Serum osmolality formula: how to calculate osmolarity from sodium, glucose and BUN
Calculated serum osmolality is 2 × sodium + glucose ÷ 18 + BUN ÷ 2.8, with sodium in mmol/L and glucose and BUN in mg/dL. For sodium 140, glucose 90 and BUN 14, that's 280 + 5 + 5 = 290 mOsm/kg.
Not a medical device. Not a diagnosis or dosing recommendation.
What is serum osmolality?
Osmolality describes how many dissolved particles a solution holds. Osmolality expresses concentration relative to the mass of the solvent (per kg of water); osmolarity expresses it per volume of solution (per litre).[1] Although the term osmolarity is used in the medical literature, osmolality is what laboratories usually measure.[1]
Serum osmolality can be measured directly in a laboratory, or it can be estimated from routine blood results. This page covers the estimate: a calculated osmolality from three blood results: sodium, glucose and blood urea nitrogen (BUN).
The calculated osmolality formula
calculated_osm_mosm_kg = 2 * sodium_mmol_l + glucose_mg_dl / 18 + bun_mg_dl / 2.8In words: double the sodium, add glucose divided by 18, and add BUN divided by 2.8. The result is in mOsm/kg and is reported to 1 decimal place.
What each part means
| Term | Plain-English meaning | Unit | Accepted range |
|---|---|---|---|
sodium_mmol_l | Serum sodium | mmol/L | 110–160 |
glucose_mg_dl | Plasma glucose | mg/dL | 50–1000 |
glucose_mmol_l | Plasma glucose, if you have SI units instead | mmol/L | 2.8–55.5 |
bun_mg_dl | Blood urea nitrogen | mg/dL | 1–200 |
measured_osm_mosm_kg | Optional laboratory-measured osmolality | mOsm/kg | 200–400 |
calculated_osm_mosm_kg | The calculated result | mOsm/kg | 1 decimal place |
Enter glucose once, either in mg/dL or in mmol/L.
How the formula works
- Multiply sodium by 2.
- Divide glucose (mg/dL) by 18.
- Divide BUN (mg/dL) by 2.8.
- Add the three parts together.
Sodium carries most of the weight. In Example 1 below, the sodium term is 280 while glucose and BUN add 5 each. A 1 mmol/L change in sodium moves the result by 2 mOsm/kg.
Glucose in mmol/L
If your glucose is in mmol/L, Magent's calculator first converts it to mg/dL by multiplying by 18.015, then uses the formula above. The conversion values below are computed from that factor and rounded to 1 decimal.
| Glucose (mmol/L) | Glucose (mg/dL, × 18.015) |
|---|---|
| 2.8 | 50.4 |
| 5.0 | 90.1 |
| 10.0 | 180.2 |
| 20.0 | 360.3 |
| 25.0 | 450.4 |
| 55.5 | 999.8 |
Worked examples
Example 1: sodium 140, glucose 90 mg/dL, BUN 14 mg/dL
- 2 × 140 = 280
- 90 ÷ 18 = 5
- 14 ÷ 2.8 = 5
- 280 + 5 + 5 = 290.0 mOsm/kg
Example 2: higher glucose (sodium 140, glucose 400 mg/dL, BUN 14 mg/dL)
- 2 × 140 = 280
- 400 ÷ 18 = 22.22
- 14 ÷ 2.8 = 5
- 280 + 22.22 + 5 = 307.2 mOsm/kg
Example 3: higher BUN (sodium 140, glucose 90 mg/dL, BUN 70 mg/dL)
- 2 × 140 = 280
- 90 ÷ 18 = 5
- 70 ÷ 2.8 = 25
- 280 + 5 + 25 = 310.0 mOsm/kg
Example 4: glucose in mmol/L (sodium 140, glucose 20.0 mmol/L, BUN 14 mg/dL)
- 20.0 × 18.015 = 360.3 mg/dL
- 2 × 140 = 280; 360.3 ÷ 18 = 20.02; 14 ÷ 2.8 = 5
- 280 + 20.02 + 5 = 305.0 mOsm/kg
The osmolar gap
The osmolal (or osmolar) gap is the difference between a measured osmolality and a calculated osmolality.[2] If you enter a measured value, Magent's calculator also returns the gap as measured minus calculated, to 1 decimal. For example, with a measured osmolality of 310 mOsm/kg and the 290.0 from Example 1, the gap is 310 − 290 = 20.0 mOsm/kg.
The calculator reports the number. It doesn't say what a given gap means.
Calculated osmolality reference table
These values are computed from the formula above, with BUN fixed at 14 mg/dL, and rounded to 1 decimal as Magent's calculator reports. They show how the result moves with sodium and glucose. They are not reference ranges.
| Sodium \ Glucose | 90 mg/dL | 180 mg/dL | 270 mg/dL | 360 mg/dL | 540 mg/dL |
|---|---|---|---|---|---|
| 130 mmol/L | 270.0 | 275.0 | 280.0 | 285.0 | 295.0 |
| 135 mmol/L | 280.0 | 285.0 | 290.0 | 295.0 | 305.0 |
| 140 mmol/L | 290.0 | 295.0 | 300.0 | 305.0 | 315.0 |
| 145 mmol/L | 300.0 | 305.0 | 310.0 | 315.0 | 325.0 |
| 150 mmol/L | 310.0 | 315.0 | 320.0 | 325.0 | 335.0 |
BUN has a smaller effect. With sodium 140 and glucose 90 mg/dL:
| BUN (mg/dL) | 7 | 14 | 28 | 56 | 70 |
|---|---|---|---|---|---|
| Calculated osmolality (mOsm/kg) | 287.5 | 290.0 | 295.0 | 305.0 | 310.0 |
History of the formula
The formula is credited to a 1987 paper by Worthley, Guerin and Pain in Anaesthesia and Intensive Care (volume 15, issue 2, pages 199–202). The authors measured plasma osmolality in 100 healthy people, 100 general hospital patients and 100 intensive care patients. They then compared the measurements with values from five published formulae.[3]
The formula with the least difference from measured osmolality was 2 × Na + urea + glucose, with all three in mmol/L.[3] Magent's calculator uses the mg/dL form of that structure: 2 × Na + glucose ÷ 18 + BUN ÷ 2.8.
Calculated osmolality has a long history. Published work notes that papers proposing simple and more complex osmolality formulae have kept appearing since 1958.[2]
When it's used
A calculated osmolality is commonly paired with a measured osmolality to work out the osmolal gap. Published work describes the main use of the osmolal gap today as screening for the possible presence of exogenous toxic substances.[2] This page doesn't do that workup; it reports the calculation.
Where it's used
Osmolality is routinely measured in clinical laboratories.[1] Published work describes the osmolal gap being used mainly for patients in emergency departments and intensive care units.[2] A simple calculated-osmolality formula can be used for quick mental calculation at the bedside, and laboratory information systems can report it automatically whenever a measured osmolality is requested.[2]
Who uses it
Calculated osmolality is used by clinicians and by clinical laboratories, which can report it automatically.[2] One published proposal argues that all clinicians and laboratories should adopt a single common formula.[2]
Limits of the calculation
- It's an estimate from sodium, glucose and BUN alone, not a laboratory measurement with an osmometer.
- It doesn't include ethanol or mannitol, and it doesn't use the alternative 1.86 × Na + 9 form of the equation.
- It isn't a toxic-alcohol test or a full osmolar-gap workup.
Clinical decisions belong to a qualified clinician who knows the patient.
How it differs from related calculators
- Stool osmotic gap also subtracts a calculated value from an osmolality, but it uses stool sodium and potassium, not serum values.
- Winters' formula is in the same electrolyte and acid-base family. It estimates an expected PCO2 from bicarbonate; it doesn't calculate osmolality.
- Corrected sodium estimates an expected sodium in hyperglycaemia. Serum osmolality uses the measured sodium as entered.
- Corrected calcium adjusts total calcium for albumin. It doesn't calculate osmolality.
Glossary
- Osmolality: dissolved-particle concentration per kg of solvent (mOsm/kg).[1]
- Osmolarity: dissolved-particle concentration per litre of solution.[1]
- Calculated osmolality: an estimate from sodium, glucose and BUN.
- Measured osmolality: a value from a laboratory osmometer.
- Osmolal (osmolar) gap: measured minus calculated osmolality.[2]
- BUN: blood urea nitrogen, in mg/dL.
Common mistakes
- Mixing glucose units. Dividing a mmol/L glucose by 18 gives a far-too-small glucose term. Convert to mg/dL first (× 18.015), or enter mmol/L in the calculator's mmol/L field.
- Forgetting to double sodium. The sodium term is 2 × Na.
- Comparing results from different formulae. Another equation, such as one with a 1.86 × Na term, won't exactly match this one.
- Entering values outside the accepted range. Sodium outside 110–160 mmol/L, glucose outside 50–1000 mg/dL (2.8–55.5 mmol/L), BUN outside 1–200 mg/dL and measured osmolality outside 200–400 mOsm/kg are rejected. They aren't estimated.
Source
Worthley LI, Guerin M, Pain RW. For calculating osmolality, the simplest formula is the best. Anaesth Intensive Care. 1987;15(2):199-202. DOI: 10.1177/0310057X8701500214
Further reading
- Najem O, Shah MM, Zubair M, De Jesus O. Serum Osmolality. StatPearls. Treasure Island (FL): StatPearls Publishing; 2024.
- Choy KW, Wijeratne N, Lu ZX, Doery JC. Harmonisation of Osmolal Gap - Can We Use a Common Formula? Clin Biochem Rev. 2016;37(3):113-119.
- Worthley LI, Guerin M, Pain RW (the source above), abstract.
Frequently asked questions
How do you calculate serum osmolality?
Use 2 × sodium + glucose ÷ 18 + BUN ÷ 2.8, with sodium in mmol/L and glucose and BUN in mg/dL. For sodium 140, glucose 90 and BUN 14: 280 + 5 + 5 = 290 mOsm/kg.
What is the serum osmolarity formula?
The same calculation is often called "calculated osmolarity". The formula on this page is 2 × Na + glucose/18 + BUN/2.8, reported in mOsm/kg.
What is the difference between serum osmolarity and osmolality?
Osmolality is per kg of solvent; osmolarity is per litre of solution.[1] The calculated result here is reported in mOsm/kg.
How do you check osmolarity?
There are two ways. A laboratory can measure osmolality directly, or you can estimate it from sodium, glucose and BUN with the formula above. Comparing the two gives the osmolar gap.
How do you calculate serum osmolality in hyperglycaemia?
The calculation is the same in every setting. High glucose raises the glucose term: in Example 2, glucose of 400 mg/dL gives 307.2 mOsm/kg. This page doesn't give condition-specific thresholds.
What does low serum osmolality mean?
This page doesn't give a normal range or interpret results. It calculates the number; what a value means depends on clinical context and belongs to a clinician.