Acid-Base Equation Calculator

pH = 6.1 + log([HCO₃⁻] / (0.03 × pCO₂))

The Henderson-Hasselbalch equation is the fundamental relationship between pH, bicarbonate, and carbon dioxide. Calculate any one variable from the other two. Visualize acid-base balance on an interactive pH scale.

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Henderson-Hasselbalch Calculator

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Acid-Base Values

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Formula & Calculation

Henderson-Hasselbalch Equation

The cornerstone equation of acid-base physiology, linking pH to the bicarbonate buffer system.

The Equation

pH = 6.1 + log([HCO₃⁻] / (0.03 × pCO₂))

This equation describes the relationship between pH and the bicarbonate buffer system. The 6.1 is the pKa of carbonic acid. The 0.03 is the solubility coefficient of CO₂ in plasma. The ratio of bicarbonate to dissolved CO₂ determines the pH.

Rearranged Forms

HCO₃⁻ = 0.03 × pCO₂ × 10^(pH − 6.1)

The equation can be rearranged to solve for any of the three variables. To find pCO₂: pCO₂ = HCO₃⁻ / (0.03 × 10^(pH − 6.1)). This calculator handles all three modes automatically.

Step-by-Step Calculation

1
Get lab values. You need at least two of: pH (from ABG), HCO₃⁻ (from BMP or ABG), pCO₂ (from ABG).
2
Calculate dissolved CO₂. Multiply pCO₂ by 0.03: 40 × 0.03 = 1.2 mmol/L.
3
Find the ratio. Divide HCO₃⁻ by dissolved CO₂: 24 / 1.2 = 20.
4
Take the log and add 6.1. log(20) = 1.301. pH = 6.1 + 1.301 = 7.401.

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Understanding the Basics

What is the Henderson-Hasselbalch Equation?

The fundamental equation that connects pH to the body's primary buffer system.

Definition

The Henderson-Hasselbalch equation describes how the pH of a buffer solution depends on the ratio of the conjugate base to the acid. In the blood, the primary buffer is the bicarbonate system: CO₂ dissolves in water to form carbonic acid (H₂CO₃), which dissociates into H⁺ and HCO₃⁻.

The equation shows that pH depends on the ratio of HCO₃⁻ to dissolved CO₂, not their absolute values. A 20:1 ratio gives pH 7.40.

Clinical Importance

This equation is the basis for understanding all acid-base disorders. Metabolic disorders change HCO₃⁻ (the numerator). Respiratory disorders change pCO₂ (the denominator). The body compensates by adjusting the other variable to maintain the ratio close to 20:1.

Reference Values

Acid-Base Normal Ranges

Normal arterial blood gas values and acid-base parameters.

ParameterNormal RangeUnitNotes
pH7.35 – 7.45unitsArterial blood
pCO₂35 – 45mmHgRespiratory component
HCO₃⁻22 – 26mEq/LMetabolic component
pO₂80 – 100mmHgOxygenation
HCO₃⁻:CO₂ Ratio20 : 1—Maintains pH 7.40

Where Does Your pH Fall?

This gauge shows the calculated pH. Change values above to see the needle move.

Clinical Interpretation

Acid-Base Interpretation

How to interpret pH, bicarbonate, and pCO₂ together.

🔴

Acidemia (pH < 7.35)

Low pH
  • Metabolic acidosis (low HCO₃⁻)
  • Respiratory acidosis (high pCO₂)
  • Mixed acidosis
  • DKA, lactic acidosis
  • COPD exacerbation
  • Hypoventilation
🟢

Normal pH (7.35–7.45)

Balanced
  • Normal acid-base status
  • Compensated metabolic acidosis
  • Compensated respiratory alkalosis
  • Mixed disorder (opposing effects)
  • Early or mild disturbance
🔵

Alkalemia (pH > 7.45)

High pH
  • Metabolic alkalosis (high HCO₃⁻)
  • Respiratory alkalosis (low pCO₂)
  • Vomiting, NG suction
  • Diuretic use
  • Hyperventilation, anxiety
  • Liver failure
Common Questions

Frequently Asked Questions

Answers to common questions about the Henderson-Hasselbalch equation.

The Henderson-Hasselbalch equation is pH = 6.1 + log([HCO₃⁻] / (0.03 × pCO₂)). It describes the relationship between pH and the bicarbonate buffer system. The 6.1 is the pKa of carbonic acid, and 0.03 is the solubility coefficient of CO₂ in plasma. This equation is the foundation of clinical acid-base analysis.
Multiply pCO₂ by 0.03 to get dissolved CO₂. Divide HCO₃⁻ by that number. Take the log₁₀ of the result and add 6.1. Example: HCO₃⁻ = 24, pCO₂ = 40. Dissolved CO₂ = 40 × 0.03 = 1.2. Ratio = 24 / 1.2 = 20. log(20) = 1.301. pH = 6.1 + 1.301 = 7.401.
Normal arterial blood pH is 7.35–7.45, with 7.40 as the ideal value. A pH below 7.35 is called acidemia, and above 7.45 is alkalemia. Life-threatening pH extremes are below 6.8 or above 7.8. The body uses buffer systems, respiratory compensation, and renal compensation to keep pH within this narrow range.
The 0.03 is the solubility coefficient of CO₂ in plasma at 37°C, measured in mmol/L per mmHg. It converts the partial pressure of CO₂ (pCO₂ in mmHg) to the concentration of dissolved CO₂ in plasma (in mmol/L). This dissolved CO₂ is in equilibrium with carbonic acid (H₂CO₃), which is the acid form in the bicarbonate buffer pair.
Yes. Rearranging the equation: HCO₃⁻ = 0.03 × pCO₂ × 10^(pH − 6.1). Example: pH = 7.40, pCO₂ = 40. HCO₃⁻ = 0.03 × 40 × 10^(7.40 − 6.1) = 1.2 × 10^1.3 = 1.2 × 19.95 = 23.9 mEq/L. This is the "calculated bicarbonate" that appears on ABG reports.
When pCO₂ rises, the denominator of the ratio increases, the ratio decreases, and pH falls (becomes more acidic). This is respiratory acidosis. For every 10 mmHg rise in pCO₂ above 40, pH drops by approximately 0.08 acutely. The kidneys compensate over 3–5 days by retaining HCO₃⁻ to restore the ratio toward 20:1.