Winters' formula: how to calculate expected PCO2 in metabolic acidosis

Winters' formula estimates the expected arterial PCO2 from plasma bicarbonate: expected PCO2 = 1.5 × HCO3 + 8, with a band of ±2 mm Hg. For a bicarbonate of 12 mmol/L, the expected PCO2 is 26.0 mm Hg, with a band of 24.0–28.0.

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

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What is Winters' formula?

Winters' formula is a published equation for the arterial PCO2 to expect in metabolic acidosis, given the bicarbonate level. It comes from a 1967 paper by Albert, Dell and Winters.

The physiology behind it: the body compensates for a metabolic acidosis by hyperventilating, which lowers the arterial PCO2.[1] The PCO2 at maximal compensation has been measured in many patients with metabolic acidosis, and a consistent relationship between bicarbonate and PCO2 has been found.[1] Winters' formula expresses that relationship as a simple line.

This page explains what the formula computes. It doesn't interpret blood gases.

The Winters formula

expected_pco2_mm_hg = 1.5 * bicarbonate_mmol_l + 8

In words: multiply bicarbonate by 1.5, then add 8. The band is the expected value minus 2 to the expected value plus 2. That ±2 mm Hg band is the published Winters range. Magent's calculator returns the expected value, the low end and the high end, each to 1 decimal.

What each part means

How the formula works

1. Multiply bicarbonate (mmol/L) by 1.5.
2. Add 8. That's the expected PCO2 in mm Hg.
3. Subtract 2 for the low end of the band and add 2 for the high end.

Each 1 mmol/L change in bicarbonate moves the expected PCO2 by 1.5 mm Hg. The width of the band stays at 4 mm Hg whatever the bicarbonate.

Units

The formula works in mmol/L for bicarbonate and mm Hg for PCO2. Magent's calculator doesn't accept PCO2 in kPa, so if your blood gas reports kPa, this page doesn't give a conversion.

Worked examples

Example 1: bicarbonate 12 mmol/L

1. 1.5 × 12 = 18
2. 18 + 8 = 26.0 mm Hg
3. Band: 26.0 − 2 = 24.0 and 26.0 + 2 = 28.0 → 24.0–28.0 mm Hg

Example 2: bicarbonate 6 mmol/L

1. 1.5 × 6 = 9
2. 9 + 8 = 17.0 mm Hg
3. Band: 15.0–19.0 mm Hg

Example 3: bicarbonate 20 mmol/L

1. 1.5 × 20 = 30
2. 30 + 8 = 38.0 mm Hg
3. Band: 36.0–40.0 mm Hg

Expected PCO2 reference table

These values are computed from the formula, 1.5 × HCO3 + 8 ± 2, across the accepted bicarbonate range. They're rounded to 1 decimal as Magent's calculator reports. They show what the formula returns for each bicarbonate level; they aren't targets.

Entering a measured PCO2

If you also enter a measured arterial PCO2, Magent's calculator returns a label comparing it with the ±2 band. The label is "appropriate" if it falls inside the band, "below_expected" if it's lower, and "above_expected" if it's higher. The label is a comparison with the band and nothing more. The page doesn't say what any result means for a patient.

History of Winters' formula

The formula comes from Albert MS, Dell RB and Winters RW, Quantitative displacement of acid-base equilibrium in metabolic acidosis, published in the Annals of Internal Medicine in 1967 (volume 66, issue 2, pages 312–322). It's commonly called Winters' formula, and is sometimes called the Albert–Winters formula, after the paper's authors.

It's still taught. One open acid-base physiology textbook works through the same bicarbonate of 12 mmol/L used above and reaches an expected PCO2 of 26 mm Hg.[1]

When it's used

Winters' formula is used to estimate the expected arterial PCO2 at maximal respiratory compensation for a metabolic acidosis.[1] The same source describes maximal compensation as taking 12 to 24 hours to develop.[1]

Where it's used

The formula appears in acid-base physiology teaching, with a worked example.[1] It also comes up in kidney care. Published nephrology work discusses which formula to use for expected PCO2 in people on haemodialysis, where respiratory and metabolic acid-base disorders often overlap.[2]

Who uses it

Published work names nephrologists caring for people on haemodialysis as needing to work out the expected PCO2 alongside the bicarbonate.[2]

Limits of the calculation

• It estimates an expected PCO2 for metabolic acidosis. Bicarbonate must be between 2 and 24 mmol/L.
• It's not a target for any intervention.
• It doesn't compute expected PCO2 for metabolic alkalosis, and it doesn't cover respiratory acid-base formulas.

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

How it differs from related calculators

• Serum osmolality is in the same electrolyte family. It calculates osmolality from sodium, glucose and BUN. It doesn't use bicarbonate or PCO2.
• Bicarbonate deficit is also in the record's related list. It estimates a deficit from weight and bicarbonate, not an expected PCO2, so it's out of scope for this page.

Glossary

• PCO2 (PaCO2): partial pressure of carbon dioxide in arterial blood, in mm Hg.
• Bicarbonate (HCO3): plasma bicarbonate concentration, in mmol/L.
• Expected PCO2: the value Winters' formula returns, 1.5 × HCO3 + 8.
• Winters range: the ±2 mm Hg band around the expected PCO2.
• Compensation: the body's hyperventilation response that lowers PCO2 in metabolic acidosis.[1]

Common mistakes

• Forgetting the +8. The formula is 1.5 × HCO3 plus 8, not 1.5 × HCO3 alone.
• Using kPa. The constants assume mm Hg.
• Using it outside metabolic acidosis. The calculator accepts bicarbonate from 2 to 24 mmol/L, and it rejects values outside that range or a measured PCO2 outside 8–80 mm Hg.
• Reading the expected value as a single number. The published result is a band of ±2 mm Hg.

Source

Albert MS, Dell RB, Winters RW. Quantitative displacement of acid-base equilibrium in metabolic acidosis. Ann Intern Med. 1967;66(2):312-322. DOI: 10.7326/0003-4819-66-2-312

Further reading

1. Brandis K. Acid-base Physiology, 5.5: Compensation/05%3A_Metabolic_Acidosis/5.05%3A_Compensation). Medicine LibreTexts.
2. Marano M, D'Amato A, Cantone A. Carbon dioxide: global warning for nephrologists. World J Nephrol. 2016;5(5):429-436.

Frequently asked questions

What is Winters' formula?

It's a published equation for the expected arterial PCO2 in metabolic acidosis: expected PCO2 = 1.5 × HCO3 + 8, ±2 mm Hg.

How do you calculate expected PCO2?

Multiply bicarbonate (mmol/L) by 1.5 and add 8. Subtract and add 2 for the band. For HCO3 12, that's 18 + 8 = 26.0 mm Hg, with a band of 24.0–28.0.

Can you give a Winters' formula example?

With a bicarbonate of 6 mmol/L, 1.5 × 6 + 8 = 17.0 mm Hg, with a band of 15.0–19.0. The table above covers every even value from 2 to 24.

What is the normal range for Winters' formula?

The formula gives a band, not a normal range: the expected value ±2 mm Hg. This page doesn't interpret where a measured PCO2 falls.

Does Winters' formula work in kPa?

The constants are for mm Hg, and Magent's calculator accepts mm Hg. This page doesn't give a kPa version.

Is there a Winters' formula for metabolic alkalosis or respiratory acidosis?

Winters' formula is for metabolic acidosis. This calculator doesn't compute expected PCO2 for metabolic alkalosis or respiratory disorders.

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