What is the Winters formula?

The Winters formula predicts the expected arterial pCO2 during metabolic acidosis: pCO2 = 1.5 x [HCO3] + 8 (+/- 2 mmHg). It was derived empirically and published by Winters et al. in 1967.

What does it mean if the measured pCO2 is higher than the expected range?

A pCO2 above the expected range suggests inadequate respiratory compensation, indicating a concurrent respiratory acidosis in addition to the metabolic acidosis.

What does it mean if the measured pCO2 is lower than the expected range?

A pCO2 below the expected range indicates over-compensation, which is physiologically impossible by compensation alone. This points to a concurrent primary respiratory alkalosis.

What HCO3 range is this formula valid for?

The Winters formula is validated for HCO3 levels roughly between 5 and 25 mEq/L in the setting of metabolic acidosis. Values outside this range or in metabolic alkalosis require different compensatory formulas.

Is this tool a substitute for clinical judgment?

No. This calculator is for educational and reference purposes only. Always interpret ABG results alongside the full clinical picture, patient history, and other laboratory findings.

What is a normal HCO3 value?

Normal serum bicarbonate is approximately 22-26 mEq/L. Metabolic acidosis is generally defined as HCO3 below 22 mEq/L.

Winters Formula Calculator

Enter serum bicarbonate (HCO3) to calculate expected pCO2 compensation in metabolic acidosis using the Winters formula.

Input Values

Enter the patient's serum bicarbonate from a metabolic panel or ABG.

Serum HCO3 (mEq/L)

Normal range: 22–26 mEq/L. Metabolic acidosis: < 22 mEq/L.

Measured pCO2 (mmHg, optional)

From ABG report. Leave blank to see the expected range only.

Results

Winters formula: pCO2 = 1.5 × HCO3 + 8 (±2 mmHg)

Enter HCO3 and click Calculate to see results.

Quick Reference — Winters Formula Table

HCO3 (mEq/L)	Expected pCO2 (mmHg)	pCO2 Range (±2)

Summary

The Winters formula estimates the expected respiratory compensation in metabolic acidosis: pCO2 = 1.5 x HCO3 + 8, with a tolerance of +/- 2 mmHg. Comparing the patient's measured pCO2 to this range reveals whether compensation is appropriate or whether a concurrent respiratory acid-base disorder is present. This tool is used widely in emergency medicine, critical care, and nephrology to interpret arterial blood gas results.

How it works

Enter the patient serum bicarbonate (HCO3) value in mEq/L.
Optionally enter the measured arterial pCO2 from the ABG report.
The calculator applies the Winters formula: pCO2 = 1.5 x HCO3 + 8.
The expected pCO2 range is displayed as the calculated value +/- 2 mmHg.
If a measured pCO2 is provided, the tool compares it to the expected range and interprets the result.
Review the interpretation to identify simple compensation, concurrent respiratory acidosis, or concurrent respiratory alkalosis.

Use cases

Interpreting arterial blood gas results in patients with metabolic acidosis.
Identifying a superimposed respiratory acidosis (pCO2 higher than expected).
Detecting a concurrent respiratory alkalosis (pCO2 lower than expected).
Confirming appropriate respiratory compensation before attributing dyspnea to another cause.
Teaching acid-base physiology in medical education.
Quick bedside ABG interpretation in the emergency department or ICU.
Nephrology consult workup for chronic metabolic acidosis.
Cross-checking manual calculations to reduce arithmetic errors.

Frequently Asked Questions

Last updated: 2026-09-30 · Reviewed by Nham Vu