the way.

Rule used: The rule, stated with its units before it is used: weight in kilograms = weight in pounds ÷ 2.2, and then dose in milligrams = ordered dose in mg/kg × weight in kilograms. The 2.2 is the rounded number of pounds in one kilogram.

  1. Write down the two quantities the problem gives you, each with its unit.

    Reveal this step

    The measured weight is 44 lb, and the order is 15 mg/kg. Writing the units down first is what stops the two systems being mixed later.

  2. The order is written per kilogram. What unit must the weight be in before you multiply, and what tells you so?

    Reveal the answer

    Kilograms. The unit mg/kg carries “per kg” inside it, so the kilogram must cancel with the kilogram of the weight and leave plain milligrams. Pounds would leave a meaningless unit and a wrong dose.

  3. Convert the weight. Divide the pounds by the conversion factor and keep the unit on the answer.

    Reveal this step

    44 lb ÷ 2.2 = 20 kg. Asking “how many groups of 2.2 pounds are there in 44 pounds?” gives 20 groups, so the child weighs 20 kg.

  4. Before using 20 kg, how can you check the conversion without looking up the answer?

    Reveal the answer

    Multiply back: 20 kg × 2.2 = 44 lb, which returns the original measurement, so the conversion is consistent. A second check is size: a kilogram is heavier, so the kilogram number must be smaller than 44.

  5. Now apply the order: multiply the ordered dose by the weight in kilograms.

    Reveal this step

    Dose = 15 mg/kg × 20 kg = 300 mg. The kilograms cancel, leaving milligrams, which is the unit the medicine is measured in.

  6. What would the dose have been if a hurried colleague had used 44 as the number of kilograms? Is the mistake visible in the arithmetic?

    Reveal the answer

    The colleague would compute 15 × 44 = 660 mg, more than double the correct 300 mg. Nothing in the multiplication looks wrong, which is exactly why the unit check, and not the arithmetic, is what protects the patient.

Answer: The child weighs 20 kg, and the ordered dose of 15 mg/kg works out to 300 mg.

Keep this habit: Read the unit on the order before you touch the numbers, convert the measured weight into that unit, check the conversion by multiplying back, and only then calculate. Remember that 2.2 is a rounded factor: the result is a sound estimate for a body weight, not an exact physical constant.

Tutorial 2 — checking a colleague’s conversion

A colleague has written on the worksheet: “patient 154 lb = 80 kg”, and has calculated a dose of 240 mg from an order of 3 mg/kg. Before the medicine is given, check the conversion and the dose by converting back.

Rule used: The rule used for checking: weight in pounds = weight in kilograms × 2.2. If multiplying the claimed kilograms by 2.2 does not return the original pounds, the conversion is wrong and the dose built on it must be recalculated.

  1. Write the colleague’s claim as two quantities with units, so the claim itself is visible.

    Reveal this step

    The measured weight is 154 lb. The colleague claims this equals 80 kg, and from that figure calculates 3 mg/kg × 80 kg = 240 mg.

  2. Without dividing anything yet, is 80 kg plausible for 154 lb? Estimate in your head first.

    Reveal the answer

    80 kg × 2.2 is about 176 lb, well above 154 lb, so 80 kg is too heavy. Since a kilogram is the heavier unit, the correct kilogram number must be smaller than 80.

  3. Reverse the colleague’s conversion exactly: multiply the claimed kilograms by 2.2.

    Reveal this step

    80 kg × 2.2 = 176 lb. The patient does not weigh 176 lb, so the claim of 80 kg is off by 22 lb — the conversion is wrong, not merely imprecise.

  4. Do the conversion correctly: divide the measured pounds by 2.2.

    Reveal this step

    154 lb ÷ 2.2 = 70 kg. This is the weight to use for the order.

  5. Check your own conversion in the opposite direction. Does it return the measurement, and what does that tell you?

    Reveal the answer

    70 kg × 2.2 = 154 lb, exactly the number on the scale. A conversion that survives the reverse operation is consistent, and this is the check to run every time before a dose is calculated.

  6. Compare the two doses. How much would the colleague’s weight have over-dosed the patient, and why does the size of the gap matter?

    Reveal the answer

    The correct dose is 3 mg/kg × 70 kg = 210 mg. The colleague’s 80 kg gives 240 mg, which is 30 mg too much — about 14 % high. For a medicine with a narrow safety margin, a 14 % overdose can cause harm, so the conversion is a safety step, not a formality.

Answer: The correct weight is 70 kg and the correct dose is 210 mg; the colleague’s figure would have given 240 mg, a 30 mg overdose.

Keep this habit: Convert back to check every conversion. If the reverse operation does not return the weight you started with, the figure is wrong, however confident the person who wrote it. Checking by reversing takes seconds and catches the errors that arithmetic alone never reveals.

Now you try

Attempt each one on paper first. Write the formula, substitute the numbers, then check the unit of your answer.

  1. A child weighs 88 lb. The order reads 5 mg/kg. Convert the weight to kilograms, state the dose in milligrams, and show the check that proves your conversion.

    Hint

    Read the unit of the order first, so you know which unit the weight must be in. Then divide by 2.2, and multiply by 2.2 to check.

    Show the worked answer

    The order is per kilogram, so the weight must be in kilograms. 88 lb ÷ 2.2 = 40 kg. Check: 40 × 2.2 = 88 lb, which matches. Dose = 5 mg/kg × 40 kg = 200 mg. The kilograms cancel and leave milligrams.

  2. An adult weighs 35 kg. Convert the weight to pounds, then decide whether a colleague’s note of “60 lb” for this patient is acceptable or must be queried.

    Hint

    Going from kilograms to pounds means multiplying, because you are turning heavy units into light ones. A weight of 35 kg must come out clearly heavier than 35 lb.

    Show the worked answer

    35 kg × 2.2 = 77 lb, so the patient weighs about 77 lb. The colleague’s 60 lb would correspond to 60 ÷ 2.2 ≈ 27.3 kg, roughly 8 kg lighter than the patient. The note is wrong and must be queried before any mg/kg dose is calculated from it.

  3. A patient weighs 45 lb. An order reads 10 mg/kg. Round the converted weight to one decimal place, calculate the dose, and explain what would change if the weight were rounded to a whole kilogram first.

    Hint

    45 ÷ 2.2 does not stop neatly. Round once, at the end of the conversion, then multiply — do not round the dose after that.

    Show the worked answer

    45 lb ÷ 2.2 = 20.4545… kg, recorded as 20.5 kg. Dose = 10 mg/kg × 20.5 kg = 205 mg. If the weight were rounded to 20 kg first, the dose would be 200 mg, so early rounding would lose 5 mg and understate the dose by about 2.4 %.

Common misconception

Many beginners treat 2.2 as a definition, in the same category as 60 minutes in an hour, and therefore believe the conversion is exact and the resulting dose is exact too. It is not. One kilogram equals about 2.2046 pounds, so 2.2 is a rounded teaching estimate. The same beginners often divide when they should multiply, or keep the pounds number and use it as if it were kilograms, because the two numbers look like ordinary quantities once the units are out of sight. The habit that prevents both errors is to write the unit on every line and to run the reverse conversion as a check: 70 kg × 2.2 = 154 lb confirms 154 lb ÷ 2.2 = 70 kg, and no such check rescues a pounds figure used directly in a mg/kg order.

Check your reasoning

Explain, in your own words, why the unit attached to a patient’s weight can change the dose even when the arithmetic is perfect, and describe the two habits you will use to keep the unit under control.

Reveal an answer

A mg/kg order is a rule about kilograms: it says how many milligrams to give for each kilogram. If the number substituted is a number of pounds, then the calculation is answering a different question from the one the prescriber asked, and the milligrams that come out are wrong by roughly a factor of two, while the multiplication itself remains flawless. The two habits are: write the unit on every line so the kilogram can be seen cancelling, and always check a conversion by running it backwards. Together they catch both the wrong-unit error and the division-versus-multiplication error before the dose reaches the patient.

Where this comes from

  • BMS 1110 Applied Mathematics and Medical Biostatistics lecture notes (supplied) · Chapter 1, section 1.5 “Pounds and Kilograms”, lines 394–397: when a dose is prescribed in mg/kg the patient’s weight should be expressed in kilograms; the conversion kg = lb ÷ 2.2; and the two worked examples 44 lb ÷ 2.2 = 20 kg and 154 lb ÷ 2.2 = 70 kg.
  • Beyond the supplied notes: the exact value behind 2.2 and the status of the estimate · The supplied notes give 2.2 without saying that it is rounded. The international avoirdupois pound as exactly 0.45359237 kg, the resulting exact value 1 kg ≈ 2.20462 lb, the associated 0.2 % discrepancy, and the distinction between accuracy and precision in metrology are standard measurement science that the notes assume rather than teach.
  • Beyond the supplied notes: weighing, documentation and unit analysis · The supplied notes say only that the weight should be in kilograms. The weight-record procedure (calibrated scale, fixed hour, baseline on admission, conditions such as oedema, ascites, casts and amputation), the requirement to document the unit and date, and dimensional analysis as the defence against substituting a pounds figure into a mg/kg order are standard nursing practice added here.
  • Beyond the supplied notes: Note on the course code · The supplied cover page reads “Course Number: BMS 110”. The curriculum catalogue in this project records “BMS 1110”; the catalogue is treated as authoritative and the notes’ cover value is retained here for provenance.

Lesson progress is saved on this device for the current learner. Practice answers stay separate and are not stored.

About this course and its sources

Bilingual lessons organised from the supplied BMS 1110 Applied Mathematics and Medical Biostatistics lecture notes (Mr. Ebangan Prosper Achuanoh). Diagrams are original educational schematics; sections that go beyond the supplied notes say so in their sources. Mathematics, clinical and French-language review are pending.