# A Review of the Usefulness of the Winter’s Formula: Predicted PaCO2 = 1.5 x [HCO3-] + 8 + 2

So here we are… not another formula, right? No worries. This one is actually quite straight forward and relatively easy to work out. The tricky part lies in the interpretation of the result – isn’t that always seemingly the case. But, it’s ok. You’re either a respiratory therapy student or a RT who is in pursuit of greater knowledge, so once you have taken a moment to review and digest some key concepts, you will be well on your way to putting the Winter’s formula into practice and with great efficiency the more you use it.

To begin, you must recognize that every formula renders a result only as credible as the numbers put into the equation. Particularly with dynamic patient blood parameters, it is extremely important that the initial diagnostic test, in this case the arterial blood gas (ABG) is accomplished under ideal conditions, free of sampling or processing error.

That said, it is important to also note that an ABG measurement only represents a single snapshot in time. Furthermore, there is always a slight margin for error regardless of the clinician’s technique and steps to processing this highly metabolic arterial blood sample. If one assumes the ABG values are credible, then feel free to proceed accordingly with utilizing the Winter’s formula.

## What is the Winter’s Formula?

For any pH less than 7.35 with an accompanying bicarbonate (HCO3) level less than 22 mEq/L, metabolic acidosis is clearly present. However, when given standard ABG values, the respiratory component (represented by PaCO2) should not be discounted even if there is no obvious contribution by the respiratory system to the acidosis. For example, one would assume if pH is less than 7.35, indicating acidosis, with a low HCO3 (i.e. less than 22 mEq/L) and a normal PaCO2 (35-45 mmHg), this represents a pure metabolic acidosis. At face value, this is a correct assumption, but consider the Winter’s formula.

Taking it a step further, there are many complex cases in which patients will display an ABG-confirmed metabolic acidosis (low pH, low HCO3) but have an additional respiratory condition (high PaCO2: acidosis or low PaCO2: alkalosis) that may be less detectable without keen insight. This is where the Winter’s formula is helpful.

## What does the Winter’s Formula Tell Us?

The Winter’s formula allows a calculation of a PaCO2 that would be expected (aka. predicted PaCO2) for a particular HCO3 level and is based upon the following estimation equation:

Predicted PaCO2 = 1.5 x [HCO3-] + 8 + 2

This predicted PaCO2 is a value representative of the respiratory system, for what arterial CO2 level you should expect for a certain HCO3 level. In other words, if HCO3 is lower than normal (lower than 22 mEq/L), indicating a metabolic acidosis, you would expect PaCO2 to decrease as the respiratory system normally readily compensates for a metabolic acidosis in attempt to efficiently normalize pH back to within physiologic normal range (7.35 – 7.45). When HCO3 is lower than normal, typically causing (metabolic) acidosis, PaCO2 will usually decrease in order to allow pH to return to normal range. When HCO3 is higher than normal (greater than 26 mEq/L), PaCO2 will usually increase in order to allow pH to return to normal range.

## Winter’s Formula Practice

### Example 1

Take for instance the following ABG for a patient with a history of poorly controlled diabetes and recent diagnosis of diabetic ketoacidosis (DKA). DKA is commonly associated with an ABG-confirmed metabolic acidosis, so it would be no surprise when the following ABG values are revealed:

The ABG indicates, at face value, an acute/uncompensated metabolic acidosis. Let’s apply the Winter’s formula in order to evaluate what PaCO2 should be present under conditions where a pure metabolic acidosis exists. Winter’s formula: Predicted PaCO2 = 1.5 x [HCO3-] + 8 + 2

1. Plug in the known values from the ABG

Predicted PaCO2 = 1.5 x [17] + 8 +2

2. Work out the multiplication portion first

Predicted PaCO2 = 25.5 + 8 + 2

3. Continue by adding in the ‘8’

Predicted PaCO2 = 33.5 + 2

4. The “+ 2” represents the range above and below your now known, expected (predicted) value for PaCO2.

You now know your expected PaCO2 would be 31.5 to 35.5

Because in the scenario, the patient’s actual PaCO2 is higher than the expected PaCO2 range (it’s 38 mmHg instead of the predicted 31.5 to 35.5), you also now can confirm this patient has a separate respiratory acidosis also contributing to the lower-than-normal pH. If the patient’s actual PaCO2 would have fallen within the calculated predicted PaCO2 range of 31.5 to 35.5 mmHg, it would have confirmed the presence of a pure metabolic acidosis. If the patient’s actual PaCO2 would have fallen below the lower value within the predicted PaCO2 range (below 31.5 mmHg), it would indicate a separate respiratory alkalosis.

### Example 2

If you acquire the following ABG values on a patient in which there is no known clinical history, you should still be able to determine whether the patient has a pure metabolic acidosis or an accompanying respiratory condition. The patient’s ABG results are as follows:

The ABG indicates, at face value, a partially compensated metabolic acidosis. HCO3 is obviously low (less than 22 mEq/L) with a lower than normal pH (acidosis). PaCO2 is lower than normal (less than 35mmHg), so there is no indication that the respiratory system contributed to the acidosis. But, can you be sure?

Let’s apply the Winter’s formula in order to evaluate what PaCO2 should be present under conditions where a pure metabolic acidosis exists.

Winter’s formula: Predicted PaCO2 = 1.5 x [HCO3-] + 8 + 2

1. Simply plug in the known values from the ABG: Predicted PaCO2 = 1.5 x [12] + 8 + 2
2. Work out the multiplication portion first: Predicted PaCO2 = 18 + 8 + 2
3. Continue by adding in the ‘8’: Predicted PaCO2 = 26 +
4. The “+ 2” represents the range above and below your now known, expected (predicted) value for PaCO2. You now know your expected PaCO2 would be 24 to 28

Because in the scenario, the patient’s actual PaCO2 is lower than the expected PaCO2 range (it’s 21 mmHg instead of the predicted 24 to 28), you also now can confirm this patient has a separate respiratory alkalosis not contributing to the lower-than-normal pH. If the patient’s actual PaCO2 would have fallen within the calculated predicted PaCO2 range of 24 to 28, it would have confirmed the presence of a pure metabolic acidosis. If the patient’s actual PaCO2 would have fallen above the higher value within the predicted PaCO2 range (above 28 mmHg), it would indicate a separate respiratory acidosis.

### Example 3

Let’s look at a final example in which an ABG is acquired on a patient with current diagnosis of metabolic acidosis.

Again, we simply are wanting to evaluate whether this patient has a pure metabolic acidosis or whether there is also respiratory derangement present. In other words, is the respiratory system currently acting as it should with the current state of metabolic acidosis?

Let’s apply the Winter’s formula in order to evaluate what PaCO2 should be present under conditions where a pure metabolic acidosis exists.

Winter’s formula: Predicted PaCO2 = 1.5 x [HCO3-] + 8 + 2

1. Simply plug in the known values from the ABG: Predicted PaCO2 = 1.5 x [19] + 8 + 2
2. Work out the multiplication portion first: Predicted PaCO2 = 28.5 + 8 + 2
3. Continue by adding in the ‘8’: Predicted PaCO2 = 36.5 + 2
4. The “+ 2” represents the range above and below your now known, expected (predicted) value for PaCO2. You now know your expected PaCO2 would be 34.5 to 38.5

Because in the scenario, the patient’s actual PaCO2 is within the calculated range (aka. predicted PaCO2), you now can confirm this patient has a pure metabolic acidosis without any particular respiratory derangement. If the patient’s actual PaCO2 would have fallen outside the calculated predicted PaCO2 range of 34.5 to 38.5 mmHg, it would have confirmed the presence of respiratory derangement, indicating a separate respiratory acidosis (if PaCO2 above 38.5) or  separate respiratory alkalosis (if PaCO2 below 34.5). In this patient’s case, the metabolic acidosis is the only abnormality present with no respiratory system abnormality.

## Conclusion

In summary, the Winter’s formula is an equation that can be quickly applied at bedside even without a calculator (scary thought, I know). It is a quick way to assess a metabolic acidosis and put into perspective whether the metabolic acidosis is a stand-alone abnormality or whether there is a separate respiratory system abnormality. Always remember that numbers are just numbers, and a full clinical assessment is always superior to a single calculation. With the benefit of knowing a portion of your patient’s history or most recent current state of being, you will likely have an idea whether something more detrimental is in progress. However, when you simply need to evaluate whether the respiratory system is also displaying an abnormality aside from the obvious metabolic acidosis, the Winter’s formula can be very helpful.

About Tim Gilmore, PhD, RRT, RRT-NPS, RRT-ACCS, CPFT, AE-C
Dr. Gilmore is an Associate Professor of Cardiopulmonary Science (CPS) and the CPS Program Director at Louisiana State University Health Shreveport. He holds a PhD in Health Science from Nova Southeastern University, a Masters in Health Sciences and BS in Cardiopulmonary Science from LSU Health Shreveport and an AS in Respiratory Therapy from Bossier Parish Community College (BPCC). Dr. Gilmore’s research interests include ICU care, mechanical ventilation, asthma, and patient education. He is a member of the Louisiana Society for Respiratory Care, American Association for Respiratory Care, and National Board for Respiratory Care. He is a Registered Respiratory Therapist with specialty credentials as a Neonatal Pediatric Specialist and Adult Critical Care Specialist, with national certifications as a Pulmonary Functions Technologist and Asthma Educator. He also serves as a peer reviewer for Respiratory Care Journal and an item-writer for the NBRC.