Enter all but one of the sodium concentration, potassium concentration, blood urea nitrogen concentration, and blood glucose concentration into the calculator to determine the serum osmolality; this calculator can also evaluate any of the variables given the others are known.
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Serum Osmolality Formula
Serum osmolality is an estimate of how concentrated the blood is. It reflects the number of dissolved particles in plasma, with sodium contributing the largest share and glucose and urea adding smaller but still important effects. This calculator is useful for estimating serum concentration, checking lab consistency, and solving for a missing value when three of the four inputs are known.
\mathrm{Osm} = 2\mathrm{Na} + \frac{\mathrm{Glucose}}{18} + \frac{\mathrm{BUN}}{2.8}Where:
- Osm = serum osmolality, typically reported in mOsm/kg
- Na = serum sodium concentration in mEq/L or mmol/L
- Glucose = blood glucose in mg/dL
- BUN = blood urea nitrogen in mg/dL
Some references use an expanded version that includes potassium in the doubled cation term:
\mathrm{Osm} = 2(\mathrm{Na} + \mathrm{K}) + \frac{\mathrm{Glucose}}{18} + \frac{\mathrm{BUN}}{2.8}Because serum potassium is much lower than serum sodium, many bedside estimates and calculators use the simplified sodium-based equation. The key is to use one convention consistently when comparing values.
Rearranged Equations for Any Missing Variable
If you know any three values, you can solve for the fourth:
\mathrm{Na} = \frac{\mathrm{Osm} - \frac{\mathrm{Glucose}}{18} - \frac{\mathrm{BUN}}{2.8}}{2}\mathrm{Glucose} = 18\left(\mathrm{Osm} - 2\mathrm{Na} - \frac{\mathrm{BUN}}{2.8}\right)\mathrm{BUN} = 2.8\left(\mathrm{Osm} - 2\mathrm{Na} - \frac{\mathrm{Glucose}}{18}\right)How to Use the Calculator
- Enter any three known values: sodium, glucose, BUN, or serum osmolality.
- Select the correct units for each field before calculating.
- Leave the unknown field blank.
- Click Calculate to solve for the missing value.
- Double-check that the entered numbers come from the same lab draw and use the same unit system.
Input Guide
| Variable | Common Units | What It Represents | Why It Matters |
|---|---|---|---|
| Sodium | mEq/L or mmol/L | Main extracellular cation | Usually the largest contributor to serum osmolality |
| Glucose | mg/dL or mmol/L | Circulating blood sugar | Can raise osmolality significantly when elevated |
| BUN | mg/dL or mmol/L | Blood urea nitrogen | Adds to total osmolality and often rises with impaired renal clearance or dehydration |
| Serum Osmolality | mOsm/kg or mOsm/L | Total particle concentration in serum | Helps describe water balance and compare measured versus calculated values |
Unit note: for sodium, mEq/L and mmol/L are numerically the same because sodium is monovalent. For glucose and BUN, the unit choice matters, so use the calculator’s unit selector carefully to avoid double conversion.
Useful Unit Conversions
\mathrm{Glucose}_{mmol/L} = \frac{\mathrm{Glucose}_{mg/dL}}{18}\mathrm{BUN}_{mmol/L} = \frac{\mathrm{BUN}_{mg/dL}}{2.8}If your lab report already lists glucose or BUN in mmol/L, let the calculator work with those units directly instead of converting twice by hand.
Example Calculation
If sodium is 140 mEq/L, glucose is 90 mg/dL, and BUN is 14 mg/dL, the estimated serum osmolality is:
\mathrm{Osm} = 2(140) + \frac{90}{18} + \frac{14}{2.8}\mathrm{Osm} = 280 + 5 + 5\mathrm{Osm} = 290\ \text{mOsm/kg}This result sits near the middle of the usual adult reference interval and illustrates how strongly sodium drives the final number.
How to Interpret Serum Osmolality
Many laboratories use a typical adult serum osmolality reference range near 275 to 295 mOsm/kg, although the exact interval can vary by lab and testing method.
- Lower values generally reflect relatively more water compared with dissolved particles.
- Higher values generally reflect relatively less water, more dissolved solute, or both.
- Calculated values estimate the concentration from routine chemistry inputs.
- Measured values come directly from the laboratory and may differ when unmeasured osmoles are present.
Calculated vs. Measured Osmolality
The calculator provides an estimate, not a direct lab measurement. A direct serum osmolality test may be higher or lower than the calculated result because the equation only includes the major routinely reported contributors.
\text{Osmolar Gap} = \text{Measured Osmolality} - \text{Calculated Osmolality}A difference between measured and calculated osmolality can be clinically useful because it may suggest additional dissolved substances that are not included in the standard equation. This is one reason serum osmolality is often reviewed alongside electrolytes, glucose, kidney markers, and the broader clinical picture.
Osmolality vs. Osmolarity
These terms are related but not identical:
- Osmolality describes particles per kilogram of solvent.
- Osmolarity describes particles per liter of solution.
- In body fluids, the values are often numerically close, but osmolality is the standard term used for serum interpretation.
Practical Tips
- Use values from the same blood sample whenever possible.
- Confirm whether the lab reports BUN or urea, since those are not interchangeable labels.
- Match the unit selector to the lab report before calculating.
- Use measured serum osmolality when a direct laboratory value is available and precise interpretation is needed.
- Remember that this calculator estimates concentration; diagnosis depends on the full clinical context.
