How to Calculate pH: Formula, Examples, and the pH Scale

pH is the measure of how acidic or basic a solution is. Understanding how to calculate it from first principles is fundamental to chemistry, biology, medicine, and environmental science.

The pH Formula

pH is defined as the negative base-10 logarithm of the hydrogen ion concentration:

pH = −log₁₀[H⁺]

Where [H⁺] is the concentration of hydrogen ions in moles per litre (mol/L or M).

Example 1: [H⁺] = 0.001 M (10⁻³ M):

• pH = −log(0.001) = −(−3) = 3 (acidic)

Example 2: [H⁺] = 1 × 10⁻⁷ M (pure water):

• pH = −log(10⁻⁷) = 7 (neutral)

Example 3: [H⁺] = 1 × 10⁻¹¹ M:

• pH = 11 (basic/alkaline)

The pH Scale

Calculating [H⁺] from pH

The reverse calculation — finding ion concentration from pH:

[H⁺] = 10^(−pH)

Example: pH = 4.5:

• [H⁺] = 10^(−4.5) = 3.16 × 10⁻⁵ mol/L

The Relationship Between pH and pOH

In aqueous solutions at 25°C:

pH + pOH = 14
pOH = −log₁₀[OH⁻]

If you know the hydroxide ion concentration instead of hydrogen ions:

Example: [OH⁻] = 1 × 10⁻³ M:

• pOH = −log(10⁻³) = 3
• pH = 14 − 3 = 11 (basic)

Calculating pH of Strong Acids

Strong acids (HCl, HNO₃, H₂SO₄) dissociate completely in water:

[H⁺] = Concentration of acid (for monoprotic acids)
pH = −log[acid concentration]

Example: 0.05 M HCl:

• [H⁺] = 0.05 M
• pH = −log(0.05) = 1.30

For H₂SO₄ (diprotic): [H⁺] = 2 × [H₂SO₄]

Calculating pH of Weak Acids (Using Ka)

Weak acids partially dissociate. Use the acid dissociation constant Ka:

[H⁺] = √(Ka × C)
pH = −log(√(Ka × C)) = ½ × (pKa − log C)

Where C = initial acid concentration, Ka = dissociation constant.

Example: 0.1 M acetic acid (Ka = 1.8 × 10⁻⁵):

• [H⁺] = √(1.8 × 10⁻⁵ × 0.1) = √(1.8 × 10⁻⁶) = 1.34 × 10⁻³
• pH = −log(1.34 × 10⁻³) = 2.87

(Compared to strong acid: 0.1 M HCl would have pH = 1.0 — much more acidic)

Calculating pH of Strong Bases

Strong bases (NaOH, KOH) dissociate completely:

[OH⁻] = concentration of base
pOH = −log[OH⁻]
pH = 14 − pOH

Example: 0.02 M NaOH:

• pOH = −log(0.02) = 1.70
• pH = 14 − 1.70 = 12.30

Buffer Solutions

A buffer resists pH change. The Henderson-Hasselbalch equation calculates buffer pH:

pH = pKa + log([A⁻]/[HA])

Where [A⁻] = conjugate base concentration, [HA] = weak acid concentration.

Example: Acetic acid/acetate buffer, pKa = 4.74, equal concentrations:

• pH = 4.74 + log(1) = 4.74 + 0 = 4.74

Buffers work best within ±1 pH unit of the pKa.

Practical Applications

Blood pH: Maintained at 7.35–7.45 by bicarbonate buffering. Below 7.35 = acidosis; above 7.45 = alkalosis.

Swimming pools: Optimal pH 7.2–7.8. Below 7.0 irritates eyes and corrodes equipment; above 7.8 reduces chlorine effectiveness.

Soil pH: Affects nutrient availability. Most plants thrive at 6.0–7.0; blueberries prefer 4.5–5.5.

Use our logarithm calculator to quickly compute −log values for pH and pOH calculations.