Some laboratory concepts come up again and again, on the board exam, in ASCPi review, and at the bench when a result does not look right. These are the formulas worth knowing by heart, with worked examples and the caveats that matter.
Red cell indices
| Index | Formula | Typical adult range |
|---|---|---|
| MCV | Hct (%) × 10 ÷ RBC (×10¹²/L) | about 80–100 fL |
| MCH | Hgb (g/dL) × 10 ÷ RBC (×10¹²/L) | about 27–33 pg |
| MCHC | Hgb (g/dL) × 100 ÷ Hct (%) | about 32–36 g/dL |
Worked example: Hgb 12 g/dL, Hct 36%, RBC 4.0 ×10¹²/L. MCV = 36 × 10 ÷ 4.0 = 90 fL; MCH = 12 × 10 ÷ 4.0 = 30 pg; MCHC = 12 × 100 ÷ 36 = 33.3 g/dL.
Bench tip: an MCHC well above 36 g/dL is a red flag for a sample or instrument problem, such as lipemia, cold agglutinins or hemolysis, more often than true disease (spherocytosis aside). Investigate before releasing.
Rule of three (for normocytic, normochromic samples): Hgb × 3 ≈ Hct. A big mismatch suggests an error.
Anion gap
AG = (Na⁺ + K⁺) − (Cl⁻ + HCO₃⁻). Many laboratories omit potassium: Na⁺ − (Cl⁻ + HCO₃⁻). Reference ranges depend on the method and whether K⁺ is included, commonly around 4–12 mmol/L without potassium. Low albumin lowers the anion gap, so interpret it alongside albumin.
Example: Na 140, Cl 104, HCO₃ 24 → AG = 140 − 128 = 12 mmol/L.
Calculated LDL cholesterol (Friedewald)
LDL-C = Total cholesterol − HDL-C − (Triglycerides ÷ 5), in mg/dL. In SI units (mmol/L), use TG ÷ 2.2.
Caveat: the Friedewald equation is not valid when triglycerides are high (commonly ≥400 mg/dL, or ≥4.5 mmol/L) or in non-fasting samples with very high TG. It also tends to underestimate LDL-C when triglycerides are above about 150 mg/dL. Direct LDL measurement or newer equations are preferred in those cases.
Calculated serum osmolality and the osmolal gap
Calculated Osm = 2 × Na⁺ + (BUN ÷ 2.8) + (Glucose ÷ 18), with Na in mmol/L and BUN and glucose in mg/dL. Reference range is roughly 275–295 mOsm/kg.
Osmolal gap = Measured − Calculated. A gap above about 10 suggests unmeasured osmoles such as ethanol, methanol, ethylene glycol or mannitol, which is useful in suspected poisoning.
QC statistics in one line each
- CV (%) = SD ÷ mean × 100
- Sigma = (TEa − |bias|) ÷ CV
- 1-2s is a warning; 1-3s and R-4s catch random error; 2-2s, 4-1s and 10x catch systematic error.
Memorize the formula, but understand the caveat. The caveat is what the patient needs you to know.
How to use these notes
Write each formula from memory once a day for a week, then solve one worked example. When you see real results at the bench, recalculate them, because nothing makes a formula stick like catching an error with it.
References
- The Blood Project, RBC indices: thebloodproject.com
- MedlinePlus, Red blood cell (RBC) indices: medlineplus.gov
- NCBI Bookshelf (StatPearls), Anion Gap: ncbi.nlm.nih.gov
- MSD Manuals, Friedewald equation (SI units): msdmanuals.com
- American College of Cardiology, accuracy of Friedewald LDL-C calculation: acc.org
- Serum osmolality formula review, PMC: pmc.ncbi.nlm.nih.gov
- Westgard QC, Westgard Sigma Rules: westgard.com
