Delta Gap Formula
The delta gap formula (AG − 12) − (24 − HCO₃⁻) detects mixed acid–base disorders by comparing the rise in anion gap to the fall in bicarbonate. Here is the derivation, interpretation, and a worked example.
The delta gap equation
The delta gap formula compares two deviations from normal: how much the anion gap has risen (ΔAG) and how much the bicarbonate has fallen (ΔHCO₃⁻). Written out, it is simply the difference of those two deviations:
The first parenthesized term, (AG − 12), is the ΔAG — the amount by which the observed anion gap exceeds the normal value of 12 mEq/L. The second term, (24 − HCO₃⁻), is the ΔHCO₃⁻ — the amount by which the observed bicarbonate falls short of the normal value of 24 mEq/L. In a pure high-anion-gap metabolic acidosis, each extra unmeasured anion consumes one bicarbonate as a buffer, so ΔAG equals ΔHCO₃⁻ and the delta gap is zero. When the two deviations do not match, a second acid–base disorder is present — and the sign and magnitude of the delta gap tell you which.
Derivation from the 1:1 buffering assumption
The delta gap rests on a simple biochemical assumption: in HAGMA, the unmeasured anions accumulating in serum (lactate, ketones, sulfate, toxin metabolites) are buffered one-for-one by bicarbonate. For every milliequivalent of new anion that appears, one milliequivalent of bicarbonate is consumed. So if the anion gap rises by 10 mEq/L, the bicarbonate should fall by 10 mEq/L, and the two deltas should be equal. Any mismatch between them must come from a separate process acting on the bicarbonate independently — a metabolic alkalosis adding bicarbonate back, or a second acid (a hyperchloremic acidosis) consuming extra bicarbonate. Subtracting the two deltas isolates exactly that mismatch. This logic is the foundation for detecting mixed disorders from a single set of electrolytes.
Interpreting positive and negative values
The delta gap carries the same units as the anion gap itself (mEq/L), and its sign points directly at the hidden disorder.
| Delta gap | Meaning | Hidden disorder |
|---|---|---|
| +6 or higher | Bicarbonate fell less than expected | Concurrent metabolic alkalosis (vomiting, diuretics, NG suction) or chronic respiratory acidosis with renal compensation. |
| −6 to +6 | Deltas match | Pure HAGMA — no second disorder. The rise in AG and fall in HCO₃⁻ are proportional. |
| −6 or lower | Bicarbonate fell more than expected | Concurrent normal-anion-gap (hyperchloremic) metabolic acidosis — diarrhea, renal tubular acidosis, saline dilution. |
A positive delta gap means the bicarbonate did not fall as much as the gap rose — something is holding the bicarbonate up. The classic bedside story is a DKA patient who has also been vomiting: the ketoacidosis raises the gap and lowers the bicarbonate, but the vomiting (loss of gastric acid) generates a metabolic alkalosis that lifts the bicarbonate back up, producing a large positive delta gap. A negative delta gap means the bicarbonate fell further than the gap rose — something extra is pulling it down. The classic story is a ketoacidosis patient with concurrent diarrhea, where the gastrointestinal bicarbonate loss adds a hyperchloremic acidosis on top of the HAGMA, dragging the bicarbonate below what the gap alone would predict.
Worked example
Consider a patient with an anion gap of 24 and a bicarbonate of 14 mEq/L. ΔAG = 24 − 12 = 12; ΔHCO₃⁻ = 24 − 14 = 10. Delta gap = 12 − 10 = +2 mEq/L — within the −6 to +6 band, so this reads as a pure HAGMA with no second disorder. Now picture the same gap of 24 but with a bicarbonate of 20: ΔAG = 12, ΔHCO₃⁻ = 4, delta gap = 12 − 4 = +8 mEq/L — a concurrent metabolic alkalosis is holding the bicarbonate up (think vomiting). And a gap of 24 with a bicarbonate of 6: ΔAG = 12, ΔHCO₃⁻ = 18, delta gap = 12 − 18 = −6 mEq/L — a concurrent normal-anion-gap metabolic acidosis is pulling the bicarbonate down (think diarrhea). You can reproduce all three of these scenarios in the delta gap calculator.
The delta gap is a subtraction; the delta ratio formula (ΔAG ÷ ΔHCO₃⁻) is the division of the same two quantities. The two carry identical information — they detect the same mixed disorders — but modern references more often quote the ratio because its cut-offs (1 for pure HAGMA, 2 for concurrent alkalosis, 0.4–0.8 for mixed HAGMA + NAGMA) are easier to remember. Use whichever your team prefers; the delta gap tends to read more intuitively at the bedside because it stays in mEq/L.
The delta gap formula and its interpretation bands are reviewed against StatPearls and LITFL acid–base references. The −6 to +6 mEq/L "pure HAGMA" band is a clinical convention that accommodates biological noise; some references use slightly tighter or looser cut-offs. Always interpret alongside the full clinical picture and the arterial blood gas when available.