What is serum osmolality?

Serum osmolality describes the concentration of dissolved particles in serum and is reported in mOsm/kg. Sodium and its accompanying anions provide most of the routinely estimated contribution, while glucose and urea also contribute. A laboratory can measure osmolality directly with an osmometer; this calculator estimates total and effective osmolality from routine chemistry values.

What is the difference between measured and calculated serum osmolality?

Measured osmolality comes directly from a laboratory osmometer; calculated osmolality is an estimate made from chemistry values. They are related but are not interchangeable and are not expected to be identical in every sample. For an osmol gap, verify that the laboratory result was directly measured rather than itself calculated from sodium, glucose and urea/BUN. Freezing-point depression is the standard relevant osmometry method for volatile-solute assessment, and contemporaneous chemistry and osmometry values should be used where possible.

What formula does this serum osmolality calculator use?

MedMaths uses the simple Smithline-Gardner-associated equation: 2 × sodium + glucose + urea, with glucose and urea expressed in mmol/L. For US units, glucose in mg/dL is divided by 18 and BUN in mg/dL is divided by 2.8. Different published equations use different coefficients, so formula choice can change the calculated value and the osmol gap.

What is the osmol gap?

The osmol gap is measured serum osmolality minus calculated serum osmolality. A positive gap means the measured value is higher than the amount predicted by the selected equation. The gap is an interpretive clue rather than a diagnosis, and it depends partly on the formula and laboratory method used.

What osmol gap is considered normal?

There is no single universal osmol-gap cutoff that applies to every calculation formula, analyser and clinical setting. For the Smithline-Gardner calculation used here, harmonisation work proposed 10 mOsm/kg as a reference limit, but that number is method-specific rather than a universal toxicology threshold. Reference intervals vary with the equation, analytical platform, patient population and whether ethanol is included. Use the interval and method specified by the relevant laboratory, toxicology service or local protocol; never use one gap value alone to diagnose or exclude toxic alcohol exposure.

Does a normal osmol gap rule out toxic alcohol exposure?

No. A normal osmol gap does not independently exclude a clinically important toxic alcohol exposure. Timing matters because the parent alcohol may fall as acidic metabolites accumulate. If exposure is clinically suspected, urgent toxicology assessment and specific laboratory testing take priority over a single calculated gap.

Why does MedMaths show two ethanol-adjusted osmol gaps?

Because published studies do not agree on one ethanol coefficient, MedMaths makes the assumption visible instead of silently choosing one. The molecular-weight approach uses ethanol in mg/dL divided by 4.6, approximately ethanol mmol/L × 1.0. Purssell and colleagues derived an empirical divisor of 3.7, approximately ethanol mmol/L × 1.25, in 2001. A 2025 prospective volunteer study found the 4.6 coefficient aligned more closely with subjects' baseline osmol gap in that cohort. Use the method required by the relevant local service.

Can the osmol gap be negative?

Yes. A negative osmol gap can occur when the calculated estimate is slightly higher than the measured value. Small negative values can occur because both measured and calculated values have analytical and biological variation. Check units, formula choice and whether values came from the same sample or clinical time point.

What is the difference between urea and BUN in this formula?

Urea and BUN use different reporting conventions; MedMaths accepts urea in mmol/L or BUN in mg/dL. Australian and UK laboratories commonly report urea in mmol/L, while US laboratories commonly report BUN in mg/dL. When BUN is entered in mg/dL, the calculator divides it by 2.8 for the equation.

How do I enter glucose in mg/dL?

Select mg/dL and enter the laboratory value exactly as reported; MedMaths divides glucose by 18 internally. Do not manually divide the glucose first and then leave the calculator set to mg/dL, because that converts the value twice.

Why do different serum osmolality calculators give different answers?

Several published equations exist and they use different sodium coefficients, constants or included analytes. A different calculated value also produces a different osmol gap from the same measured osmolality. For serial interpretation, use the same calculation method recommended by the relevant service.

What is the difference between osmolality and osmolarity?

Osmolality is expressed per kilogram of solvent, while osmolarity is expressed per litre of solution. Clinical laboratories usually report measured serum or plasma osmolality in mOsm/kg. The terms are sometimes used loosely in clinical discussion; this page reports calculated osmolality in mOsm/kg to match laboratory convention.

Is serum osmolality the same as tonicity?

No. Total osmolality includes urea; effective osmolality (tonicity estimate) excludes urea and is calculated here as 2 × sodium + glucose. MedMaths now shows effective osmolality as a separate secondary result so it is not confused with total calculated osmolality or the osmol gap. ADA hyperglycaemic-crisis criteria use effective osmolality >300 mOsm/kg as one possible HHS hyperosmolarity criterion, but this number alone does not diagnose HHS or replace the full criteria and serial assessment.

What is a normal serum osmolality range?

Use the reference interval reported by the laboratory for measured osmolality rather than applying one universal range to every method. Calculated-osmolality intervals also depend on the equation used. An Australian healthy-reference study reported a central 95% interval of 282–299 mOsm/kg for calculated osmolality using the simple Smithline-Gardner equation; this should not be substituted for a local measured-osmolality interval.

Should sodium, glucose, urea, measured osmolality and ethanol come from the same sample?

Ideally, yes, especially when an osmol gap or ethanol-adjusted gap is being calculated. Rapid changes in glucose, sodium, renal function, fluids, treatment or ethanol concentration can make values from different time points less comparable. Use contemporaneous results where possible.

Serum Osmolality Calculator

Lab corrections

What is the calculated serum osmolality?

Enter sodium, glucose and urea/BUN. Add measured osmolality for the osmol gap, with optional measured ethanol when an ethanol-adjusted gap is required.

Sodium (Na⁺)*mmol/L

Enter the reported serum sodium. For sodium, mmol/L and mEq/L are numerically equivalent.

Glucose unit

Choose the unit shown on the laboratory result.

Glucose*mmol/L

Enter the reported glucose value exactly as shown on the laboratory result.

Urea / BUN unit

Choose urea in mmol/L or BUN in mg/dL to match the report.

Urea*mmol/L

Enter the reported urea value exactly as shown.

Include measured osmolalityOptional. Add the laboratory measured osmolality to calculate the osmol gap.

Use contemporaneous laboratory values

Enter sodium, glucose, urea/BUN, measured osmolality and ethanol from the same sample or clinical time point where possible, and match every input to the unit actually reported.

Simple answer

How is calculated serum osmolality worked out?

MedMaths uses the simple Smithline-Gardner-associated equation with sodium, glucose and urea/BUN.

Example: Na 140, glucose 5 and urea 5 gives 2 × 140 + 5 + 5 = 290 mOsm/kg.

For US units: glucose mg/dL ÷ 18 and BUN mg/dL ÷ 2.8.

Simple answer

How is the osmol gap calculated?

A directly measured laboratory osmometer result is required before the osmol gap can be calculated.

Example: Measured osmolality 310 minus calculated osmolality 290 gives an osmol gap of 20 mOsm/kg.

MedMaths reports the numeric gap without assigning one universal normal/abnormal cutoff.

An osmol gap is not a toxicology diagnosis

Formula choice, laboratory method, timing, ethanol and other unmeasured solutes can all change the gap. First verify that the laboratory osmolality was directly measured by an osmometer rather than calculated from chemistry values. A normal gap does not independently exclude toxic alcohol exposure, and an increased gap does not identify one substance. Use the relevant laboratory and local toxicology pathway when exposure is suspected.

Clinical use and safety

When to use this calculator — and its limits

The arithmetic can be correct while the clinical decision is still wrong. These boundaries show what the calculator can and cannot establish.

When to use

Use to estimate total calculated serum osmolality from sodium, glucose and urea/BUN using one explicit equation.
Use the separate effective-osmolality estimate (2 × sodium + glucose) when that physiological quantity is specifically required; do not treat it as an HHS diagnosis by itself.
Add a contemporaneous directly measured osmometer result when you need the numeric osmol gap: measured minus calculated.
If measured ethanol is available and the local clinical question requires ethanol adjustment, compare the two explicitly labelled ethanol assumptions rather than hiding the coefficient.

Key limitations

Calculated osmolality is an estimate and is not interchangeable with a directly measured laboratory osmolality. A chemistry-derived calculated osmolality must not be re-entered as the measured value for an osmol gap.
Use contemporaneous chemistry and osmometry values where possible; treatment and metabolism can change the inputs over time.
Urea/BUN and ethanol are reported in different unit systems internationally. Match the selector to the laboratory report rather than inferring units from magnitude.
Many equations exist. Formula choice changes the calculated value and therefore changes the osmol gap.
Published ethanol coefficients disagree. Purssell et al. derived mg/dL ÷ 3.7 in 2001, while a 2025 prospective volunteer study found ÷ 4.6 produced closer baseline-adjusted gaps in that cohort. MedMaths shows both rather than averaging them.
No single osmol-gap threshold is universal across formulas, analysers and patient populations.
A small or normal osmol gap cannot rule out toxic alcohol exposure, particularly as the parent alcohol is metabolised.

What MedMaths does not decide

Whether a toxic alcohol or other unmeasured osmole is present or absent.
Which ethanol coefficient, reference interval or toxicology pathway a local service should use.
Whether antidotal treatment, dialysis, IV fluids or another emergency intervention is indicated.
The cause of hyperosmolality, altered mental status or an abnormal osmol gap.

Evidence and method checks

Harmonisation of Osmolal Gap — Can We Use a Common Formula? — Clinical Biochemist Reviews / PubMed
Osmolality, Serum — freezing-point depression method — Mayo Clinic Laboratories
Minding the osmol gap: a sentinel event and subsequent laboratory investigation — Clinical Toxicology / PubMed
Toxic Alcohol Poisoning — Emergency Medicine Clinics of North America / PubMed
Diabetes Care in the Hospital: Standards of Care in Diabetes—2026 — American Diabetes Association
Derivation and validation of a formula to calculate the contribution of ethanol to the osmolal gap — Annals of Emergency Medicine / PubMed
Ethanol and the Limitations of the Osmol Gap — Annals of Emergency Medicine / PubMed
An evaluation of the osmole gap as a screening test for toxic alcohol poisoning — BMC Emergency Medicine / PubMed Central

Formula logic and known-value examples are checked as part of the MedMaths review process.

See how MedMaths checks calculator methods →

Calculated is not measured

The calculator estimates serum osmolality from routine chemistry. For an osmol gap, the comparison value must come directly from a laboratory osmometer rather than another calculated chemistry result; freezing-point depression is the standard relevant method for volatile-solute assessment.

Ethanol stays explicit

The base Smithline-Gardner result never changes. If ethanol is entered, MedMaths shows the original gap plus separate ÷4.6 and Purssell ÷3.7 ethanol-adjusted gaps so the assumption remains visible.

Formula, units, examples and FAQs

Review the formula convention, ethanol adjustment, unit handling, worked examples, common mistakes and focused questions.

Serum osmolality formula used by MedMaths

Calculated serum osmolality visual showing two times sodium plus glucose plus urea using mmol per litre inputs, with a worked example giving about 290 mOsm per kg.

Smithline-Gardner-associated simple equation

In simple words

The sodium term provides most of the routine estimate; glucose and urea are added in mmol/L.

US units

Osmolality = 2 × Na⁺ + glucose (mg/dL) ÷ 18 + BUN (mg/dL) ÷ 2.8

Smithline and Gardner's 1976 JAMA paper is associated with this simple bedside osmol-gap framework. MedMaths does not claim they were the first researchers ever to calculate serum osmolality; other equations existed and produce different gaps.

Research profiles: Neil Smithline → Kenneth D. Gardner Jr →

How ethanol adjustment is handled

Molecular-weight method

Ethanol contribution ≈ ethanol mg/dL ÷ 4.6

Equivalent to approximately ethanol mmol/L × 1.0. A 2025 prospective volunteer study found this coefficient produced closer baseline-adjusted osmol gaps than 3.7 in that study population.

Purssell empirical method

Ethanol contribution ≈ ethanol mg/dL ÷ 3.7

Purssell and colleagues prospectively derived and validated this relationship in 2001; in SI units it is approximately ethanol mmol/L × 1.25.

Research profile: Roy A. Purssell →

Do not average the two results. Use the coefficient and osmol-gap reference interval specified by the relevant laboratory, toxicology service or protocol.

Get the units right

Glucose

Enter the reported value and select mmol/L or mg/dL. MedMaths divides mg/dL by 18 internally.

90 mg/dL ÷ 18 = 5 mmol/L

Urea vs BUN

Enter urea in mmol/L or BUN in mg/dL to match the report. MedMaths divides BUN by 2.8 internally.

14 mg/dL BUN ÷ 2.8 = 5 mmol/L contribution

Do not convert twice. If you select mg/dL, enter the original mg/dL number. The calculator performs the conversion.

Total osmolality is not tonicity

Total calculated osmolality includes urea. Tonicity/effective osmolality is a different physiological concept that focuses on solutes producing sustained transcellular water shifts. MedMaths now shows this separately as an effective-osmolality / tonicity estimate using 2 × sodium + glucose, so it is not confused with total osmolality or the osmol gap.

If the question is specifically how marked hyperglycaemia changes the interpretation of measured sodium, use the Corrected Sodium Calculator → instead of treating corrected sodium as an osmolality result.

Looking at an osmol gap alongside acid-base chemistry?

An osmol gap and an anion gap answer different questions. If you also have sodium, chloride and bicarbonate/total CO₂, calculate the Anion Gap → separately, then use the anion-gap interpretation Guide → for the broader context.

For measured-versus-calculated osmolality, formula differences, ethanol assumptions and toxic-alcohol limitations, read Calculated Serum Osmolality and Osmol Gap Explained →.

Worked examples

Example 1: SI units — sodium 140 mmol/L, glucose 5.5 mmol/L, urea 5 mmol/L.

Osm = 2 × 140 + 5.5 + 5 = 290.5

Calculated osmolality: 290.5 mOsm/kg

Example 2: US units — sodium 140 mmol/L, glucose 90 mg/dL, BUN 14 mg/dL.

Glucose = 90 ÷ 18 = 5
BUN = 14 ÷ 2.8 = 5
Osm = 2 × 140 + 5 + 5 = 290

Calculated osmolality: 290 mOsm/kg

Example 3: measured osmolality 340 mOsm/kg and ethanol 185 mg/dL, with base calculated osmolality 290.

Unadjusted gap = 340 − 290 = 50
Ethanol ÷ 4.6 = 40.2 → adjusted gap = 9.8
Ethanol ÷ 3.7 = 50.0 → Purssell-adjusted gap = 0.0

Same sample, different ethanol coefficient — do not hide the assumption.

Common calculation mistakes

Using a calculated value as ‘measured’ osmolality

An osmol gap requires direct osmometer measurement. Do not re-enter a chemistry-derived calculated osmolality as the measured result.

Mixing urea and BUN

Urea mmol/L and BUN mg/dL are not interchangeable numbers. Select the unit actually reported.

Mixing glucose units

A glucose value reported in mmol/L cannot be entered as the same number in mg/dL. Match the unit selector to the laboratory report.

Converting twice

Do not manually divide glucose or BUN and then also select mg/dL; MedMaths converts those inputs internally.

Using results from different times

Rapid treatment or metabolism can make sodium, glucose, urea, measured osmolality and ethanol from different time points less comparable.

Hiding the ethanol coefficient

An ethanol-adjusted gap depends on the coefficient used. Record the method instead of quoting an adjusted gap without its assumption.

Treating the gap as a diagnosis

An abnormal gap does not identify a toxin, and a normal gap does not independently exclude toxic alcohol exposure.

Frequently asked questions

Continue calculating

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Calculate anion gap from sodium, chloride and bicarbonate, with optional albumin correction.

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Corrected Calcium Calculator

Calculate the commonly used simplified albumin-adjusted calcium estimate with current evidence limitations.

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Calculate the modern race-free 2021 CKD-EPI eGFR, with optional cystatin C and BSA adjustment.

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Authorship and review

Clear authorship, review timing, and limits of use.

Formula authorNeil Smithline, MDSmithline-Gardner Calculated Serum Osmolality formula · 1976 Formula authorKenneth D. Gardner Jr, MDSmithline-Gardner Calculated Serum Osmolality formula · 1976 Ethanol-adjustment evidenceRoy A. Purssell, MD, FRCPC, ABEM, FACMTPurssell et al. empirical coefficient · 2001

Written and reviewed byGeorge Lambroglou, RNReviewed 28 August 2026

Smithline and Gardner are credited for the 1976 JAMA osmolal-gap framework associated with the simple calculated-osmolality equation used by MedMaths; MedMaths does not claim first invention. Roy A. Purssell is linked to the 2001 four-author study deriving the empirical ethanol coefficient, not to sole authorship or the base equation. George Lambroglou, RN wrote and reviewed the MedMaths calculator content.

References and sources

Open the formula-history, reference-interval, osmol-gap and ethanol-coefficient evidence used to review this calculator.

These sources support the calculation method, formula-specific gap interpretation, ethanol handling and safety limitations. Local laboratory and toxicology guidance remains authoritative for clinical interpretation.

Smithline & Gardner (1976) — Gaps—Anionic and Osmolal

JAMA paper associated with the simple bedside calculated-osmolality and osmolal-gap framework used here.

Dorwart & Chalmers (1975) — Comparison of calculated osmolality methods

Compared 13 published calculation methods and illustrates why different equations produce different calculated values and gaps.

Hughes et al. (2016) — Harmonising calculated osmolality reference intervals

Reference-interval study supporting the practical use of the simple 2 × sodium + glucose + urea equation.

Choy et al. (2016) — Harmonisation of Osmolal Gap

Compared formula performance across clinical samples and analytical platforms and supports formula-specific osmol-gap interpretation.

Mayo Clinic Laboratories — Serum osmolality by freezing-point depression

Laboratory source confirming direct serum osmolality measurement by freezing-point depression.

Pires et al. (2023) — Minding the osmol gap

Sentinel toxicology case showing how a calculated laboratory osmolality mistaken for a measured value produced a falsely reassuring negative osmol gap.

Ross et al. (2022) — Toxic Alcohol Poisoning

Toxicology review covering toxic-alcohol metabolism and the utility and limitations of the osmol gap.

ADA Standards of Care in Diabetes—2026 — HHS hyperosmolarity criteria

Uses effective osmolality 2 × Na + glucose and total osmolality 2 × Na + glucose + urea as distinct hyperosmolarity calculations within the full HHS diagnostic criteria.

Lynd et al. (2008) — Osmole gap as a screening test for toxic alcohol poisoning

Diagnostic-accuracy evidence supporting the warning that the osmol gap should not be used as a stand-alone exclusion test.

Purssell et al. (2001) — Ethanol contribution to the osmolal gap

Prospective derivation and validation of the empirical ethanol contribution: mg/dL ÷ 3.7 or approximately mmol/L × 1.25.

Garrard et al. (2012) — Ethanol contribution validation

Validation study in 603 emergency-department patients that estimated an ethanol contribution of approximately mg/dL ÷4.0, showing that published coefficients are not limited to 3.7 and 4.6.

Marino et al. (2025) — Ethanol and the Limitations of the Osmol Gap

Prospective volunteer study comparing ethanol coefficients; in that cohort, ÷4.6 produced closer baseline-adjusted gaps than ÷3.7, while baseline variation remained important.

Evidence review updated 28 August 2026. The base Smithline-Gardner arithmetic remains unchanged. Optional ethanol handling shows the molecular-weight 4.6 and Purssell 3.7 methods separately, and MedMaths does not assign a universal osmol-gap diagnostic cutoff.

Serum Osmolality Calculator

Lab corrections

What is the calculated serum osmolality?

Enter sodium, glucose and urea/BUN. Add measured osmolality for the osmol gap, with optional measured ethanol when an ethanol-adjusted gap is required.

Sodium (Na⁺)*mmol/L

Enter the reported serum sodium. For sodium, mmol/L and mEq/L are numerically equivalent.

Glucose unit

Choose the unit shown on the laboratory result.

Glucose*mmol/L

Enter the reported glucose value exactly as shown on the laboratory result.

Urea / BUN unit

Choose urea in mmol/L or BUN in mg/dL to match the report.

Urea*mmol/L

Enter the reported urea value exactly as shown.

Include measured osmolalityOptional. Add the laboratory measured osmolality to calculate the osmol gap.

Use contemporaneous laboratory values

Enter sodium, glucose, urea/BUN, measured osmolality and ethanol from the same sample or clinical time point where possible, and match every input to the unit actually reported.

Simple answer

How is calculated serum osmolality worked out?

MedMaths uses the simple Smithline-Gardner-associated equation with sodium, glucose and urea/BUN.

Example: Na 140, glucose 5 and urea 5 gives 2 × 140 + 5 + 5 = 290 mOsm/kg.

For US units: glucose mg/dL ÷ 18 and BUN mg/dL ÷ 2.8.

Simple answer

How is the osmol gap calculated?

A directly measured laboratory osmometer result is required before the osmol gap can be calculated.

Example: Measured osmolality 310 minus calculated osmolality 290 gives an osmol gap of 20 mOsm/kg.

MedMaths reports the numeric gap without assigning one universal normal/abnormal cutoff.

An osmol gap is not a toxicology diagnosis

Clinical use and safety