What is the formula to calculate serum osmolality?

How to Calculate Serum Osmolality

Use the formula: 2 × [Na (mEq/L)] + glucose (mg/dL)/18 + BUN (mg/dL)/2.8, which is the standard calculation recommended for clinical practice. 1

Standard Calculation Formula

The most widely accepted formula for calculating serum osmolality is:

Calculated Osmolality = 2 × [Na] + (Glucose/18) + (BUN/2.8)

Where:

• Sodium (Na) is measured in mEq/L 1
• Glucose is measured in mg/dL 1
• Blood Urea Nitrogen (BUN) is measured in mg/dL 1

This formula is specifically endorsed by the American Diabetes Association for calculating effective serum osmolality in hyperglycemic crises 1 and is widely used across clinical settings 1.

Alternative Formulas for Different Clinical Contexts

For Geriatric Populations

When direct osmolality measurement is unavailable in older adults, use this more comprehensive equation:

Osmolarity = 1.86 × (Na + K) + 1.15 × glucose + urea + 14 (all in mmol/L) 1, 2

• This formula has been validated specifically for adults ≥65 years with diabetes, poor renal function, and various health conditions 1
• Use an action threshold of >295 mmol/L to trigger intervention 1, 2
• This equation demonstrates 85% sensitivity and 59% specificity for detecting dehydration in older adults 1

Simplified Mental Calculation

For rapid bedside estimation without a calculator:

Osmolality = 2 × [Na] + (Glucose/18) + (BUN/2.8) 3, 4, 5

Some sources suggest adding a constant (ranging from +5 to +13.5) to improve accuracy 3, 5, but the basic formula without the constant is adequate for most clinical decisions 4.

Understanding the Components

Why Multiply Sodium by 2?

• Sodium is multiplied by 2 to account for its accompanying anions (primarily chloride and bicarbonate) 1, 6
• The osmotic coefficient for sodium solutes is approximately 0.949, which is why some formulas use 1.86 or 1.89 instead of exactly 2.0 5, 7
• For practical purposes, using 2.0 is acceptable and simplifies calculation 4

Why Include Glucose and BUN?

• Glucose contributes significantly to osmolality, especially in hyperglycemic states 1, 6
• BUN (urea) affects measured osmolality but not tonicity, since urea crosses cell membranes freely 1, 4
• Including BUN increases correlation with measured osmolality by approximately 450% and decreases error by 35% 5

Should Potassium Be Included?

• Some formulas include potassium: 1.86 × (Na + K) 1, 5, 7
• Including potassium improves accuracy slightly but adds complexity 5, 7
• For most clinical purposes, potassium can be omitted since its contribution is small (normal range 3.5-5.3 mEq/L) 5

Normal Values and Clinical Thresholds

Normal Range

• 275-295 mOsm/kg is the normal plasma osmolality range 1, 4
• 308 mOsm/L is typical for human plasma 1, 8

Pathologic Thresholds

• >300 mOsm/kg: Indicates low-intake dehydration requiring intervention 1, 2, 9
• >320 mOsm/kg: Diagnostic criterion for Hyperosmolar Hyperglycemic State (HHS) 1, 2
• <275 mOsm/kg: Indicates hyposmolality, suggesting overhydration or SIADH 2

Effective Osmolality (Tonicity)

To calculate effective osmolality (tonicity), which determines water shifts across cell membranes, exclude BUN:

Effective Osmolality = 2 × [Na] + (Glucose/18) 1, 2, 4

• This is the clinically relevant calculation for assessing risk of cerebral edema or cellular dehydration 1, 4
• Urea is excluded because it freely crosses cell membranes and doesn't create osmotic gradients 1, 4

Osmolal Gap

The osmolal gap is the difference between measured and calculated osmolality:

Osmolal Gap = Measured Osmolality - Calculated Osmolality 4, 6

• Normal osmolal gap: 0 ± 2 mOsm/L 4
• An elevated gap suggests unmeasured osmoles (toxic alcohols, mannitol, ethylene glycol) 1, 6

Important Clinical Caveats

When to Use Direct Measurement vs. Calculation

• Direct measurement (freezing point depression) is the gold standard and should be used when available 1, 2, 9
• Calculated osmolality is acceptable for screening but may miss unmeasured osmoles 1, 2
• In older adults, directly measured osmolality >300 mOsm/kg has the strongest evidence for diagnosing dehydration (Grade B recommendation) 1, 2

Adjustments for Hyperglycemia

When glucose is elevated, correct sodium for the dilutional effect:

Corrected Na = Measured Na + 1.6 × [(Glucose - 100)/100] 2

• For every 100 mg/dL glucose above 100 mg/dL, add 1.6 mEq/L to the sodium value 2
• This prevents underestimating true osmolality in hyperglycemic states 2

Unit Conversions

If laboratory values are in different units:

• mmol/L to mg/dL for glucose: multiply by 18 1, 4
• mmol/L to mg/dL for BUN: multiply by 2.8 1, 4
• Most U.S. laboratories report glucose and BUN in mg/dL, while international labs use mmol/L 4

Common Pitfalls to Avoid

• Do not use clinical signs (skin turgor, dry mouth, urine color) to assess osmolality—these are unreliable, especially in older adults 1, 2, 9
• Do not confuse osmolality with osmolarity: osmolality is per kg of water, osmolarity is per liter of solution 1, 4
• Do not ignore glucose and urea: verify these are within normal range when interpreting elevated osmolality 2, 9
• Do not use formulas with osmotic coefficients (like Dorwart-Chalmers) for routine calculation—they underestimate osmolality unless additional corrections are made 4, 5, 7