ABG Calculator: Arterial Blood pH from HCO₃ and PaCO₂

Two values, one number, no fuss. Enter the bicarbonate and PaCO₂ from any arterial blood gas report, and this calculator returns the arterial pH instantly using the Henderson-Hasselbalch equation — the same equation built into your blood gas analyzer. PaCO₂ can be entered in Torr, mmHg, kPa, or inches of mercury, so you don't have to convert before plugging in numbers.

This tool is built for the moment you actually need it: a nursing student trying to make sense of acid-base on a Tuesday night, a respiratory therapist verifying a printout, or a clinician who wants a fast pH derivation without filling out the eight-field forms most ABG analyzers demand. Below the calculator you'll find a quick-reference card, the math explained without hand-waving, four worked clinical scenarios, the mnemonics nurses actually remember on shift, and the small mistakes that quietly throw your numbers off.

If pH, PaCO₂, and HCO₃ all sit inside these ranges, you're looking at normal acid-base balance.

Blood pH lives inside an unforgiving window. Drift below 6.8 or above 7.8 and most patients won't survive long, which is why the body defends 7.35–7.45 with two organ systems running in parallel:

• Lungs clear CO₂, which dissolves to form an acid (more CO₂ = more acid)
• Kidneys manage HCO₃⁻, which acts as a base

When sepsis, DKA, COPD, vomiting, or kidney failure pushes pH off course, one system tries to compensate for the other. That's why pH alone isn't the whole story — pH tells you the patient's current state, while PaCO₂ and HCO₃ tell you which system caused the problem and which is trying to fix it.

This calculator runs the Henderson-Hasselbalch equation for the bicarbonate buffer system:

```
pH = 6.1 + log₁₀(HCO₃⁻ / (0.03 × PaCO₂))
```

The big idea: pH depends on the ratio of base (bicarbonate) to dissolved acid (CO₂), not the absolute values. A normal 20:1 ratio gives you pH 7.40. Halve the ratio and pH drops by 0.30. Double it and pH rises by 0.30.

If you enter PaCO₂ in kPa, Torr, or inHg, the calculator converts to mmHg internally — your unit choice doesn't change your answer.

1. Enter HCO₃ in mEq/L (normal: 22–26)
2. Enter PaCO₂ as your lab reports it (normal: 35–45 mmHg)
3. Pick the PaCO₂ unit — Torr, mmHg, kPa, or inHg
4. Read the pH — calculated to two decimals, instantly

No accounts, no submit button. Change any input and the answer updates.

Once you know pH is abnormal, ROME tells you which system caused it:

• Respiratory = Opposite — pH and PaCO₂ move in opposite directions (low pH + high PaCO₂ = respiratory acidosis)
• Metabolic = Equal — pH and HCO₃ move in the same direction (low pH + low HCO₃ = metabolic acidosis)

The 0.08 rule (acute respiratory changes): Every 10 mmHg acute rise in PaCO₂ drops pH by about 0.08. Every 10 mmHg drop raises pH by about 0.08. Useful for sanity-checking calculated values when you suspect the patient just hypoventilated or hyperventilated.

Winters' formula (expected compensation in metabolic acidosis):

```
Expected PaCO₂ = (1.5 × HCO₃) + 8 ± 2
```

If the actual PaCO₂ falls outside this range, you're looking at a mixed disorder — not pure metabolic acidosis.

Healthy adult
HCO₃ 24, PaCO₂ 40 → 6.1 + log₁₀(24 / 1.2) = 7.40
The classic 20:1 ratio. Everything balanced.

COPD exacerbation (respiratory acidosis, partial renal compensation)
HCO₃ 28, PaCO₂ 60 → 6.1 + log₁₀(28 / 1.8) = 7.29
The patient can't blow off CO₂. Kidneys have raised HCO₃ to compensate, but pH is still acidic — they need ventilatory support, not more bicarbonate.

Diabetic ketoacidosis (metabolic acidosis, respiratory compensation)
HCO₃ 10, PaCO₂ 25 → 6.1 + log₁₀(10 / 0.75) = 7.22
Ketoacids consumed bicarbonate. The patient is breathing fast and deep (Kussmaul respirations) to drop PaCO₂. Winters' check: expected PaCO₂ = (1.5 × 10) + 8 = 23 ± 2. Actual is 25 — within range, so this is a pure metabolic acidosis with appropriate compensation.

Prolonged vomiting (metabolic alkalosis)
HCO₃ 36, PaCO₂ 48 → 6.1 + log₁₀(36 / 1.44) = 7.50
Loss of stomach acid drove HCO₃ up. The respiratory system has nudged PaCO₂ up to compensate, but pH is still alkalotic. Treatment is volume and chloride, not "fixing the pH."

A normal PaCO₂ of 40 mmHg = 5.33 kPa. The mental shortcut for kPa users: multiply by 7.5.

• Mixing venous and arterial values. A VBG reads ~0.03–0.05 lower in pH and ~4–6 mmHg higher in CO₂ than an ABG. The math still runs, but your output reflects venous chemistry — useful, but not interchangeable with arterial.
• Wrong unit selected. Plug a kPa value in with the dropdown set to Torr and you'll roughly multiply your true PaCO₂ by 7.5, crashing the calculated pH. Always confirm the dropdown matches the lab report.
• Reading pH in isolation. A "normal" pH can hide a fully compensated mixed disorder. If both PaCO₂ and HCO₃ sit far off baseline, something's going on even when pH looks fine.
• Trusting calculated pH over measured. Your analyzer's pH electrode is the gold standard. This calculator is for derivation, learning, and double-checking — not for replacing the measured value when you have one.

To keep this tool fast and focused, we left out things you'd need a full ABG analyzer for:

• Anion gap (requires sodium, chloride, HCO₃)
• Compensation classification (acute vs. chronic, primary vs. mixed)
• Oxygenation assessment (PaO₂, A-a gradient)
• Base excess / base deficit

If you need any of those, pair this calculator with a full ABG interpretation framework or analyzer. For derivation of pH itself, you're in the right place.

This calculator is a learning and reference tool. It calculates arterial pH from your inputs using a well-established physiological equation, but it does not replace clinical assessment, full ABG interpretation, or measured lab values. At the bedside, treat it as a check on the analyzer-reported pH, not a substitute for it.