 # Winters’ Formula Made Easy (Expected PaCO2)

by | Updated: Sep 23, 2023

Winters’ formula is an equation used to calculate a patient’s expected PaCO2 (partial pressure of carbon dioxide) based on their arterial blood gas results. The formula is used to evaluate respiratory compensation in response to metabolic acidosis.

This article will explain Winters’ formula in a way that’s easy to learn and understand. We’ll break down each part of the equation so that you’ll understand what each parameter means.

Not to mention, we included step-by-step examples with real patient data to show you exactly how to use Winters’ formula. So, if you’re ready, let’s get into it!

## What is Winters’ Formula?

Winters’ formula is used to calculate a patient’s predicted PaCO2 based on their arterial blood gas (ABG) results. The formula uses the following equation:

Expected PaCO2 = (1.5 x HCO3-) + 8 ± 2

The patient’s bicarbonate value (HCO3-) is obtained by collecting and analyzing a sample of arterial blood. Then you can use Winters’ formula to determine the expected PaCO2 simply by inserting the HCO3- value into the equation.

## How to Use Winters’ Formula

As previously mentioned, you can estimate a patient’s PaCO2 simply by inserting the measured HCO3- value into the equation.

Then you can compare the estimated PaCO2 value to the patient’s actual measured PaCO2. This can result in three possible scenarios:

• Measured PaCO2 = Estimated PaCO2
• Measured PaCO2 > Estimated PaCO2
• Measured PaCO2 < Estimated PaCO2

### Measured PaCO2 = Estimated PaCO2

If the patient’s PaCO2 is within the expected PaCO2 range, it indicates that respiratory compensation is taking place. This is considered to be pure metabolic acidosis.

However, if the patient’s PaCO2 is not within the expected range, it means that a mixed disorder is present.

### Measured PaCO2 > Estimated PaCO2

If the patient’s measured PaCO2 is greater than the estimated PaCO2, it indicates that the patient has respiratory acidosis in addition to metabolic acidosis.

This is because the patient’s respiratory system is not compensating enough for the metabolic acidosis, resulting in an increase in PaCO2.

### Measured PaCO2 < Estimated PaCO2

If the patient’s measured PaCO2 is less than the estimated PaCO2, it indicates that the patient has respiratory alkalosis in addition to metabolic acidosis.

This is because the patient’s respiratory system is overcompensating for the metabolic acidosis, resulting in a decrease in PaCO2.

## Parts of the Winters’ Formula Equation

Let’s take a closer look at each part of the equation to better understand how to use Winters’ formula.

Expected PaCO2 = (1.5 x HCO3-) + 8 ± 2

As you can see, the equation includes the following parts:

• Expected PaCO2
• HCO3-
• 1.5 constant
• 8 constant
• ± 2 constant

### Expected PaCO2

PaCO2 stands for partial pressure of carbon dioxide in arterial blood. This represents how much CO2 is dissolved in the blood and how well the lungs are exchanging gases.

The primary purpose of Winters’ formula is to calculate the patient’s expected PaCO2. This is helpful because it allows you to see if respiratory compensation is taking place.

If the patient’s actual PaCO2 is within the expected range, it means that respiratory compensation is working as it should.

### HCO3-

HCO3- stands for bicarbonate. This is a measure of the acid-base balance in the blood, and it’s measured by collecting and analyzing an arterial blood gas (ABG) from the patient.

The HCO3- value is the only piece of information needed to calculate the expected PaCO2 using Winters’ formula.

### 1.5 Constant

The 1.5 constant is a fixed value in the equation that does not change. It is multiplied by the HCO3- value in order to help calculate the expected PaCO2 range.

### 8 Constant

The 8 constant is another fixed value in the equation that does not change. After the HCO3- value has been multiplied by 1.5, the 8 constant is added to help calculate the expected PaCO2.

### ± 2 Constant

The ± 2 constant in the equation represents the standard deviation of the expected PaCO2. Therefore, the expected PaCO2 range is plus or minus two from the result calculated with Winters’ formula.

If the measured PaCO2 is within this range, it confirms respiratory compensation and pure metabolic acidosis.

## Types of Acid-Base Disorders

There are four primary types of acid-base disorders:

1. Metabolic acidosis
2. Metabolic alkalosis
3. Respiratory acidosis
4. Respiratory alkalosis

Each type of disorder is caused by a different problem. For example, metabolic disorders are caused by an imbalance in the body’s ability to maintain proper pH levels.

Respiratory disorders, on the other hand, occur when the lungs remove too much or too little CO2 due to problems with ventilation.

### Metabolic Acidosis

Metabolic acidosis is a condition where the blood pH is decreased, the PaCO2 is normal, and the HCO3- is decreased. This occurs when the body produces too much acid or when the kidneys are not able to remove enough acid from the blood.

When metabolic acidosis is present, it forces the lungs to work harder to exhale more CO2. This helps to offset the acidosis in order to bring the pH back within the normal range, which is known as respiratory compensation.

### Metabolic Alkalosis

Metabolic alkalosis is a condition where the blood pH is increased, the PaCO2 is normal, and the HCO3- is increased. This occurs when there is an excess of bicarbonate in the blood.

Some of the most common causes of metabolic alkalosis include a loss of stomach acid, diuretic medications, and hypokalemia.

### Respiratory Alkalosis

Respiratory alkalosis is a condition where the blood pH is increased, the PaCO2 is decreased, and the HCO3- is normal. This occurs when there is too much CO2 being removed from the blood by the lungs.

Respiratory alkalosis is caused by hyperventilation, which occurs due to factors such as anxiety, pain, or fever.

### Respiratory Acidosis

Respiratory acidosis is a condition where the blood pH is decreased, the PaCO2 is increased, and the HCO3- is normal. This occurs when there is too little CO2 being removed from the blood by the lungs.

Respiratory acidosis is caused by hypoventilation, which occurs due to factors such as lung disorders, obesity, and sleep apnea.

## What is Respiratory Compensation?

Respiratory compensation is the body’s way of trying to maintain a normal pH level when a metabolic acid-base disorder is present.

In order to do this, the lungs will either remove more CO2 from the blood (in the case of metabolic acidosis) or less CO2 from the blood (in the case of metabolic alkalosis).

This helps to offset the acid-base imbalance and bring the pH level back into the normal range (7.35–7.45).

## Winters’ Formula Practice Examples

One of the most effective ways to learn how to use Winters’ formula is to practice inserting patient data into the equation. Let’s walk through a few example scenarios:

### Example #1

A patient has the following arterial blood gas results:

• pH = 7.34
• PaCO2 = 28 mmHg
• HCO3- = 14 mEq/L

The pH is slightly decreased and falls outside of the normal range. The PaCO2 and HCO3- are both decreased as well.

Therefore, this ABG can be interpreted as partially compensated metabolic acidosis.

In other words, the patient has a metabolic issue, which is causing the lungs to work harder in order to compensate and raise the pH back to normal.

Now, let’s calculate the expected PaCO2 using Winters’ formula:

Expected PaCO2 = (1.5 x HCO3-) + 8 ± 2

Expected PaCO2 = (1.5 x 14) + 8 ± 2

Expected PaCO2 = 29 ± 2

Expected PaCO2 Range = 27–31 mmHg

As you can see, the patient’s measured PaCO2 of 28 mmHg falls within the expected PaCO2 range.

Therefore, by using Winters’ formula, you can confirm that this patient has pure metabolic acidosis with appropriate respiratory compensation and no primary lung disorders.

### Example #2

Now, let’s look at another example. A patient has the following arterial blood gas results:

• pH = 7.30
• PaCO2 = 43 mmHg
• HCO3- = 18 mEq/L

The pH is low and outside of the normal range. The PaCO2 normal, while the HCO3- is decreased.

Therefore, this ABG can be interpreted as acute or uncompensated metabolic acidosis.

In other words, the patient has a metabolic issue, but the lungs have not yet had a chance to compensate and raise the pH back to normal.

Now, let’s calculate the expected PaCO2 using Winters’ formula:

Expected PaCO2 = (1.5 x HCO3-) + 8 ± 2

Expected PaCO2 = (1.5 x 18) + 8 ± 2

Expected PaCO2 = 35 ± 2

Expected PaCO2 Range = 33–37 mmHg

In this case, the patient’s measured PaCO2 of 42 mmHg is higher than the expected PaCO2 range.

Therefore, this indicates that the patient has primary respiratory acidosis in addition to metabolic acidosis.

### Example #3

Finally, let’s take a look at one more example. A patient has the following arterial blood gas results:

• pH = 7.32
• PaCO2 = 27 mmHg
• HCO3- = 16 mEq/L

Again, the pH is low and outside of the normal range, while the PaCO2 and HCO3- are both decreased.

This ABG can be interpreted as partially compensated metabolic acidosis.

Now, let’s calculate the expected PaCO2 using Winters’ formula:

Expected PaCO2 = (1.5 x HCO3-) + 8 ± 2

Expected PaCO2 = (1.5 x 16) + 8 ± 2

Expected PaCO2 = 32 ± 2

Expected PaCO2 Range = 30–34 mmHg

In this case, the patient’s measured PaCO2 of 27 mmHg is lower than the expected PaCO2 range.

Therefore, this indicates that the patient has primary respiratory alkalosis in addition to metabolic acidosis.

## Final Thoughts

Winters’ formula is a tool that can be used to calculate the expected PaCO2 in a patient with metabolic acidosis. It is helpful in confirming respiratory compensation and can be used to differentiate between different types of acid-base disorders.

Remember, the expected PaCO2 must be plus or minus two from the measured PaCO2 in order to confirm respiratory compensation and pure metabolic acidosis.

If the PaCO2 is higher or lower than what is expected, then there may be another disorder present, such as respiratory acidosis or alkalosis.

By understanding this equation and the different types of acid-base disorders, you will be better equipped to care for your patients. Thanks for reading!

Written by:

John Landry, BS, RRT

John Landry is a registered respiratory therapist from Memphis, TN, and has a bachelor's degree in kinesiology. He enjoys using evidence-based research to help others breathe easier and live a healthier life.