Delta ratio: find the hidden second acid–base disorder
The delta ratio compares the rise in the anion gap with the fall in bicarbonate. In a high anion gap acidosis, it shows whether a second metabolic disorder is hiding.
Chapters (9)
Given an ABG and electrolytes showing a high anion gap metabolic acidosis, calculate the delta ratio (ΔAG/ΔHCO₃⁻) and state whether a concurrent normal anion gap acidosis (< 1) or metabolic alkalosis (> 2) is present, as the final step of the five-step approach.
The short version
- The delta ratio is the rise in the anion gap divided by the fall in bicarbonate: (AG − 12) / (24 − HCO₃⁻).
- Between 1 and 2, a high anion gap acidosis is on its own.
- Below 1, a normal anion gap acidosis is also present; above 2, usually a metabolic alkalosis.
- Work in order: pH, primary disorder, anion gap, Winters' formula, then the delta ratio.
- Cut-offs differ between sources and the ratio varies widely between patients, so treat it as a clue, not a verdict.
The puzzle the delta ratio solves
A patient's bicarbonate is 18, only a little below normal. But the anion gap is 32. That mismatch is a clue that a second disorder is hiding, and the delta ratio is the tool that finds it.[3][4]
This is the last step of a five-step approach to acid–base problems, so it builds on the earlier tools.
The toolkit: pH, anion gap and Winters' formula
- A pH below 7.35 is acidemia.[1]
- Anion gap = Na⁺ − (Cl⁻ + HCO₃⁻), using the common normal value of 12.[1]
- If albumin is low, lower the expected gap by 2.5 for every 1 g/dL fall.[1]
- Winters' formula predicts the PaCO₂: 1.5 × HCO₃⁻ + 8 ± 2.[1]
Each tool answers one question. The pH says whether there is acidemia, the bicarbonate says the primary disorder is metabolic, the anion gap says whether it is a high gap acidosis, and Winters' formula checks the breathing. Only then does the delta ratio look for a second metabolic disorder.
Why the anion gap rises as bicarbonate falls
When a strong acid, such as a ketoacid, enters the blood, bicarbonate buffers its hydrogen ions, so bicarbonate goes down. But the acid's anion stays behind, unmeasured, so the gap goes up. In a simple high gap acidosis, it is roughly a one-for-one swap.[1][6]
So the two changes can be compared. If the fall in bicarbonate does not match the rise in the gap, something else is moving the bicarbonate.
In the opening puzzle, the gap rose by 20 (32 − 12) while bicarbonate fell by only 6 (24 − 18). The two changes are far from a one-for-one swap, which is exactly the mismatch the delta ratio measures.
The delta ratio formula and how to read it
12 = normal anion gap; 24 = normal HCO₃⁻ (mEq/L); the ratio has no units
| Delta ratio | What it means | Why |
|---|---|---|
| Below 1 | High gap acidosis plus a normal gap acidosis | Bicarbonate fell more than the gap rose, so a normal gap acidosis is also pulling it down |
| 1–2 | High gap acidosis on its own | The changes roughly match |
| Above 2 | High gap acidosis plus (usually) a metabolic alkalosis | Bicarbonate fell too little, so something pushed it up |
These are the bands used in this lesson.[3][4] Other sources draw them differently (see below).
Why a pure high gap acidosis is not exactly 1
Some acid is buffered inside cells while its anion stays in the blood, so the gap rises more than bicarbonate falls. Lactic acidosis averages about 1.6.[4]
Ketoacidosis sits nearer 1, because ketones are lost in the urine.[4]
That is why the band for a high gap acidosis on its own runs from 1 to 2 rather than sitting at exactly 1.
Worked case: the five-step approach with the delta ratio
A 30-year-old with type 1 diabetes has had 2 days of vomiting. Na⁺ 138, Cl⁻ 88, HCO₃⁻ 18 (all mEq/L); PaCO₂ 35 mm Hg; pH 7.33; albumin normal.
- pH7.33 is below 7.35: acidemia.
- Primary disorderWith acidemia, a low bicarbonate means the primary disorder is a metabolic acidosis.
- Anion gap138 − (88 + 18) = 32, and albumin is normal: a high anion gap.
- Winters' formula1.5 × 18 + 8 = 35 ± 2, so the PaCO₂ of 35 is appropriate compensation.
- Delta ratioThe gap rose by 20 (32 − 12), but bicarbonate fell by only 6 (24 − 18). 20 / 6 ≈ 3.3.
A ratio above 2 means a metabolic alkalosis is hiding inside the acidosis. Diabetes explains the ketoacidosis, and vomiting, which loses stomach acid, explains the alkalosis.[1]
Delta ratio cut-offs differ: conventions and caveats
- Some sources call 0.4–0.8 a mixed high and normal gap acidosis[4][5], and some call 0.8–2 a high gap acidosis on its own.[5]
- Some use 25 for normal bicarbonate, and your lab's normal gap may be lower than 12.[1][2]
- Another version subtracts instead of dividing (Wrenn's delta gap: ΔAG − ΔHCO₃⁻) and calls a difference beyond ±6 significant.[7] Some sources, such as Merck, use "delta gap" for ΔAG alone.[1]
- A high ratio can also mean a compensated chronic respiratory acidosis.[4]
- The ratio varies widely between patients.[6]
Practice question
Original · USMLE styleA 58-year-old woman is brought to the emergency department after 3 days of profuse watery diarrhea. She is lethargic. Blood pressure is 82/50 mm Hg and pulse is 124/min. Laboratory studies show:
| Serum Na⁺ | 136 mEq/L |
|---|---|
| Serum Cl⁻ | 108 mEq/L |
| Serum HCO₃⁻ | 8 mEq/L |
| Serum albumin | 4.0 g/dL |
| Lactate | 7.0 mmol/L |
| Arterial pH | 7.22 |
| Arterial PCO₂ | 20 mm Hg |
Common questions
How do you calculate the delta ratio?
Take the anion gap minus 12 and divide it by 24 minus the bicarbonate. It compares the rise in the gap with the fall in bicarbonate.
What does a delta ratio above 2 mean?
Bicarbonate fell too little for the rise in the gap, so something pushed it up, usually a metabolic alkalosis. A high ratio can also mean a compensated chronic respiratory acidosis.
What does a delta ratio below 1 mean?
Bicarbonate fell more than the gap rose, so a normal anion gap acidosis is usually also present alongside the high gap acidosis. A low ratio is also common in the acidosis of renal failure, and an uncorrected low albumin can pull it down.
What is the difference between the delta gap and the delta ratio?
The delta ratio divides the rise in the gap by the fall in bicarbonate. Wrenn's delta gap subtracts the fall in bicarbonate from the rise in the gap and calls a difference beyond ±6 significant: above +6 suggests a metabolic alkalosis, below −6 a normal gap acidosis. Note that some sources use "delta gap" to mean the rise in the gap alone.
Why is the delta ratio in lactic acidosis about 1.6?
Some of the acid is buffered inside cells while its anion stays in the blood, so the gap rises more than bicarbonate falls. Ketoacidosis sits nearer 1 because ketones are lost in the urine.
Transcript
Read the full narration, by chapter639 words
0:00The puzzle: HCO3⁻ 18 but anion gap 32
Here's a puzzle. A patient's bicarbonate is 18, only a little below normal. But the anion gap is 32. That mismatch is a clue that a second disorder is hiding, and today the delta ratio will find it.
0:14Toolkit: pH, anion gap, Winters' formula
First, the tools from the last three lessons. A pH below 7.35 is acidemia. The anion gap is sodium minus the sum of chloride and bicarbonate, and we'll use the common normal value of 12. If albumin is low, lower that expected gap by 2.5 for every 1 g/dL fall. And Winters' formula predicts the PaCO2: 1.5 times bicarbonate, plus 8, plus or minus 2.
0:44Why the gap rises as HCO3⁻ falls
Now the new idea. When a strong acid, like a ketoacid, enters the blood, bicarbonate buffers its hydrogen ions, so bicarbonate goes down. But the acid's anion stays behind, unmeasured, so the gap goes up. In a simple high gap acidosis, it's roughly a one-for-one swap.
1:05The delta ratio formula and how to read it (below 1, 1–2, above 2)
So we compare the two changes. Take the gap minus 12, and divide it by 24 minus the bicarbonate. That's the delta ratio. Between 1 and 2, you have a high gap acidosis on its own. Below 1, bicarbonate fell more than the gap rose, so a normal gap acidosis is also pulling it down. Above 2, bicarbonate fell too little, so something pushed it up, usually a metabolic alkalosis.
1:34Why not exactly 1? (lactic ≈ 1.6, DKA ≈ 1)
Why not exactly 1? Some acid is buffered inside cells while its anion stays in the blood, so lactic acidosis averages about 1.6. Ketoacidosis sits nearer 1, because ketones are lost in the urine.
1:50Worked case: the five-step approach
Now the whole approach, step by step. A 30-year-old with type 1 diabetes has had 2 days of vomiting. Sodium 138, chloride 88, bicarbonate 18, all in milliequivalents per litre. PaCO2 35 mm Hg, pH 7.33. Step one: acidemia. Step two: bicarbonate is low, so it's a metabolic acidosis. Step three: the gap is 138 minus 106, which is 32, and albumin is normal. Step four: Winters' gives 35, plus or minus 2, so the PaCO2 of 35 is appropriate compensation. Step five: the gap rose by 20, but bicarbonate fell by only 6. 20 over 6 is about 3.3. Above 2, so a metabolic alkalosis is hiding inside the acidosis. Diabetes explains the ketoacidosis, and vomiting, which loses stomach acid, explains the alkalosis.
2:59Conventions differ (and caveats)
One honest warning: sources draw these cut-offs differently. Some call 0.8 to 2 pure, and 0.4 to 0.8 mixed. Some use 25 for bicarbonate, and your lab's normal gap may be lower than 12. An older version subtracts instead of dividing, and calls a difference beyond 6 significant. A high ratio can also mean compensated chronic respiratory acidosis. And the ratio varies widely between patients, so treat it as a clue, not a verdict.
3:33Practice question
Your turn. A 58-year-old woman has 3 days of profuse watery diarrhea, and her blood pressure is 82/50. Sodium 136, chloride 108, bicarbonate 8. PaCO2 20, pH 7.22, lactate 7 mmol/L, albumin normal. Which disorders are present? Pause and work it out. The gap is 20, so it's high. Winters' predicts 18 to 22, and her PaCO2 fits, so there's no extra respiratory disorder: that rules out D and E. The gap rose by 8, but bicarbonate fell by 16, a ratio of 0.5. Below 1, so a normal gap acidosis is hiding too, and the answer is B. Lactic acidosis from shock raises the gap, and the diarrhea loses bicarbonate. A ignores that low ratio, and C would need a ratio above 2.
4:39High-yield recap and next lesson
Three things to remember. One: the delta ratio is the rise in the gap divided by the fall in bicarbonate. Two: below 1, add a normal gap acidosis; above 2, add a metabolic alkalosis. Three: work in order: pH, primary disorder, gap, Winters', then the delta ratio. Next, we move from the kidney to the heart, with the four phases of the pressure-volume loop.
Sources
Numbers in the text, e.g. [1], point here- Lewis JL III. Acid-Base Disorders; Metabolic Acidosis; Metabolic Alkalosis; Lactic Acidosis. MSD Manual Professional Version (2025). msdmanuals.com/professional/endocrine-and-metabolic-disorders/acid-base-regulation-and-disorders/acid-base-disorders
- MSD Manual: Anion Gap / Delta-Delta calculator. msdmanuals.com/iframe/manual/medical-calculators/aniongapdeltagradient.htm
- AMBOSS. Delta gap. amboss.com/us/snippet/Delta_gap
- Brandis K. Acid-base Physiology, §3.03 The Delta Ratio (LibreTexts, CC BY-NC-SA). med.libretexts.org/Bookshelves/Anatomy_and_Physiology/Book%3A_Acid-base_Physiology_(Brandis)/03%3A_Acid-Base_Disorders/3.03%3A_The_Delta_Ratio
- Yartsev A. Delta gap and delta ratio: advantages and disadvantages. Deranged Physiology, ch. 123. derangedphysiology.com/main/required-reading/acid-base-disorders/Chapter-123/delta-gap-and-delta-ratio-advantages-and-disadvantages
- Rastegar A. Use of the ΔAG/ΔHCO3⁻ ratio in the diagnosis of mixed acid-base disorders. J Am Soc Nephrol 2007;18:2429–31. doi:10.1681/ASN.2006121408
- Wrenn K. The delta (Δ) gap: an approach to mixed acid-base disorders. Ann Emerg Med 1990;19(11):1310–3. doi:10.1016/s0196-0644(05)82292-9
The practice question is original and its patient is synthetic. Every fact is checked against the sources above in independent accuracy reviews. Always follow your local guidelines and your own laboratory’s ranges.
Image credits. Illustrations: Servier Medical Art (smart.servier.com), licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/); adapted (recoloured, outlined, resized): lungs, cell, nephron, stomach, intestine. All other diagrams are original.
Corrections. None so far. Spotted an error? Email info@medservatory.com with the lesson code MS-S1-REN-004.
For exam study only, not medical advice. Read the medical disclaimer.
In this series
Playlist on YouTube- EP 01ABG interpretation, made simple5:35
- EP 02Anion gap explained: high vs normal gap metabolic acidosis5:25
- EP 03Winters' formula: the expected PaCO₂ in metabolic acidosis5:10
- EP 04Delta ratio: find the hidden second acid–base disorder5:09
- EP 05New bicarbonate: how the kidney excretes acid with ammonium5:23
- EP 06High anion gap metabolic acidosis causes, sorted by the anion5:54
- EP 07Osmolar gap: how toxic alcohols hide from the anion gap5:31
- EP 08Urine anion gap: telling diarrhea from RTA5:33
- EP 09Renal tubular acidosis: tell RTA types 1, 2 and 4 apart5:24
- EP 10Metabolic alkalosis: generation, maintenance and urine chloride5:30
- EP 11Vomiting metabolic alkalosis: why the urine turns acid5:36
- EP 12Bartter vs Gitelman: NKCC2, NCC and urine calcium5:21
- EP 13Respiratory acidosis compensation: acute vs chronic5:22
- EP 14Respiratory alkalosis compensation: acute vs chronic5:33
- EP 15Metabolic alkalosis compensation: the expected PaCO₂5:12
- EP 16Salicylate poisoning acid-base: a classic mixed disorder5:31
- EP 17Type A vs type B lactic acidosis: split it by mechanism5:33
- EP 18DKA anion gap explained: from high gap to hyperchloraemic acidosis5:42
- EP 19Acidosis and hyperkalemia: how pH shifts potassium5:43
- EP 20ABG interpretation in 6 steps: the acid-base algorithm5:32
- EP 21Acid-base practice cases: three ABG vignettes, one algorithm5:44