Serum Osmolality and Osmolar Gap Calculator

What the formula counts, and what it misses

Osmolality counts dissolved particles per kilogram of water, regardless of what they are. Plasma osmolality is normally 275 to 295 mOsm/kg, and three solutes account for almost all of it:

• Sodium and its accompanying anions, around 96 percent of the total.
• Glucose, about 5 mOsm/kg at a normal blood sugar.
• Urea, about 5 mOsm/kg at a normal renal function.

calculated osmolality = 2 × [Na⁺] + [glucose]/18 + [BUN]/2.8

The sodium is doubled because osmolality counts particles and electroneutrality forces an anion to accompany every sodium ion, mostly chloride with some bicarbonate. Doubling is a shortcut for adding those separately, and it works because they track sodium closely. One consequence worth internalising: an error of 2 mmol/L in the sodium moves the answer by 4 mOsm/kg, so sodium is the term worth reading twice.

The divisors are not arbitrary. They convert mg/dL into mmol/L and are fixed by molar mass. Glucose is 180.16 g/mol, so mg/dL divided by 18 gives mmol/L. Urea is 60.06 g/mol and contains 28.014 g of nitrogen in its two nitrogen atoms, so BUN in mg/dL divided by 2.8 gives mmol/L of urea.

Blood urea against BUN, which is where this goes wrong

This is the trap, and it is a geographical one.

• Indian and British reports print blood urea, the whole molecule.
• American reports print BUN, blood urea nitrogen, which counts only the nitrogen.

They differ by 60.06 / 28.014 = 2.144. A blood urea of 30 mg/dL is a BUN of 14 mg/dL. The formula’s divisor of 2.8 expects BUN, so feeding a whole urea straight in adds about 5 mOsm/kg that is not there, which is enough to turn a normal osmolar gap negative and hide a poisoning. The field above asks for whole urea and does the conversion visibly in the working, so you can see which number went where.

In SI units the same relation is cleaner: blood urea in mg/dL divided by 6.006 gives mmol/L, and a urea of 30 mg/dL is 5 mmol/L, the same 5 mmol/L a BUN of 14 mg/dL gives. If your report is already in mmol/L, that number goes straight into the sum with no divisor at all.

The osmolar gap

osmolar gap = measured osmolality − calculated osmolality, normally under 10 mOsm/kg. The measured value comes from an osmometer, almost always by freezing point depression, which counts every particle present. The calculated value counts only the three the formula knows about. The difference is therefore whatever is dissolved in the plasma that nobody asked for.

Causes of a raised gap, roughly in order of how much they matter:

• Toxic alcohols. Methanol and ethylene glycol. The gap is the earliest clue, appearing while the parent alcohol is still circulating and before the anion gap acidosis from its metabolites has developed. As the poisoning progresses the gap falls and the anion gap rises, so a normal gap late on does not exclude it.
• Ethanol. Much the commonest cause, and easily accounted for: divide the ethanol concentration in mg/dL by 3.7 and add it to the calculated value. A residual gap after doing so is the finding that matters.
• Isopropanol, which raises the gap with ketosis but no acidosis.
• Mannitol, glycine and sorbitol, iatrogenic and usually obvious from the chart.
• Severe hypertriglyceridaemia or paraproteinaemia, which cause pseudo hyponatraemia and a spurious gap when sodium is measured by an indirect method.

A markedly negative gap is almost never physiology. It means a data problem, and the commonest one by a wide margin is putting a whole blood urea into a field expecting BUN.

Osmolality against tonicity

This distinction is the one worth carrying away, because it decides whether a cell swells or shrinks.

An osmole only pulls water across a membrane if it cannot cross that membrane itself. Urea crosses freely and equilibrates within hours, so it raises measured osmolality on both sides equally and exerts no osmotic force. Sodium and glucose are effectively excluded from cells, so they do.

effective osmolality = 2 × [Na⁺] + [glucose]/18

Two consequences. Someone in advanced renal failure can have an osmolality of 340 mOsm/kg from urea alone and no cellular dehydration whatsoever, because their cells contain the same urea. And when chronic hyponatraemia is corrected too quickly, it is the effective osmolality that is changing, which is why the risk of osmotic demyelination tracks tonicity and not the total. The readouts above separate the two for exactly this reason.

Glucose is the exception that proves the rule. In diabetic ketoacidosis or a hyperosmolar state a glucose of 900 mg/dL contributes 50 mOsm/kg on its own, and because insulin deficiency keeps it out of cells it is fully effective, which is what drives the water out of the brain and produces the obtundation.

Common mistakes

• Comparing a calculated value with a measured one from a different draw. The gap is only meaningful when both come from the same sample, since sodium and glucose move quickly.
• Expecting the calculated and measured values to match exactly. The formula is an approximation and several versions exist. This page uses the taught form; another common one is 1.86 × sodium plus glucose over 18 plus BUN over 2.8 plus 9, which fits measured data slightly better. A few mOsm/kg of disagreement is expected, which is why the threshold sits at 10 rather than at zero.
• Forgetting to account for ethanol before calling the gap unexplained.
• Using the gap to exclude a late presenting toxic alcohol ingestion. By the time the metabolites have formed the gap has closed and the acidosis has opened.