Convert amount concentration into mass concentration by following the substance and every unit. A creatinine example shows where the factor of 10,000 comes from.
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The calculation
mg/dL = µmol/L × molar mass (g/mol) ÷ 10,000
Worked example
For creatinine with molar mass 113.12 g/mol, 100 µmol/L gives 11.312 mg/L, then 1.1312 mg/dL. At the same 100 µmol/L, bilirubin with approximate molar mass 584.7 g/mol gives 5.847 mg/dL.
Use the molar mass of the correct chemical species. Micromoles and millimoles differ by 1,000. Unit conversion does not interpret a laboratory result.
Video chapters
- 0:00 — Same concentration, different mass
- 0:15 — Follow the units in three steps
- 0:33 — One liter contains ten deciliters
- 0:51 — Example: creatinine at 100 µmol/L
- 1:12 — Divide by ten, then check backward
- 1:34 — Change the substance, change the factor
- 1:55 — Read the prefix before calculating
- 2:15 — Identify → multiply → divide
Read the full transcript
One hundred micromoles per liter does not have one universal answer in milligrams per deciliter. The answer depends on the substance. A mole describes an amount of particles; a gram describes mass. To connect them, we need the substance's molar mass.
Start with micromoles per liter. A micromole is one millionth of a mole. Multiply by molar mass in grams per mole to get grams per liter, then multiply by one thousand for milligrams. Together, those two steps divide the numerical product by one thousand.
There is one more change: the volume in the denominator. One liter contains ten deciliters. The mass in each deciliter is one tenth of the mass in the full liter, assuming a uniform solution. Divide by ten again. That makes the combined divisor ten thousand.
Use creatinine with a molar mass of one hundred thirteen point one two grams per mole. Multiply one hundred by one hundred thirteen point one two. Dividing by one thousand gives eleven point three one two milligrams per liter. Keep the extra digits until the final answer.
Divide eleven point three one two by ten. The result is one point one three one two milligrams per deciliter, about one point one three. Check backward using the unrounded result: multiply by ten thousand and divide by one hundred thirteen point one two. You recover one hundred micromoles per liter.
Now keep one hundred micromoles per liter, but change the substance to bilirubin. Using approximately five hundred eighty-four point seven grams per mole gives five point eight four seven milligrams per deciliter. Equal amounts of different molecules can have different masses. Never reuse creatinine's factor for every substance.
Check the small prefix on the original result. One millimole equals one thousand micromoles. Confusing those labels changes the answer by a factor of one thousand. Also distinguish a unit conversion from a medical interpretation: the arithmetic does not say whether a laboratory result is normal.
Identify the substance and its molar mass, verify micromoles per liter, multiply, and divide by ten thousand. Keep the substance attached to the answer. For our creatinine example, one hundred micromoles per liter becomes about one point one three milligrams per deciliter.
Sources
- NIST — Handbook 130, Appendix A: exact unit relationships
- Sigma-Aldrich / USP — Creatinine molecular weight
- PubChem — Bilirubin