Stool osmotic gap: how to calculate the fecal osmotic gap

The stool (fecal) osmotic gap is stool osmolality minus 2 × (stool sodium + stool potassium). If stool osmolality isn't measured, 290 mOsm/kg is assumed. For stool sodium 30 and potassium 75 mmol/L, the gap is 290 − 2 × (30 + 75) = 290 − 210 = 80.0 mOsm/kg.

Not a medical device. Not a diagnosis or dosing recommendation.

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What is the stool osmotic gap?

The stool osmotic gap, also called the fecal osmotic gap or stool osmolar gap, compares the total osmolality of stool water with the part explained by sodium and potassium. It subtracts twice the sum of sodium and potassium from the stool osmolality.

Stool electrolytes and the osmotic gap are used in the work-up of chronic watery diarrhoea.[1] This page explains how the number is calculated. It doesn't interpret it.

The stool osmotic gap formula

osmotic_gap = stool_osm_mosm_kg - 2 * (stool_sodium_mmol_l + stool_potassium_mmol_l)

In words: add stool sodium and stool potassium, double the sum, and subtract that from stool osmolality. Magent's calculator reports the gap to 1 decimal place, in mOsm/kg.

What each part means

How the formula works

1. Add stool sodium and stool potassium.
2. Multiply the sum by 2.
3. Take the stool osmolality: the measured value if you have one, or 290 mOsm/kg if not.
4. Subtract the doubled sum from the osmolality.

When the osmolality is assumed rather than measured, Magent's calculator says so in its response (assumed_osmolality is true).

Negative results

If 2 × (Na + K) is larger than the osmolality used, the gap is negative. Magent's calculator returns the negative number instead of rejecting it, since a negative value can come from things like laboratory error. It's reported, not corrected.

Units

Stool sodium and potassium are in mmol/L, and osmolality and the gap are in mOsm/kg. The formula uses those units directly, so there's nothing to convert.

Worked examples

Example 1: sodium 30, potassium 75, osmolality not measured

1. 30 + 75 = 105
2. 2 × 105 = 210
3. Assumed osmolality: 290 mOsm/kg
4. 290 − 210 = 80.0 mOsm/kg

Example 2: same electrolytes, measured osmolality 250 mOsm/kg

1. 2 × (30 + 75) = 210
2. 250 − 210 = 40.0 mOsm/kg

Using a measured osmolality instead of the assumed 290 changes the gap by the difference between the two (here 290 − 250 = 40).

Example 3: sodium 100, potassium 40, osmolality not measured

1. 100 + 40 = 140
2. 2 × 140 = 280
3. 290 − 280 = 10.0 mOsm/kg

Example 4: sodium 10, potassium 20, osmolality not measured

1. 10 + 20 = 30
2. 2 × 30 = 60
3. 290 − 60 = 230.0 mOsm/kg

Stool osmotic gap reference table

These values are computed from the formula, osmolality − 2 × (Na + K), and rounded to 1 decimal as Magent's calculator reports. The middle column uses the assumed 290 mOsm/kg. They show how the gap moves with the sodium + potassium sum and with osmolality. They are not reference ranges or cutoffs.

Every row is 2 × the sum lower than the osmolality in that column, and the one negative value shows the calculator keeps negative results.

History of the formula

Magent's calculator cites Eherer and Fordtran, Fecal osmotic gap and pH in experimental diarrhea of various causes, published in Gastroenterology in 1992 (volume 103, issue 2, pages 545–551). In that study, diarrhoea was induced in healthy volunteers by different mechanisms. The fecal fluid osmotic gap was calculated using an assumed fecal fluid osmolality of 290 mOsm/kg.[2] That's the same 290 mOsm/kg the calculator assumes when no measured value is given.

When it's used

Chronic diarrhoea can be grouped as fatty, watery or inflammatory. Watery diarrhoea is further divided into secretory and osmotic types, which can be told apart by measuring fecal electrolytes and the osmotic gap.[1] This page reports the number and doesn't classify anything.

Where it's used

Stool sodium and potassium are measured in clinical laboratories. Published laboratory work notes that approved electrolyte assays aren't cleared for stool as a specimen type. Laboratories therefore check the tests' performance on stool themselves before offering them.[1] The same work found that, with endoscopy now widespread, it had been unclear how much these measurements were still used clinically.[1]

Who uses it

Clinical laboratories run the stool electrolyte tests, and clinicians use the results in chronic diarrhoea work-up. In one laboratory's chart audit, stool electrolytes and the osmotic gap were judged useful in every chronic diarrhoea case it looked at.[1]

Limits of the calculation

• It's a calculated value from stool sodium, potassium and osmolality. It doesn't include other stool electrolytes.
• If osmolality isn't measured, the result depends on the assumed 290 mOsm/kg.
• It doesn't classify diarrhoea or apply any separator value.

Clinical decisions belong to a qualified clinician who knows the patient.

How it differs from related calculators

• Serum osmolality calculates the osmolality of blood from serum sodium, glucose and BUN, and can return a serum osmolar gap when a measured value is given. The stool osmotic gap uses stool sodium and potassium, not serum values, and doesn't use glucose or BUN.

Glossary

• Stool (fecal) osmotic gap: stool osmolality − 2 × (stool Na + stool K).
• Stool osmolality: total dissolved-particle concentration of stool water, in mOsm/kg.
• Assumed osmolality: the 290 mOsm/kg used when stool osmolality isn't measured.
• Stool electrolytes: sodium, potassium and other ions measured in stool water.[1]
• Secretory and osmotic diarrhoea: the two types of watery diarrhoea that stool electrolytes and the osmotic gap help tell apart.[1]

Common mistakes

• Forgetting to double the sum. The formula uses 2 × (Na + K), not Na + K.
• Leaving out potassium. Both sodium and potassium go into the sum.
• Mixing measured and assumed osmolality. Note which one you used. The two can give quite different gaps (Examples 1 and 2).
• Throwing out a negative result. The calculator reports it; a negative gap can point to an input or laboratory problem.
• Entering values outside the accepted range. Stool sodium or potassium outside 1–150 mmol/L and a measured osmolality outside 200–600 mOsm/kg are rejected. They aren't estimated.

Source

Eherer AJ, Fordtran JS. Fecal osmotic gap and pH in experimental diarrhea of various causes90845-P). Gastroenterology. 1992;103(2):545-551. DOI: 10.1016/0016-5085(92)90845-P90845-P)

Further reading

1. Parakh R, Greene DN, Mathias PC, Block DR, Ranjitkar P. Laboratory Utilization and Analytical Validation of Fecal Electrolyte Tests. J Appl Lab Med. 2017;1(6):668-677.
2. Eherer AJ, Fordtran JS (the source above), abstract.

Frequently asked questions

How do you calculate the stool osmotic gap?

Use 290 (or measured stool osmolality) − 2 × (stool sodium + stool potassium). For Na 30 and K 75 with no measured osmolality: 290 − 210 = 80.0 mOsm/kg.

What is the fecal osmotic gap?

It's the same measure under another name: stool osmolality minus twice the sum of stool sodium and potassium.

Why is 290 mOsm/kg used?

When stool osmolality isn't measured, 290 mOsm/kg is assumed. The 1992 source study used the same assumed value.[2]

Can the stool osmotic gap be negative?

Yes. If 2 × (Na + K) is larger than the osmolality used, the result is negative, and the calculator reports it rather than rejecting it.

What is the difference between the stool osmotic gap and the stool osmolar gap?

They're names for the same calculation.

What is a normal stool osmotic gap?

This page doesn't give a normal range or a cutoff. It calculates the gap; what a value means depends on clinical context.

Related

• Electrolyte calculators
• Serum osmolality
• All calculator explainers