# Winters' Formula Calculator

Created by Łucja Zaborowska, MD, PhD candidate
Reviewed by Steven Wooding
Last updated: Jun 05, 2023

Winters' formula calculator is a simple tool for computing the **range of pCO₂ compensation in patients with metabolic acidosis (e.g. diabetic ketoacidosis).

Follow the article below to find out more about Winters' formula and discover the physiological basis of acid-base homeostasis and acid-base compensation formulas. 💨

## What is Winters' equation, and what do we use it for?

Winters' formula is a simple way to evaluate your patient's respiratory compensation, that is, the patient's ability to sustain the acid-base homeostasis at a given moment. It's also a way to roughly assess the organism's performance as a whole.

💡 Winters' equation is used for metabolic acidosis with respiratory compensation.

Winter's formula allows us to check whether our patient's CO₂ partial pressure is normal:

• ⬆️ If your patient's results are higher than the calculated range, their compensation is insufficient – they may also suffer from respiratory acidosis. Keep in mind that these results may be as well a result of a mixed acid-base disorder.

• ⬇️ If your patient's results are lower than the calculated range, their respiratory compensation is too severe – they might have a secondary respiratory alkalosis. You should also keep in mind that these results may be due to a mixed acid-base disorder.

You should also monitor your patient's state using the anion gap calculations and the blood pH.

## Physiology of the acid-base homeostasis

In normal conditions, our blood pH is constant and takes a value between 7.35-7.45. The pH depends mostly on the [H⁺] (hydrogen) ions' concentration, which is also constant and equals 35–45 nmol/l. 🩸

The substances that allow the human body to sustain this homeostasis are the pH buffers. These substances, such as bicarbonate buffer system (H₂CO₃ + CO₂ + HCO₃⁻), give or take hydrogen ions, depending on the [H⁺] amount surrounding them. Of course, their effect has its limits – they cannot hold the pH still in an extremely acidic or alkaline environment. This property of buffers is called the buffer capacity. See the buffer capacity calculator for more details.

Two organs cooperate to regulate the hydrogen ions concentration: lungs and kidneys. They both perform their duties in different ways:

• Lungs excrete CO₂
• Kidneys excrete H⁺ formed as the ammonium ion

We distinguish five main types of acid-base disorders.

Follow the table below to find significant differences between acidosis vs alkalosis.

 Respiratory acidosis ↑pCO₂ ↑[H⁺] ↓pH Metabolic acidosis ↓[HCO₃⁻] ↑[H⁺] ↓pH Respiratory alkalosis ↓pCO₂ ↓[H⁺] ↑pH Metabolic alkalosis ↑[HCO₃⁻] ↓[H⁺] ↑pH

In the case of a mixed metabolic-respiratory disorder, there are changes in both HCO₃⁻ and pCO₂.

## How to use the Winters' formula calculator?

Our metabolic acidosis calculator is a tool of precisely one step:

• Enter your HCO₃⁻ concentration (normal range: 23 to 30 mmol/L).

Our calculator will display a direct result, along with the correct range, both given in kilopascals (kPa) and millimeters of mercury (mmHg).

💡 In order to modify the range units, you need to click on the advanced mode button at the bottom of the calculator.

## How to calculate Winter's formula?

We used the following metabolic acidosis compensation formula:

pCO₂ = (1.5 × HCO₃⁻) + 8 , ±2,

where:

• pCO₂ – carbon dioxide partial pressure, given in mmHg;

• HCO₃⁻ – bicarbonates concentration, given in mmol/L = mEq/L; and

• ±2 means that your result is a range. Add two to your result to receive the upper limit of the range, and subtract 2 to obtain the lower limit.

❗ Keep in mind that the ±2 range is only correct when you use mmHg as your partial pressure unit.

Let's follow it with the example:

HCO₃⁻ = 32 mmol/L

pCO₂ = (1.5 × 32 mmol/L) + 8 , ±2

pCO₂ = 56 mmHg

• Lower range: 56 mmHg - 2 mmHg = 54 mmHg

• Upper range: 56 mmHg + 2 mmHg = 58 mmHg

Pss! The formula presented in our metabolic acidosis compensation calculator derives from the Henderson-Hasselbalch calculations. 🤓

Łucja Zaborowska, MD, PhD candidate
HCO₃⁻
mmol/L
pCO₂
mmHg
pCO₂ compensation range: -
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