What is Winter's formula?

Winter's formula predicts the expected arterial pCO2 during metabolic acidosis: pCO2 = 1.5 × [HCO3] + 8 (±2 mmHg). It was derived empirically and published by Winters et al. in 1967 based on observed respiratory responses to metabolic acidosis.

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

A measured pCO2 higher than the expected range indicates inadequate respiratory compensation, suggesting a concurrent primary respiratory acidosis is present alongside the metabolic acidosis.

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

A measured pCO2 lower than the expected range indicates over-compensation, which cannot occur by physiological compensation alone. This points to a concurrent primary respiratory alkalosis.

What HCO3 range is Winter's formula valid for?

The formula is validated for HCO3 levels roughly between 5 and 25 mEq/L in the setting of metabolic acidosis. Outside this range, or in mixed disorders, interpret results carefully alongside the full clinical picture.

Is this tool a substitute for clinical judgment?

No. This calculator is for educational and reference purposes only. Always interpret ABG results in context with the full clinical picture, patient history, and other laboratory findings. Clinical decisions should never be based solely on a formula.

What is a normal serum bicarbonate?

Normal serum bicarbonate is approximately 22–26 mEq/L. Metabolic acidosis is generally defined as HCO3 below 22 mEq/L in the appropriate clinical context.

Winter's Formula Compensation Calculator

Name: Winter's Formula Compensation Calculator
Availability: InStock
Author: Nham Vu

Enter serum bicarbonate and measured pCO2 to check whether respiratory compensation in metabolic acidosis is appropriate, inadequate, or excessive.

Patient Values

Serum HCO₃ (mEq/L)

Normal: 22–26 mEq/L. Enter the value from ABG or BMP.

Measured pCO₂ (mmHg) — optional

Normal: 35–45 mmHg. Leave blank to see expected range only.

Formula Reference

Expected pCO₂ = 1.5 × HCO₃ + 8 ± 2

Winters et al., 1967 — validated for metabolic acidosis

Results

Enter HCO₃ and click Calculate to see results.

Summary

Enter serum bicarbonate and measured pCO2 to check whether respiratory compensation in metabolic acidosis is appropriate, inadequate, or excessive.

How it works

Enter the patient serum bicarbonate (HCO3) in mEq/L from the arterial blood gas or basic metabolic panel.
Enter the measured arterial pCO2 in mmHg from the ABG report.
The calculator applies the formula: expected pCO2 = 1.5 × HCO3 + 8.
The expected range is shown as the calculated value ± 2 mmHg.
Your measured pCO2 is compared to the expected range and the result is interpreted.
Review the interpretation to identify simple compensation, concurrent respiratory acidosis, or concurrent respiratory alkalosis.

Use cases

Interpreting arterial blood gas results in patients with confirmed metabolic acidosis.
Identifying a superimposed respiratory acidosis when measured pCO2 is higher than expected.
Detecting a concurrent primary respiratory alkalosis when measured pCO2 is lower than expected.
Confirming appropriate respiratory compensation before attributing dyspnea to a separate cause.
Quick bedside ABG interpretation in the emergency department or ICU.
Nephrology consult workup for chronic metabolic acidosis (e.g., renal tubular acidosis, CKD).
Teaching acid-base physiology in medical education and clinical training.
Cross-checking manual calculations to reduce arithmetic errors at the bedside.

Frequently Asked Questions

Last updated: 2026-07-17 · Reviewed by Nham Vu