pH Calculator

pH = −log₁₀[H⁺]

Convert between pH and hydrogen ion concentration. Understand the logarithmic nature of the pH scale and its clinical significance. Visualize where your value falls on an interactive pH scale.

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pH ↔ [H⁺] Converter

Convert between pH and hydrogen ion concentration. Select the conversion direction below.

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Formula & Calculation

pH Formula & Conversions

The mathematical relationship between pH and hydrogen ion concentration.

pH from [H⁺]

pH = −log₁₀[H⁺]

pH is the negative base-10 logarithm of the hydrogen ion concentration in mol/L. For clinical use, [H⁺] is often expressed in nmol/L (nanomoles per liter). Normal blood [H⁺] is 35–45 nmol/L, corresponding to pH 7.35–7.45.

[H⁺] from pH

[H⁺] = 10^(−pH)

The inverse conversion. Each unit change in pH represents a 10-fold change in [H⁺]. A pH of 7.0 means [H⁺] = 100 nmol/L. A pH of 7.4 means [H⁺] = 40 nmol/L. A pH of 8.0 means [H⁺] = 10 nmol/L.

Step-by-Step Conversion

1
pH → [H⁺]: Take 10 raised to the power of negative pH. For pH 7.40: [H⁺] = 10⁻⁷·⁴⁰ = 3.98 × 10⁻⁸ mol/L = 39.8 nmol/L.
2
[H⁺] → pH: Take the negative log of [H⁺] in mol/L. For 40 nmol/L: pH = −log(40 × 10⁻⁹) = −log(4 × 10⁻⁸) = 7.40.
3
Quick estimate: At pH 7.40, [H⁺] = 40 nmol/L. For each 0.01 pH change, [H⁺] changes by ~1 nmol/L in the opposite direction. pH 7.30 ≈ [H⁺] 50; pH 7.50 ≈ [H⁺] 32.
4
pOH: pOH = 14 − pH. At pH 7.40, pOH = 6.60. [OH⁻] = 10⁻⁶·⁶⁰ = 251 nmol/L.

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Understanding the Basics

What is pH?

The universal measure of acidity and alkalinity — and why it matters in medicine.

Definition

pH stands for "power of hydrogen" (or "potential of hydrogen"). It is a dimensionless number that describes how acidic or alkaline a solution is. The pH scale runs from 0 to 14: values below 7 are acidic, 7 is neutral, and values above 7 are alkaline (basic).

Because pH is logarithmic, each unit change represents a 10-fold change in hydrogen ion concentration. A solution at pH 6 has 10× more H⁺ than pH 7, and 100× more than pH 8.

Clinical Importance

Blood pH is tightly regulated between 7.35 and 7.45. Even small deviations can be life-threatening. Enzymes, ion channels, and oxygen delivery all depend on precise pH control. Acidemia (pH < 7.35) and alkalemia (pH > 7.45) trigger compensatory responses and require clinical investigation.

Reference Values

pH Reference Ranges

Normal pH values for blood and common substances.

Sample / SubstancepH[H⁺] (nmol/L)Clinical Significance
Arterial blood7.35 – 7.4535 – 45Normal physiological range
Venous blood7.32 – 7.4238 – 48Slightly more acidic than arterial
Gastric acid1.0 – 3.01,000,000 – 10,000,000Digestive enzyme activation
Urine4.5 – 8.010 – 31,623Varies with diet and acid load
Life-threatening< 6.8 or > 7.8< 16 or > 158Incompatible with life

Where Does Your pH Fall?

This gauge shows your current pH value.

Clinical Interpretation

pH Interpretation

What different pH values mean clinically.

🔴

Acidemia (pH < 7.35)

[H⁺] > 45 nmol/L
  • Metabolic acidosis (DKA, lactic acid)
  • Respiratory acidosis (COPD, hypoventilation)
  • Cardiac depression
  • Hyperkalemia risk
  • Altered mental status
  • Kussmaul breathing (compensation)
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Normal pH (7.35–7.45)

[H⁺] 35–45 nmol/L
  • Normal acid-base homeostasis
  • Optimal enzyme function
  • Normal oxygen delivery
  • May still have compensated disorder
  • Check HCO₃⁻ and pCO₂ for hidden disorders
🔵

Alkalemia (pH > 7.45)

[H⁺] < 35 nmol/L
  • Metabolic alkalosis (vomiting, diuretics)
  • Respiratory alkalosis (hyperventilation)
  • Hypokalemia risk
  • Ionized calcium falls (tetany)
  • Leftward O₂ dissociation shift
  • Seizures at extreme pH
Common Questions

Frequently Asked Questions

Answers to common questions about pH and hydrogen ion concentration.

pH is the negative logarithm (base 10) of the hydrogen ion concentration: pH = −log₁₀[H⁺]. It measures how acidic or alkaline a solution is on a scale of 0–14. Lower pH means more H⁺ ions (more acidic). Higher pH means fewer H⁺ ions (more alkaline). A pH of 7 is neutral (pure water at 25°C).
Use the formula [H⁺] = 10^(−pH). For blood pH 7.40: [H⁺] = 10^(−7.40) = 3.98 × 10⁻⁸ mol/L = 39.8 nmol/L. A quick clinical shortcut: at pH 7.40, [H⁺] ≈ 40 nmol/L. For each 0.01 change in pH, [H⁺] changes by approximately 1 nmol/L in the opposite direction.
Normal arterial blood pH is 7.35–7.45, corresponding to [H⁺] of 35–45 nmol/L. The ideal pH is 7.40. Venous blood is slightly more acidic (7.32–7.42). The body maintains this narrow range through three mechanisms: chemical buffers (immediate), respiratory compensation (minutes to hours), and renal compensation (hours to days).
Acidemia is a measured state: pH < 7.35 on a blood gas. Acidosis is a process that tends to lower pH. You can have an acidosis without acidemia if the body compensates. For example, a patient with metabolic acidosis may have a normal pH if respiratory compensation (hyperventilation lowering pCO₂) is adequate.
Hydrogen ion concentrations span enormous ranges. Stomach acid has [H⁺] of ~100,000,000 nmol/L (pH 1), while blood has [H⁺] of ~40 nmol/L (pH 7.4) — a 2.5 million-fold difference. A logarithmic scale compresses this range into the manageable 0–14 scale. Each pH unit = 10-fold change in [H⁺].
A pH below 7.0 is life-threatening. At this level, [H⁺] exceeds 100 nmol/L. Enzymes denature, cardiac contractility fails, vasodilation causes refractory hypotension, and cellular metabolism breaks down. pH below 6.8 is generally considered incompatible with life. Emergency treatment includes treating the cause, ventilatory support, and possibly bicarbonate infusion.
The "80 rule" states: [H⁺] ≈ 80 − last two digits of pH. For pH 7.40: [H⁺] ≈ 80 − 40 = 40 nmol/L (exact: 39.8). For pH 7.25: [H⁺] ≈ 80 − 25 = 55 nmol/L (exact: 56.2). It works well between pH 7.20–7.50 but becomes less accurate at extremes. It's a useful bedside estimation tool.