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Osmolality revisited—Deriving and validating the best formula for
calculated osmolality
A. Khajuria, J. KrahnT
Department of Clinical Biochemistry, St. Boniface General Hospital, Winnipeg, Manitoba, Canada R2H 2A6
University of Manitoba Medical School, Winnipeg, Manitoba, Canada
Received 1 December 2004; received in revised form 2 February 2005; accepted 1 March 2005
Available online 1 April 2005
Abstract
Objective: To derive a formula that can be used (i) to calculate osmolality in normal patients as well as those that are hyperglycemic and
intoxicated, and (ii) to predict the presence of unexplained compounds with the osmol gap calculation in the presence and absence of ethanol.
Design and experiments: We performed in vitro experiments to determine the relationship of serum osmolality with sodium, potassium,
urea, glucose, ethanol, methanol, and ethylene glycol. Several formulas were then tested for their validity in predicting osmolality in normal
individuals. Finally, we assessed whether these formulas would allow us to calculate the osmolality gap (OG) that may be indicative of the
presence of other osmotically active compounds. The OG calculation was done both in the presence and absence of ethanol. In this way, the
OG should be able to detect compounds like methanol and ethylene glycol even in the presence of ethanol which is easily measured and is
very often present in the above-named poisonings.
Results: Experimental results show that glucose, ethanol, methanol, and ethylene glycol need factors of 1.15, 1.20, 1.07, and 1.00,
respectively, to accurately predict osmolality. The factors for glucose and ethanol were then validated in normal subjects as well as in a large
patient database. The formulas below predicted osmolality very well in patients whether ethanol was present or not. All concentrations are
expressed in mmol/L.
1. OSMc = 2*Na + 1.15*Glucose + Urea + 1.2*Ethanol
2. OSMc = 1.86*(Na + K) + 1.15*Glucose + Urea + 1.2*Ethanol + 14
The mean osmol gap for healthy subjects without ethanol present was 0.77 T3.80 mosM/kg with the reference interval being 6.68 to
8.23 mosM/kg for formula 1 and 8.04 to 6.50 mosM/kg for formula 2. The mean osmol gap (OG) in patients who had ethanol present was
1.22 T5.32 for formula 1 and 0.2 T5.0 for formula 2.
Conclusions: This study shows that factors of 1.20 and 1.15 have to be applied to ethanol and glucose to allow for accurate calculation of
osmolality and osmolality gap. There were insufficient patient data to verify the factors for methanol and ethylene glycol.
D2005 The Canadian Society of Clinical Chemists. All rights reserved.
Keywords: Osmolality; Calculated osmolality; Osmol gap; Methanol; Ethanol; Ethylene glycol
Introduction
Osmolality (OSM) represents a measure of number of
particles in a kilogram of water (osmoles per kilogram). In
human serum or plasma, osmolality can be measured
experimentally by freezing point depression or it can be
calculated by using different formulas that account for the
contribution of the common osmotically active constituents
(sodium, potassium, glucose, and urea) of serum. The
difference between measured osmolality (OSMm) and
calculated osmolality (OSMc) is referred to as osmol gap
(OG). When ethanol is present, it can be included in the
0009-9120/$ - see front matter D2005 The Canadian Society of Clinical Chemists. All rights reserved.
doi:10.1016/j.clinbiochem.2005.03.001
TCorresponding author. Fax: +1 204 231 2656.
E-mail address: jkrahn@sbgh.mb.ca (J. Krahn).
Clinical Biochemistry 38 (2005) 514 – 519
OSMc so the OG now becomes indicative of other osmoti-
cally active compounds, i.e., methanol, ethylene glycol,
isopropyl alcohol, propylene glycol, etc.
The calculation of OG is commonly used as a screen for
toxic alcohol ingestion (ethanol, methanol, ethylene glycol,
and propylene glycol). Elevated OG implies the presence of
unmeasured osmotically active substances. Currently, the
determination of OG for ethanol poisoning has lost its
usefulness because ethanol can be measured quickly on
most chemistry analyzers. Since other toxic alcohols can
only be measured by gas – liquid chromatography, OSMm
should still be ordered for other toxic alcohol poisoning and
in such cases ethanol should also be ordered, since it is often
consumed in these poisoning. In these cases, the laboratory
should calculate the OG incorporating ethanol in that
calculation. This should theoretically predict the presence
of other osmotically active compounds like methanol,
ethylene glycol, and propylene glycol, etc.
It has been observed that ethanol does not follow a 1:1
relationship with OG. In ethanol intoxication, where OG is
calculated by including ethanol on a molar basis, OG
increases with increasing ethanol, making it appear that
there is something else present beside ethanol [1– 4]. This
results in frequent requests for the clinical laboratory to rule
out methanol and ethylene glycol in simple ethanol
intoxication, i.e., the clinician calculates the OG and
compares it to the ethanol concentration, finds there is still
a large gap, and initiates a search for the missing osmoles.
Significant elevation in OG has also been found in diabetic
ketoacidosis due to the presence of acetone [5,6]. It has also
been observed in several instances that high glucose
concentration increases osmolality significantly without
the presence of acetone.
The formulas commonly in use do not adequately reflect
the contribution of ethanol and glucose to serum osmolality.
For this reason, OG increases with increasing ethanol and
glucose levels. The common formulas that are in use were
created to allow for the simple calculation of osmolality at
the bedside. This allowed the clinician to rapidly rule a toxic
ingestion in or out. Since computerization of our laboratory,
we offered an automated calculated OG (Dorwart et al.)
along with other laboratory data. It has long been apparent
that in cases of simple intoxication, our automated OG
calculation does not accurately predict the ethanol concen-
tration and furthermore that the error is proportional, i.e., it
increases with increasing ethanol concentration. This in fact
created unnecessary work for us, since physicians were
reluctant to discharge patients that were very inebriated but
appeared to have some other toxic compound present on the
basis of a raised OG. It is now possible to do sophisticated
calculation automatically so that the result is available at the
same time that the other results are available. For this reason,
we set out to develop a calculation that would accurately
predict the osmolality both in the presence and absence of
ethanol. This would then also accurately predict the presence
of toxic compounds other than ethanol using the OG.
The objectives of the study were to:
1. Evaluate the contribution of glucose, ethanol, methanol,
and ethylene glycol on the osmolality.
2. Determine if we could experimentally determine factors
that can be applied to these compounds to create a more
accurate determination of calculated osmolality (OSMc)
and also of the osmolal gap (OG).
3. Select an OG calculation that would be predictive of the
presence of other compounds like methanol and ethylene
glycol even when ethanol was present in the sample.
4. To validate the formula against data extracted from our
patient data base.
Materials and methods
The study was divided into two parts. In the first part, we
experimentally determined the relationship between increa-
sing analyte concentration to osmolality. This allowed us to
calculate factors, which we could then verify in our clinical
data. In the experimental part, in vitro experiments were
done to determine the contribution of glucose, ethanol,
methanol, and ethylene glycol on osmolality in pooled
plasma samples which were spiked with varied concen-
trations of glucose, 5 – 50 mmol/L (n= 100); ethanol, 10–
100 mmol/L (n= 40); methanol, 12 – 125 mmol/L (n= 40);
and ethylene glycol, 9 – 90 mmol/L (n= 34), respectively.
Osmolality was measured by freezing-point depression with
a Fiske 2400 osmometer (Fiske Associates, Norwood MA,
USA). Electrolytes, glucose, urea, and ethanol (enzymatic
method) were determined on a high volume analyzer
(Roche Modular System, Roche Diagnostics, and Montreal,
Quebec, Canada).
The calculated osmolality was obtained using common
formulas from the literature [7,8]. The calculations were all
done in SI units.
By definition, osmolality represents the number of par-
ticles (in molar amount) per kilogram of solvent. The
analytes that are the biggest contributors to osmolality are
measured in volume of plasma. However, plasma is only
93% water and hence each liter of plasma does not contain a
kilogram of water. For the calculation of osmolality, the
concentration (mmol/L) of solutes must be converted into
molality (amount of substance divided by mass of solvent,
mmol/kg) by dividing by the mass of water in plasma. A
good approximation of total cations and anions has been to
multiply sodium times two and adding to this the major non-
ionic solutes which are glucose and urea. The average value
for mass concentration of water in normal plasma is 0.933
kg/L [9]. The sodium concentration in mmol/L multiplied
by 2 accounts for all cations and anions, but since only 93%
of plasma consists of water in normal plasma, 1.86 might be
a better coefficient than 2 [10]. Dorwart et al. used a
constant factor of 9 mmol/L to account for other cations like
potassium, magnesium, and calcium as well as their
A. Khajuria, J. Krahn / Clinical Biochemistry 38 (2005) 514– 519 515
unmeasured anions and other unmeasured solutes with the
assumption that they are approximately constant. Other
authors used a factor of 2 instead of 1.86 to achieve the
same end, i.e., to account for unmeasured anion and cations
[8,10].
We modified the Dorwarts and Smithline formulas by
including potassium and ethanol when it is present. The OG
was then calculated as the difference between the measured
and the calculated osmolality (OG = OSMm OSMc). The
relationship between OG and ethanol was determined by
linear regression and a factor was derived from it. To
determine a factor for glucose or ethanol, it was necessary to
omit these compounds from the osmolality calculation so
that it would appear in the OG. In this way, we could
determine a linear relationship of the OG and both ethanol
and glucose. We applied these formulas to a healthy
population as well as patient data from our emergency
department where ethanol as well as the other necessary
analytes had been ordered. In order to determine the
reference intervals without the presence of ethanol, samples
were collected from 37 healthy subjects. Sodium, potas-
sium, glucose, urea, and osmolality were performed on the
Roche Modular and the Fiske osmometer. The samples were
run as 5 samples per day for 8 days to compensate for intra-
day variation. Data were extracted from our electronic
database on patients admitted to the emergency room on
which osmolality, electrolytes, glucose, urea, and ethanol
were ordered for the period from July to September 2003.
The factors obtained for glucose and ethanol in the
experimental study were then applied to the data from 37
healthy volunteers as well the patient data. OSMc was
calculated in all these patients using the osmolality formulas
as described in Materials and methods including and
excluding factors for ethanol and glucose. Linear regression
analysis was then used to evaluate the relationship between
OG and ethanol (with and without the factor) to generate the
best equation. All statistical analysis was done with the
Analyse-It\add-in program for the Microsoft Excel\
spreadsheet program. For all pertinent statistics, the 95%
confidence levels were always chosen.
Results and discussion
In the first part of our study, the objective was to
determine the relationship between OG and plasma
glucose, ethanol, methanol, and ethylene glycol levels.
OG was shown to increase with increasing glucose
concentration. The slope of the line that describes the
relationship between glucose and OG would provide us
with a factor. The slope obtained was 1.15 (Fig. 1),
indicating that for calculated osmolality a factor of 1.15
must be applied to glucose to account completely for its
contribution to osmolality. Similarly for ethanol, the slope
determined was 1.20 (Fig. 2). Again, this implies that for
the calculation of OG, a factor of 1.20 must be applied to
ethanol to completely account for its contribution to the
calculated osmolality. The slope obtained for methanol and
ethylene glycol was 1.07 and 1.00, respectively. In the
second part of our study, we first calculated the mean and
reference intervals for OSMm and OSMc from 37 normal
healthy subjects. The mean OSMm was 292.2 T5.0 mosM/
Fig. 1. Passing Bablok regression analysis of plasma glucose and various
OGs from in vitro experimental data. N= 100.
Fig. 2. Passing Bablok regression analysis of plasma ethanol levels and
various OGs from in vitro experimental data. N= 40.
Table 1
The comparison of mean levels of OSMm and OSMc in healthy subjects
Parameters NMean
(mosM/kg)
SE SD Reference
interval
OSMm 37 292.2 0.82 4.99 282.4 – 302.0
OSMc = 2*Na + 1.15*G + U 37 291.4 0.68 4.12 283.4 – 299.5
OSMc = 1.86*(Na + K) +
1.15*G + U + 14
37 293.0 0.64 3.91 285.3 – 300.6
A. Khajuria, J. Krahn / Clinical Biochemistry 38 (2005) 514– 519516
kg. The reference interval was 282.4 – 302.0 mosM/kg. The
two formulas of OSMc’s were calculated and compared to
OSMm (Table 1). The results show that the equation:
OSMc ¼2*Na þ1:15*Glucose þUrea
compared very well with OSMm with a mean of 291.4 T
4.1 mosM/kg. The reference interval was 283.4 – 299.5
mosM/kg. The OG was 0.8 T3.8 mosM/kg (Table 2) and
the reference interval was 6.7 to 8.2 mosM/kg. To
produce a calculated osmolality that worked in the normal
population, the Dorwart formula was amended as follows:
OSMc ¼1:86*Na þKðÞþ1:15*Glucose þUrea þ14:
The constant value of 14 plus the inclusion of potassium
makes it different from Dorwarts’ formula but makes it very
similar to the formula done in a pediatric population [11].
This calculation gave a mean of 293.0 T4.0 mosM/kg. The
reference interval was 285.3 – 300.6 mosM/kg. The mean
OG was 0.8 T3.8 mosM/kg with the reference interval
being 8.1 to 6.5 mosM/kg (Tables 1 and 2). The above
formulas were then validated in the patient population that
we had seen in our emergency department on which ethanol
was ordered. The mean ethanol levels were 41.5 T27.0
mmol/L and ranged from 0.0 to124.2 mmol/L. The formulas
we used were:
OSMc ¼1:86*Na þKðÞþ1:15*Glucose þUrea
þ1:2*Ethanol þ14 ð1Þ
OSMc ¼2*Na þ1:15*Glucose þUrea
þ1:20*Ethanol:ð2Þ
To demonstrate the effect of the ethanol factor on data
derived from the patient population who had ethanol present
in their blood, we analyzed our patient data using two
formulas first omitting the factor of 1.20. Fig. 3 shows what
happens when formula 1 is used without the factor of 1.2 for
ethanol, whereas Fig. 4 shows the results when the factor is
included. Without the factor, the slope is 0.84 and the
intercept is 45.4, with the factor it changes the slope to 0.99
and the intercept to 3.8. For formula 2, the slope and
intercept were 0.84 and 34, respectively, when the factor of
1.2 was omitted, and became 1.03 and 1 when the factor
was included.
Table 2
Osmol gap in healthy subjects
OG where OSMc is NMean
(mosM/kg)
SE SD Reference
interval
2*Na + 1.15*G + U 37 0.77 0.63 3.80 6.68 to 8.23
1.86*(Na + K) +
1.15*G + U + 14
37 0.75 0.61 3.72 8.04 to 6.54
The formula indicates what was used for OSMc in the respective OG
calculation.
Fig. 3. Passing Bablok regression analysis of OSMm and OSMc from
patient data from July to September 2003 (N= 129). OSMc was calculated
without using a factor of 1.2 for ethanol.
Fig. 4. Passing Bablok regression analysis of OSMm and OSMc from
patient data from July to September 2003 (N= 129). OSMc was calculated
including a factor of 1.2 for ethanol.
Table 3
Comparison of osmolality in patient data using two different formulas
Parameters NMean (mosM/kg) SE SD
OSMm 129 342.6 3.16 35.94
OSMc – 2* 129 341.4 3.16 35.91
OSMc – 1.86* 129 342.8 3.12 35.44
OSMc – 2* = 2*Na + 1.15*G + U + 1.20* EtOH and OSMc – 1.86* =
1.86*(Na + K) + 1.15*G + U + 1.20*EtOH + 14.
A. Khajuria, J. Krahn / Clinical Biochemistry 38 (2005) 514– 519 517
To finally validate the formulas, we calculated OGs on
this same patient population by subtracting the OSMc
(which included the factors for glucose and ethanol) from
OSMm. The mean of OSMc (calculation included ethanol)
compared very well with OSMm. The mean of OSMm
was 342.6 T35.9 mosM/kg and of OSMc were 341.4 T
35.9 and 342.8T35.4 mosM/kg, respectively (Table 3).
The mean OG was 1.2 T5.3 and 0.2 T5.0 mosM/kg,
respectively (Table 4). It is noteworthy our patient data had
mean OGs that were essentially zero and reference
intervals close to the classical 10 to +10 mosM/kg.
Cursory examination of patient data from periods prior to
the study leads us to believe that these relationships are not
stable over time. We are now studying this variability in
more detail.
The OG is a surrogate marker that helps in the diagnosis
and treatment of methanol and ethylene glycol poisoning,
till the quantitative test results become available. In small
centers, however, quantitative tests are not available, thus
OG may be a useful marker in diagnostic evaluation and
initial therapy.
Problems associated using OG as a screening test to
evaluate the presence of methanol and ethylene glycol are
well known [12]. OSMc varies greatly depending on the
formula used to estimate it, and there are no systematic
studies done to evaluate the validation of OSMc with
OSMm. Hoffman et al. calculated OG using a variety of
formulas, and the results of this study demonstrated a wide
variability in OG using different equations and with a large
standard deviation, thus preventing accurate application to
individual data [13].
In the present study, we first evaluated the commonly
used formulas for OSMc by in vitro experiments from
pooled normal plasma. It was observed that glucose and
ethanol need a factor of 1.15 and 1.20 to accurately predict
OSM and OG. Our finding of a factor for ethanol is
consistent with the result of other studies [4,14,15]. Geler et
al.’s findings showed that an increase in OSM produced by
ethanol is greater than usually calculated. A factor of 0.83
indicated that the behavior of ethanol in serum did not
conform to ideal solutions [13]. It indicates that the standard
formulas used in the calculation of OSM will overestimate
the OG in patients with high ethanol levels.
In this study, OSMm in healthy subjects agreed well with
the reference population (285 – 305 mosM/kg) interval and
the OSMc agreed well with OSMm at normal levels of
sodium, potassium, glucose, and urea. It was, however,
interesting to note that the standard deviation of OSMc was
better than OSMm, contrary to common belief. This clearly
suggests a high precision and accuracy of high volume
analyzers. The OG was 10 to 9.6 mosM/kg and does not
change with the presence of ethanol.
It is abundantly clear that a factor of 1.2 needs to be
applied to ethanol to get agreement of the OSMc with
OSMm so that it will not appear that there is another
substance present. Our data are not nearly as clear that
OSMc can be used to predict the presence of toxins
present when little or no ethanol is present. The fact that
both our formulas worked reasonably well in a small
dataset of patients but appeared to perform poorly over a
much longer time is of great concern. All papers we
reviewed have neglected the aspect of quality control on
OSMc and OG. This is a serious oversight. Different
studies using different instruments with slightly different
standards can result in a variety of formulas that can be
validated. No one to our knowledge has examined how
useful these formulas are over time. This is a deficiency
that must be addressed if these calculations are to be
useful. In our opinion, the calculation of OSMc and OG at
the bedside without knowledge of how the calculation
works in that environment is poor practice and subject to
serious error. Any laboratory that calculates OSMc and OG
has the responsibility to verify their calculations in a
population of normal patients and on data from their own
patient population. Furthermore, these calculated parame-
ters should be subject to quality control procedures so the
laboratory staff has the ability to verify that the calcu-
lations are valid.
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Table 4
Comparison of osmol gaps in patient data using two different formulas
Parameters NMean (mosM/kg) SE SD Reference interval
OG-2* 129 1.22 0.47 5.32 9.2 to 11.7
OG-1.86* 129 0.20 0.44 5.02 10.0 to 9.6
OG-2* = OSMm [2*Na + 1.15*G + U + 1.20*EtOH].
OG-1.86* = OSMm 1.86*(Na + K) + 1.15*G + U + 1.20*EtOH + 14.
A. Khajuria, J. Krahn / Clinical Biochemistry 38 (2005) 514– 519518
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