Winters' formula: the expected PaCO₂ in metabolic acidosis
Winters' formula tells you how far the PaCO₂ should fall in a metabolic acidosis. Compare the measured value with that window and a hidden respiratory disorder shows itself.
Chapters (10)
Given an ABG and electrolytes showing a metabolic acidosis, calculate the expected PaCO₂ with Winters' formula (1.5 × HCO₃⁻ + 8 ± 2 mm Hg) and classify the measured PaCO₂ as appropriate compensation, a coexisting respiratory acidosis (above the range) or a coexisting respiratory alkalosis (below the range).
The short version
- Winters' formula: expected PaCO₂ = 1.5 × HCO₃⁻ + 8 ± 2 mm Hg, with HCO₃⁻ in mEq/L.
- A measured PaCO₂ inside the window is appropriate respiratory compensation: a simple metabolic acidosis.
- Above the window means a coexisting respiratory acidosis; below it means a coexisting respiratory alkalosis.
- Compensation is partial and never overshoots, so a normal PaCO₂ or a near-normal pH can hide a second disorder.
- Winters' formula is only for metabolic acidosis, and the verdict is cleanest once compensation has had 12–24 hours.
When a normal PaCO₂ is the red flag
A patient in diabetic ketoacidosis has a bicarbonate of 12 mEq/L. Their PaCO₂ is 38 mm Hg, which sits inside the normal range of 35–45 mm Hg.[7] That normal-looking number is the red flag on this blood gas.
Winters' formula gives the expected PaCO₂ in metabolic acidosis, and comparing it with the measured value is how a hidden respiratory disorder is exposed. For this patient, the expected PaCO₂ turns out to be far lower than 38.
The mental model: a ratio and partial compensation
By the Henderson–Hasselbalch equation, pH is set by a ratio: bicarbonate on top, carbon dioxide on the bottom.[3] The usual reference point is a pH of 7.40, a PaCO₂ of 40 mm Hg and an HCO₃⁻ of 24 mEq/L.[3][4]
6.1 = pK of the bicarbonate system; 0.03 = CO₂ solubility coefficient (mmol/L per mm Hg)
In metabolic acidosis, the primary problem is a fall in bicarbonate, so the top of the ratio drops.[1] The lungs respond: chemoreceptors sense the acid, and breathing increases to blow off CO₂, pulling the pH back toward normal.[1][2]
- Before compensation, PaCO₂ 40: 6.1 + log(12 / 1.2) = 7.10
- After compensation to PaCO₂ 26: 6.1 + log(12 / 0.78) ≈ 7.29
- Closer to 7.40, but short of it
But compensation is partial: it cannot return the pH completely to normal, and it never overshoots.[1] It also takes time. Breathing rises within minutes, but maximal compensation can take 12–24 hours.[2]
Those two facts set up everything that follows. Because the response is partial, the PaCO₂ should fall by a predictable amount, and Winters' formula puts a number on it.
Winters' formula for expected PaCO₂
So how far should the PaCO₂ fall? Winters' formula predicts it.[1][2]
HCO₃⁻ in mEq/L; the answer is in mm Hg
It is an empirical rule, fitted to blood gases from 60 patients with diarrhea, diabetes or kidney disease.[4][5] The eponym is Robert W. Winters, one of the authors of the 1967 paper,[5] so the correct spelling is Winters' formula, although many people search for "Winter's formula".
Worked example: HCO₃⁻ 12
- HCO₃⁻ = 12
- 1.5 × 12 = 18
- 18 + 8 = 26
- 26 ± 2 → expected PaCO₂ 24–28 mm Hg
The measured PaCO₂ of 38 is well above that window, even though 38 is a normal value on its own.
Notice what the formula does. It does not ask whether the PaCO₂ is normal; it asks whether the PaCO₂ is right for this bicarbonate. A PaCO₂ of 26 would be the expected answer here, so 38 means the lungs are blowing off far less CO₂ than the acidosis calls for.
Measured vs expected PaCO₂: three outcomes
Once you have the expected window, compare the measured PaCO₂ with it. There are only three possible readings.[1][6]
For the opening patient, the measured 38 is above the 24–28 window. The verdict is a metabolic acidosis with a coexisting respiratory acidosis, even though 38 sits inside the normal range.
| Measured PaCO₂ | Where it falls | Interpretation |
|---|---|---|
| 26 | Inside the window | Appropriate respiratory compensation: a simple metabolic acidosis |
| 38 | Above the window | Coexisting respiratory acidosis |
| 18 | Below the window | Coexisting respiratory alkalosis |
Above the window, the lungs are not clearing as much CO₂ as this acidosis demands, so there is a coexisting respiratory acidosis. In a very sick patient, that can mean the breathing muscles are tiring, and intubation may be coming.[6]
Below the window, the patient is blowing off more CO₂ than compensation alone explains, so there is a coexisting respiratory alkalosis.
Two practical points, and where Winters' formula stops
- The verdict is cleanest once compensation has had 12–24 hours to develop.[2]
- Shortcuts such as PaCO₂ ≈ HCO₃⁻ + 15 exist, but they are imprecise rules of thumb.[1]
Winters' formula is only for metabolic acidosis. Metabolic alkalosis and the respiratory disorders have their own compensation rules.[1]
Practice question
Original · USMLE styleA 22-year-old woman with type 1 diabetes mellitus is brought to the emergency department after 2 days of vomiting and abdominal pain. She is drowsy but rousable. Respirations are 12/min and shallow. Pulse is 118/min and blood pressure is 102/64 mm Hg. Laboratory studies show:
| Serum Na⁺ | 136 mEq/L |
|---|---|
| Serum Cl⁻ | 100 mEq/L |
| Serum HCO₃⁻ | 10 mEq/L |
| Serum glucose | 540 mg/dL |
| Serum β-hydroxybutyrate | elevated |
| Arterial blood gas (room air): pH | 7.09 |
| PaCO₂ | 34 mm Hg |
| PaO₂ | 88 mm Hg |
Common questions
What is Winters' formula?
It predicts the expected PaCO₂ in metabolic acidosis: 1.5 × HCO₃⁻ + 8 ± 2 mm Hg, with HCO₃⁻ in mEq/L. It is an empirical rule fitted to blood gases from 60 patients.
Is it Winter's formula or Winters' formula?
The eponym is Robert W. Winters, so Winters' formula is the correct spelling. Winter's formula is the common search spelling for the same rule.
What does it mean if the PaCO₂ is higher than Winters' formula predicts?
The lungs are not clearing as much CO₂ as the acidosis demands, so there is a coexisting respiratory acidosis. A PaCO₂ below the window means a coexisting respiratory alkalosis.
Can I use HCO₃⁻ + 15 instead of Winters' formula?
Shortcuts like HCO₃⁻ + 15 exist, but they are imprecise rules of thumb.
Does Winters' formula work for metabolic alkalosis?
No. Winters' formula is only for metabolic acidosis; metabolic alkalosis and the respiratory disorders have their own compensation rules.
Transcript
Read the full narration, by chapter649 words
0:00A normal PaCO2 that is a red flag
A patient in diabetic ketoacidosis has a bicarbonate of 12. Their PaCO2 is 38 millimetres of mercury, which sits inside the normal range. And that normal-looking number is the red flag on this blood gas. Today: Winters' formula, the expected PaCO2 in metabolic acidosis, and how it exposes a hidden respiratory disorder.
0:24The mental model: the HCO3− / CO2 ratio
First, the mental model. By the Henderson-Hasselbalch equation, pH is set by a ratio: bicarbonate on top, carbon dioxide on the bottom. The usual reference point is a pH of 7.4, a PaCO2 of 40, and a bicarbonate of 24. In metabolic acidosis, the primary problem is a fall in bicarbonate, so the top of the ratio drops. So the lungs respond: chemoreceptors sense the acid, and breathing increases to blow off carbon dioxide, pulling the pH back toward normal. But compensation is partial: it cannot return the pH completely to normal, and it never overshoots. And it takes time: breathing rises within minutes, but maximal compensation can take 12 to 24 hours.
1:15Winters' formula
So how far should the PaCO2 fall? Winters' formula predicts it. Expected PaCO2 equals 1.5 times the bicarbonate, plus 8, plus or minus 2. Bicarbonate goes in as mEq/L, and the answer comes out in mm Hg. It's an empirical rule, fitted to blood gases from 60 patients with diarrhea, diabetes or kidney disease.
1:41Worked example
Let's run it on our patient. Bicarbonate is 12. 1.5 times 12 is 18. Add 8, and you get 26. With the plus or minus 2, the expected window is 24 to 28 mm Hg.
1:56Measured vs expected: three outcomes
Now compare the measured value with that window. One: the measured PaCO2 lands inside the window, say 26. That's appropriate respiratory compensation, a simple metabolic acidosis. Two: it's above the window, like our 38. The lungs are not clearing as much carbon dioxide as this acidosis demands, so there is a coexisting respiratory acidosis. In a very sick patient, that can mean the breathing muscles are tiring, and intubation may be coming. Three: it's below the window, say 18. The patient is blowing off more carbon dioxide than compensation alone explains, so there is a coexisting respiratory alkalosis.
2:41Bonus clue: a near-normal pH
Bonus clue: with a bicarbonate of 12 and a PaCO2 of 18, the pH works out to about 7.45. Compensation can't fully normalise pH, so a near-normal pH with a very low bicarbonate hints at a second disorder.
2:59Two practical points
Two practical points. First, the verdict is cleanest once compensation has had 12 to 24 hours to develop. Second, shortcuts like bicarbonate plus 15 exist, but they're imprecise rules of thumb. And Winters' formula is only for metabolic acidosis; metabolic alkalosis and the respiratory disorders have their own compensation rules.
3:23Practice question
Practice question. A 22-year-old woman with type 1 diabetes has had 2 days of vomiting and abdominal pain. She is drowsy and breathing shallowly at 12 breaths per minute. Sodium is 136, chloride 100, bicarbonate 10, and serum ketones are high. Arterial pH is 7.09, and the PaCO2 is 34. Which option best describes her acid-base status? Pause and try it. The anion gap is 26, so it's high, which rules out E. Expected PaCO2: 1.5 times 10 is 15, plus 8 is 23, so the window is 21 to 25. Her measured 34 is above the window, so the answer is B: a coexisting respiratory acidosis. A is the trap: 34 is below 40, but it isn't low enough for a bicarbonate of 10. C would need a PaCO2 below 21. And D is out: compensation for a respiratory acidosis raises bicarbonate, it doesn't drop it to 10.
4:36Recap
Quick recap. One: expected PaCO2 equals 1.5 times bicarbonate, plus 8, plus or minus 2. Two: above the window means a coexisting respiratory acidosis; below it means a coexisting respiratory alkalosis. Three: a normal PaCO2, or a near-normal pH, can hide a second disorder.
5:00Next lesson
Next: mixed disorders and the delta-delta, to find a second metabolic problem hiding behind the gap.
Sources
Numbers in the text, e.g. [1], point here- MSD Manual Professional (Lewis JL III, 2025): Acid-Base Disorders; Metabolic Acidosis; Acid-Base Regulation; Primary Changes and Compensations in Simple Acid-Base Disorders (table). msdmanuals.com/professional/endocrine-and-metabolic-disorders/acid-base-regulation-and-disorders/acid-base-disorders · msdmanuals.com/professional/multimedia/table/primary-changes-and-compensations-in-simple-acid-base-disorders
- Brandis K. Acid-base Physiology, 5.05 Compensation (LibreTexts). med.libretexts.org/Bookshelves/Anatomy_and_Physiology/Book%3A_Acid-base_Physiology_(Brandis)/05%3A_Metabolic_Acidosis/5.05%3A_Compensation
- Binks A. The Henderson-Hasselbalch equation. Pulmonary Physiology for Pre-Clinical Students (LibreTexts). med.libretexts.org/Courses/Virginia_Tech_Carilion_School_of_Medicine/Pulmonary_Physiology_for_Pre-Clinical_Students_(Binks)/11%3A_Alkalosis_and_Acidosis/11.03%3A_The_Henderson-Hasselbalch_equation
- Kopel J, Berdine G. Winters's formula revisited. Southwest Respir Crit Care Chron 2019;7(27). doi:10.12746/swrccc.v7i27.512
- Albert MS, Dell RB, Winters RW. Ann Intern Med 1967;66(2):312-322. doi:10.7326/0003-4819-66-2-312 (as summarised by Kopel & Berdine 2019)
- Duška F et al. A pragmatic approach to complex acid base disturbances of critical illness: the "Stewart light". Intensive Care Med 2026. doi:10.1007/s00134-026-08416-3
- Korus et al. Metabolic Acidosis in Patients with CKD: a Narrative Review. Diagnostics 2025;15(16):2052. doi:10.3390/diagnostics15162052
- USMLE Content Outline. usmle.org/sites/default/files/2022-01/USMLE_Content_Outline_0.pdf
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" https://smart.servier.com/smart_image/lungs-11/ and "Intrapulmonary airways" https://smart.servier.com/smart_image/intrapulmonary-airways-lungs/ All other drawings, charts and lettering are original.
Corrections. None so far. Spotted an error? Email info@medservatory.com with the lesson code MS-S1-REN-003.
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