pH measures acidity on a logarithmic scale: pH = −log₁₀[H⁺], where [H⁺] is the hydrogen ion concentration in moles per liter. A solution with [H⁺] = 3.2 × 10⁻⁴ M has pH = −log(3.2 × 10⁻⁴) ≈ 3.49. Lower numbers are more acidic, 7 is neutral at 25°C, and higher numbers are basic. Each step of 1 pH unit is a tenfold change in hydrogen ion concentration.
The core formulas
The last relationship comes from the ion product of water, Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25°C. Strictly, [H⁺] stands for the hydronium ion, H₃O⁺, and very precise work uses activities rather than concentrations, but concentrations are standard for coursework and dilute solutions.
| If you know | Then |
|---|---|
| [H⁺] | pH = −log[H⁺] |
| [OH⁻] | pOH = −log[OH⁻], then pH = 14 − pOH |
| pH | [H⁺] = 10⁻ᵖᴴ |
| pOH | pH = 14 − pOH |
On a scientific calculator, enter the concentration, press log, and change the sign. The logarithm calculator helps if logs are unfamiliar, and logarithm rules explains why each pH unit is a factor of ten.
Strong acids
Strong acids such as HCl, HNO₃ and HBr ionize completely, so [H⁺] equals the acid’s molarity.
0.025 M HCl → [H⁺] = 0.025 M
pH = −log(0.025) ≈ 1.60
The strong acids usually memorized in introductory courses are HCl, HBr, HI, HNO₃, HClO₄, HClO₃ and H₂SO₄; nearly every other acid you meet is weak. Sulfuric acid releases its first proton completely and its second only partly, so it needs extra care beyond introductory problems.
Strong bases
Strong bases such as NaOH and KOH dissociate completely into OH⁻. The Group 1 hydroxides and the heavier Group 2 hydroxides, such as Ca(OH)₂, Sr(OH)₂ and Ba(OH)₂, are the common strong bases. Find pOH first, then convert.
0.010 M NaOH → [OH⁻] = 0.010 M → pOH = 2.00 → pH = 14.00 − 2.00 = 12.00
Watch the formula: each Ba(OH)₂ releases two hydroxide ions.
0.050 M Ba(OH)₂ → [OH⁻] = 2 × 0.050 = 0.10 M → pOH = 1.00 → pH = 13.00
From pH back to concentration
Blood at pH 7.40: [H⁺] = 10−7.40 ≈ 4.0 × 10⁻⁸ M
Lemon juice at about pH 2.4 has roughly 10(7.4 − 2.4) = 100,000 times the [H⁺] of blood
Note the significant figures rule for logs: the number of decimal places in a pH equals the number of significant figures in [H⁺]. A pH of 7.40 corresponds to two significant figures, 4.0 × 10⁻⁸ M. See significant figures rules.
Weak acids
Weak acids such as acetic acid ionize only partly. Their strength is given by the acid dissociation constant Ka:
The approximation assumes only a small fraction of the acid ionizes, which holds when the result is under about 5% of C.
0.10 M acetic acid, Ka = 1.8 × 10⁻⁵
[H⁺] ≈ √(1.8 × 10⁻⁵ × 0.10) = √(1.8 × 10⁻⁶) ≈ 1.34 × 10⁻³ M
pH ≈ −log(1.34 × 10⁻³) ≈ 2.87
Check: 1.34 × 10⁻³ ÷ 0.10 = 1.3% ionized, well under 5%, so the shortcut is valid
Solving the full quadratic gives [H⁺] = 1.33 × 10⁻³ M and pH 2.88, essentially the same. Compare 0.10 M HCl at pH 1.00: at the same concentration, the weak acid has about 75 times less H⁺. Weak bases work the same way using Kb and [OH⁻].
Buffers: the Henderson–Hasselbalch equation
A buffer contains a weak acid and its conjugate base, which together resist pH changes. Its pH is:
0.10 M acetic acid with 0.15 M sodium acetate; pKa = −log(1.8 × 10⁻⁵) = 4.74
pH = 4.74 + log(0.15 ÷ 0.10) = 4.74 + 0.18 = 4.92
When the acid and base concentrations are equal, the log term is zero and pH = pKa. Buffers work best within about one pH unit of their pKa. The buffer pH calculator handles any acid–base pair.
The pH scale in everyday life
Values are approximate and vary by product and conditions.
| Substance | Approximate pH |
|---|---|
| Battery acid | below 1 |
| Stomach acid | 1 to 3 |
| Lemon juice | about 2 to 2.6 |
| Vinegar | about 2.4 to 3 |
| Coffee | about 5 |
| Pure water (25°C) | 7.0 |
| Blood | 7.35 to 7.45 |
| Seawater | about 8.1 |
| Baking soda solution | about 8.3 |
| Household ammonia | about 11 to 12 |
| Bleach | about 12.5 to 13 |
Measuring pH
Calculated pH values can be checked against measurement. Indicator paper changes color across a range and is good to about one pH unit; universal indicator solutions work the same way. A pH meter uses a glass electrode whose voltage changes by about 59 millivolts per pH unit at 25°C, giving readings to 0.01 pH. Meters drift, so they are calibrated before use with standard buffer solutions, typically at pH 4.00, 7.00 and 10.00, chosen to bracket the expected reading. Rinse the electrode between samples and record the temperature, because both the electrode response and the sample’s true pH change with it.
Traps and special cases
Very dilute acids. 1.0 × 10⁻⁸ M HCl does not have a pH of 8; an acid cannot make water basic. Water’s own ionization contributes about 10⁻⁷ M H⁺, and solving both together gives a pH of about 6.98.
Temperature. Kw grows with temperature, so neutral pH is 7.00 only at 25°C. At body temperature, 37°C, neutral water has a pH of about 6.8, even though it is neither acidic nor basic.
Dilution. Diluting a strong acid tenfold raises its pH by 1. To plan the dilution itself, use C₁V₁ = C₂V₂ from how to calculate molarity or the dilution calculator.
Titrations. As base is added to an acid, pH changes slowly at first, then jumps sharply near the equivalence point. The titration calculator finds the unknown concentration from the volumes used, and the general pH calculator converts between pH, pOH, [H⁺] and [OH⁻] for strong or weak acids and bases.
Frequently asked questions
What is the formula for pH?
pH = −log₁₀[H⁺], where [H⁺] is the hydrogen ion concentration in moles per liter. A solution with [H⁺] = 0.001 M has pH = −log(0.001) = 3.
How do you calculate pH from pOH?
At 25°C, pH + pOH = 14, so pH = 14 − pOH. A solution with pOH 2 has pH 12. This comes from the ion product of water, Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25°C.
How do you find [H⁺] from pH?
Take the inverse log: [H⁺] = 10^(−pH). For blood at pH 7.40, [H⁺] = 10^(−7.40) ≈ 4.0 × 10⁻⁸ M.
How is the pH of a weak acid different from a strong acid?
A strong acid ionizes completely, so [H⁺] equals the acid concentration. A weak acid ionizes only partly, so you need its Ka. For 0.10 M acetic acid (Ka = 1.8 × 10⁻⁵), [H⁺] ≈ √(Ka × C) ≈ 1.34 × 10⁻³ M and the pH is about 2.87, much higher than the pH of 1.00 for 0.10 M hydrochloric acid.
Can pH be negative or above 14?
Yes. Very concentrated strong acids can have [H⁺] above 1 M, giving a negative pH, and very concentrated strong bases can exceed 14. The familiar 0 to 14 range covers most everyday and laboratory solutions.