Winter's Formula Calculator

About the Winter's Formula Calculator

Winter's formula predicts how far the lungs should lower the arterial carbon dioxide (PaCO₂) to compensate for a metabolic acidosis. When bicarbonate falls, the respiratory centre drives faster, deeper breathing, and in a pure, steady-state metabolic acidosis the PaCO₂ settles close to 1.5 × HCO₃⁻ + 8, give or take 2 mmHg. Enter the serum or arterial bicarbonate to get the expected PaCO₂ range.

If you also enter the measured PaCO₂ from the blood gas, the calculator tells you whether respiratory compensation is appropriate. A measured value above the range means the lungs are not blowing off enough CO₂ — a second, respiratory acidosis (for example from fatigue, sedation or lung disease). A value below the range means a superimposed respiratory alkalosis, as seen in early sepsis or salicylate poisoning.

The formula was derived by Albert, Dell and Winters (1967) from patients with stable, mostly severe metabolic acidosis (mean bicarbonate around 10 mEq/L), so it applies only when the primary disorder is a metabolic acidosis and compensation has had 12–24 hours to develop. It is least well validated when bicarbonate is only mildly reduced. It is intended for clinicians and students interpreting arterial blood gases and does not replace clinical judgement.

With the default inputs, the expected paco₂ is 26 mmHg. Change any value above to recalculate instantly.

How to use the winter's formula calculator

1Confirm the primary disorder is a metabolic acidosis (low pH and low bicarbonate).
2Enter the bicarbonate value in mEq/L.
3Enter the measured PaCO₂ from the arterial blood gas, if available.
4Read the expected PaCO₂ range and the compensation verdict.

Formula and method

Expected PaCO₂ = (1.5 × HCO₃⁻) + 8 ± 2 mmHg

Albert, Dell and Winters measured arterial blood gases in patients with stable metabolic acidosis and found a linear relationship between bicarbonate and PaCO₂: PaCO₂ is about 1.5 × HCO₃⁻ plus 8 mmHg. The ±2 mmHg band reflects the scatter of measured values around that line. Because the original patients mostly had severe acidosis, some nephrology authors note the formula fits less well when bicarbonate is only mildly low.

Comparing the measured PaCO₂ with the band identifies a mixed disorder. Above the band, ventilation is inadequate (an added respiratory acidosis); below it, ventilation is excessive (an added respiratory alkalosis). The rule assumes a primary metabolic acidosis and steady-state compensation, which typically takes 12–24 hours.

HCO₃⁻: Serum or arterial bicarbonate (mEq/L)
PaCO₂: Arterial partial pressure of carbon dioxide (mmHg)

Worked examples

Appropriately compensated acidosis

With HCO₃⁻ 12 mEq/L, the expected PaCO₂ is 1.5 × 12 + 8 = 26 mmHg (range 24–28). The measured PaCO₂ of 26 mmHg sits inside the band, so respiratory compensation is appropriate.

Tiring patient with retained CO₂

Expected PaCO₂ is 1.5 × 10 + 8 = 23 mmHg (21–25). The measured 32 mmHg is higher than the lungs should allow, pointing to a superimposed respiratory acidosis.

Acidosis with hyperventilation

Expected PaCO₂ is 1.5 × 16 + 8 = 32 mmHg (30–34). A measured 22 mmHg is well below the band, which suggests an additional primary respiratory alkalosis, as can occur in sepsis or salicylate toxicity.

Frequently asked questions

What is Winter's formula used for?+

Winter's formula predicts the PaCO₂ expected from normal respiratory compensation in a metabolic acidosis. Comparing it with the measured PaCO₂ shows whether a second respiratory disorder is present alongside the metabolic acidosis.

What does it mean if PaCO₂ is higher than Winter's formula predicts?+

A PaCO₂ above the expected range means ventilation is not compensating fully, indicating a concurrent respiratory acidosis. Causes include respiratory muscle fatigue, sedation, neuromuscular weakness or significant lung disease.

What does a PaCO₂ lower than expected mean?+

A PaCO₂ below the predicted range indicates a concurrent respiratory alkalosis. Classic examples are early sepsis, salicylate poisoning, liver failure and anxiety or pain driving hyperventilation on top of the metabolic acidosis.

Can Winter's formula be used in metabolic alkalosis?+

No. It applies only to metabolic acidosis. For metabolic alkalosis a different rule is used: PaCO₂ rises by roughly 0.7 mmHg for every 1 mEq/L rise in bicarbonate above 24.

Is there a quick bedside shortcut?+

In compensated metabolic acidosis the PaCO₂ often approximates the last two digits of the pH (for example pH 7.25 with PaCO₂ near 25 mmHg). It is a rough check only; Winter’s formula is more precise.

For healthcare professionals and education only. This calculator implements a published formula or score but is not a diagnosis and does not replace clinical judgment. Verify inputs and results against the original source before using them in patient care.

Sources