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MasterMath

Serum Osmolality Calculator

Calculated serum osmolality from sodium, glucose and blood urea nitrogen, plus the osmolal gap if you also have the laboratory's measured value.

Calculated osmolality

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Calculated osmolality—
Osmolal gap—
Twice the sodium alone—
Glucose contributes—
Urea contributes—
Usual range—

How this was worked out

    Indicative result. The osmolal gap is a laboratory finding interpreted within the full clinical picture. It is not a toxicology screen on its own.

    The formula

    Osm = 2 × Na + glucose/18 + BUN/2.8

    Where it comes from

    Sodium and its accompanying anion account for most of plasma osmolality, which is why the formula starts by doubling it. Glucose and urea contribute their share, divided by 18 and by 2.8 respectively to convert from milligrams per decilitre to millimoles per litre, the unit in which the three terms add up. Normally urea contributes little, but in renal failure it can contribute a great deal.

    How to work it out by hand

    1. Multiply the sodium by two
    2. Divide the glucose in mg/dl by 18
    3. Divide the blood urea nitrogen in mg/dl by 2.8
    4. Add the three terms

    What is worth knowing

    The osmolal gap is the difference between what the laboratory measures and what the formula predicts, and it is normally below ten. A widened gap means something osmotically active is in the blood that the formula does not account for, and that is where methanol, ethylene glycol, isopropyl alcohol or ethanol get looked for. Watch the unit: the formula gives osmolarity in mOsm per litre of plasma while the laboratory measures osmolality in mOsm per kilo of water; they are not quite the same, even though they get compared in practice.

    Frequently asked questions

    What range is normal?

    Around 275 to 295 mOsm/l in most laboratories, though each one publishes its own.

    What does a high osmolal gap mean?

    That something osmotically active is in the blood that the formula does not count: toxic alcohols, ethanol or mannitol among others.

    Are osmolarity and osmolality the same?

    No. One is per litre of plasma and the other per kilo of water. They get compared in practice, but they are not identical.

    Why is glucose divided by 18?

    To go from mg/dl to mmol/l, the unit the three terms add up in. It is glucose's molecular weight divided by ten.

    And BUN by 2.8?

    For the same reason: it is the conversion factor for blood urea nitrogen from mg/dl to mmol/l.