# Winters’ Formula Calculator (Expected PaCO₂)

URL: https://speedycalculator.com/calculators/health/winters-formula/
Last updated: 2026-10-30

> Winters' formula calculator predicts the PaCO₂ expected from respiratory compensation in metabolic acidosis, and tells you whether the measured value suggests an additional respiratory disorder.

## Inputs

- Bicarbonate (mEq/L)
- Measured PaCO₂ (optional) (mmHg)

## Results

- Expected PaCO₂
- Expected range from
- Expected range to
- Measured vs expected

## Formula

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

## Explanation

In metabolic acidosis the lungs compensate by breathing faster to blow off carbon dioxide. If the measured PaCO₂ is higher than predicted, there is also a respiratory acidosis; if lower, a respiratory alkalosis.

### How to use the Winters' Formula Calculator

- **Bicarbonate**
- **Measured PaCO₂ (optional)**

Results update as you type, and every field accepts the units shown in its menu.

### How it works

Enter bicarbonate and, optionally, the measured PaCO₂.

### Inputs explained

FieldWhat to enterBicarbonateIn mEq/LMeasured PaCO₂ (optional)In mmHg

### What each result means

- **Expected PaCO₂** = 1.5×[Bicarbonate] + 8
- **Expected range from** = [Expected PaCO₂] - 2
- **Expected range to** = [Expected PaCO₂] + 2

### Example values

How the main result changes when **Bicarbonate** changes and everything else stays at the example values above:

Bicarbonate (mEq/L)Expected PaCO₂ (mmHg)617921.512261530.518352444
*Health note: this calculator is for education and screening only and is not a diagnosis or treatment advice. Discuss your results with a qualified clinician.*

## Worked example

Inputs — Bicarbonate: 12 mEq/L; Measured PaCO₂ (optional): 26 mmHg.

Results — **Expected PaCO₂ = 26 mmHg**; Expected range from = 24 mmHg; Expected range to = 28 mmHg; Measured vs expected = Appropriate compensation.

## Key terms

- **PaCO₂**: Partial pressure of carbon dioxide in arterial blood.

## FAQ

**When is Winters' formula used?**
Only in metabolic acidosis.

**What is a quick check?**
Expected PaCO₂ roughly equals the last two digits of the pH (e.g. pH 7.25 → about 25 mmHg).

**How quickly does compensation happen?**
Within 12–24 hours.


## Sources

- [Albert MS, Dell RB, Winters RW. Quantitative displacement of acid-base equilibrium in metabolic acidosis. Ann Intern Med, 1967](https://pubmed.ncbi.nlm.nih.gov/6016545/)