Plasma Osmolality Calculator
Enter serum sodium, glucose, and blood urea nitrogen (BUN) to calculate estimated plasma osmolality using the Smithline-Gardner formula. Optionally add a measured osmolality and serum ethanol to compute the osmolal gap and flag potential unmeasured osmoles. Switch glucose and BUN between mg/dL and mmol/L - results update instantly.
Formula
Worked example
For Na = 140 mEq/L, glucose = 90 mg/dL, BUN = 14 mg/dL: Osmolality = 2 x 140 + 90/18 + 14/2.8 = 280 + 5.0 + 5.0 = 290 mOsm/kg. This falls within the normal range (275-295). If the measured lab value is 302, the osmolal gap = 302 - 290 = 12 mOsm/kg, just above the upper limit of normal.
What is plasma osmolality?
Plasma osmolality measures the total concentration of dissolved particles in the blood plasma, expressed in milliosmoles per kilogram of water (mOsm/kg). The main contributors are sodium and its anion partners, glucose, and urea (blood urea nitrogen). The body tightly regulates plasma osmolality between 275 and 295 mOsm/kg through the release of antidiuretic hormone (ADH) from the posterior pituitary and the thirst mechanism. When osmolality rises, ADH increases water reabsorption in the kidney and thirst drives fluid intake; when osmolality falls, ADH is suppressed and free water is excreted. Disruptions to this system underlie many common clinical conditions from dehydration and diabetic emergencies to hyponatremia and SIADH.
The Smithline-Gardner formula explained
The most widely used bedside formula multiplies serum sodium by 2 (to account for chloride and bicarbonate), adds glucose divided by 18 (converting mg/dL to mOsm/kg using its molecular weight of 180 g/mol), and adds BUN divided by 2.8 (using urea nitrogen molecular weight of 28 g/mol). The result closely approximates the laboratory-measured osmolality in most patients without significant unmeasured osmoles. Urea is a freely diffusible solute that crosses cell membranes easily, so it contributes to measured osmolality but not to effective osmolality (tonicity), which drives water shifts between compartments. For that reason, some formulas omit BUN to estimate tonicity rather than total osmolality.
Osmolal gap and toxic alcohol detection
The osmolal gap is the difference between the directly measured osmolality (by freezing-point depression in the lab) and the calculated osmolality from the formula. In healthy people and those without toxic ingestions, the gap is typically between -10 and +10 mOsm/kg. A gap above 15 mOsm/kg suggests the presence of significant unmeasured osmoles, most notably toxic alcohols such as methanol, ethylene glycol, isopropanol, or propylene glycol, as well as acetone and in some cases severe hyperlipidemia or hyperproteinemia. Serum ethanol also contributes to osmolality (each mg/dL raises it by about 0.25 mOsm/kg, or equivalently ethanol mg/dL divided by 3.8). This calculator corrects for ethanol before computing the unexplained osmolal gap, the portion that cannot be explained by commonly measured analytes. An elevated unexplained gap combined with anion gap metabolic acidosis is a clinical emergency that warrants urgent toxic alcohol investigation.
Clinical conditions affecting plasma osmolality
High plasma osmolality (hyperosmolality) is most often caused by hypernatremia from dehydration or diabetes insipidus, hyperglycemia in uncontrolled diabetes (especially the hyperosmolar hyperglycemic state, HHS), or elevated BUN from renal failure. Low plasma osmolality (hypoosmolality) almost always reflects hyponatremia and can arise from SIADH, hypothyroidism, adrenal insufficiency, heart failure, cirrhosis, nephrotic syndrome, or excessive hypotonic fluid intake. Pseudohyponatremia is a laboratory artifact where high concentrations of lipids or proteins displace water from a fixed plasma volume, producing a falsely low measured sodium even though osmolality is normal - direct ion-selective electrode measurement resolves this.
Plasma Osmolality Reference Ranges and Clinical Interpretation
| Osmolality (mOsm/kg) | Category | Common Causes |
|---|---|---|
| < 265 | Critically Low | SIADH, severe hyponatremia, water intoxication |
| 265-274 | Low | Hyponatremia, hypothyroidism, adrenal insufficiency |
| 275-295 | Normal | Healthy equilibrium, normal ADH regulation |
| 296-320 | Elevated | Dehydration, hypernatremia, hyperglycemia, elevated BUN |
| > 320 | Critically High | Diabetic hyperosmolar coma, toxic alcohol, severe dehydration |
Standard reference ranges used by clinical laboratories. Measured by freezing-point depression osmometry.
Frequently asked questions
What is a normal plasma osmolality?
Normal plasma osmolality is 275-295 mOsm/kg water. The body uses ADH and the thirst mechanism to maintain this range very precisely. Values below 275 indicate hypoosmolality (commonly hyponatremia), and values above 295 indicate hyperosmolality (commonly hypernatremia, hyperglycemia, or dehydration).
What is the difference between osmolality and osmolarity?
Osmolality is measured per kilogram of solvent (mOsm/kg H2O) and is the quantity measured directly by laboratory instruments. Osmolarity is measured per litre of solution (mOsm/L). In dilute solutions like plasma, the two are nearly identical, but osmolality is the clinically and analytically preferred term because it does not change with temperature and is what freezing-point depression instruments actually measure.
What does an elevated osmolal gap mean?
An osmolal gap above 10-15 mOsm/kg suggests the presence of unmeasured osmoles - substances that the Smithline-Gardner formula does not account for. The most clinically important causes are toxic alcohols: methanol, ethylene glycol, isopropanol, and propylene glycol. Ethanol also raises the gap and should be corrected for before interpreting results. A large gap combined with anion gap metabolic acidosis is a potential toxicological emergency requiring urgent evaluation.
Why is urea included in the formula if it is not a true osmole?
Urea is freely permeable across cell membranes, so it equilibrates between intracellular and extracellular compartments without causing water shifts. This makes it an ineffective osmole for tonicity purposes. However, it does raise measured osmolality, and the formula includes it to match the lab value. If you want to estimate effective osmolality (tonicity), the BUN term is simply omitted: effective osmolality = 2 x Na + glucose/18.
When should I measure osmolality in the lab rather than calculate it?
A direct laboratory measurement (by freezing-point depression) is essential whenever you need the osmolal gap - for example, when toxic alcohol ingestion is suspected, when anion gap metabolic acidosis has no clear explanation, or when a patient is comatose of unknown cause. Calculated osmolality alone cannot reveal unmeasured osmoles. The two measurements together, calculated and measured, are more informative than either alone.
Can glucose units affect the calculation?
Yes. The Smithline-Gardner formula divides glucose in mg/dL by 18. If your lab reports glucose in mmol/L, the formula simplifies: osmolality = 2 x Na + glucose (mmol/L) + BUN (mmol/L). This calculator handles both unit systems automatically - just select the unit your lab uses and enter the value as reported.
Sources
- Smithline N, Gardner KD Jr. Gaps - anionic and osmolal. JAMA. 1976;236(14):1594-1597.
- Bhave G, Neilson EG. Volume depletion versus dehydration: how understanding the difference can guide therapy. Am J Kidney Dis. 2011;58(2):302-309.
- Purssell RA, Pudek M, Brubacher J, Abu-Laban RB. Derivation and validation of a formula to calculate the contribution of ethanol to the osmolal gap. Ann Emerg Med. 2001;38(6):653-659.