Formula
This calculator uses the standard ph calculator formula:
Frequently Asked Questions
pH measures the acidity or alkalinity of a solution on a scale of 0–14. pH = −log₁₀[H⁺]. pH < 7 is acidic, pH = 7 is neutral, and pH > 7 is basic.
Pure water at 25°C has a pH of exactly 7.0, because [H⁺] = [OH⁻] = 1×10⁻⁷ mol/L.
pH = −log₁₀[H⁺]. For example, if [H⁺] = 0.001 mol/L, pH = −log₁₀(0.001) = −(−3) = 3.
pOH = −log₁₀[OH⁻]. At 25°C, pH + pOH = 14. So if pH = 3, pOH = 11.
Lemon juice ≈ pH 2, stomach acid ≈ pH 1.5–3.5, vinegar ≈ pH 2.5–3. These are strongly acidic.
A buffer solution resists changes in pH when small amounts of acid or base are added. Buffers are typically mixtures of a weak acid and its conjugate base.
Understanding the pH Scale
pH is a logarithmic measure of the hydrogen-ion activity in an aqueous solution. The scale, introduced by Danish chemist S. P. L. Sørensen in 1909, compresses a vast range of [H+] — from about 1 mol/L (strongly acidic) down to 1 × 10⁻¹⁴ mol/L (strongly basic) — onto a convenient 0-to-14 axis. Each one-unit change in pH corresponds to a tenfold change in hydrogen-ion concentration, so a solution at pH 4 is ten times more acidic than one at pH 5 and a hundred times more acidic than one at pH 6. This is why small pH movements matter so much in practice: a swimming pool that drops from pH 7.5 to pH 6.5 has experienced a tenfold increase in acidity, more than enough to corrode metal fittings and irritate swimmers’ eyes.
The Water Self-Ionisation Equilibrium
Even pure water dissociates very slightly into H+ and OH− ions. The equilibrium constant for this auto-ionisation at 25 °C is Kw = [H+][OH−] = 1.0 × 10⁻¹⁴. Taking the negative logarithm of both sides gives the famous relationship pH + pOH = 14 at 25 °C. This means whenever you know the pH of an aqueous solution at room temperature, the pOH is immediately determined, and vice versa. Note that Kw is temperature-dependent: at 50 °C it rises to about 5.5 × 10⁻¹⁴, which shifts neutral pH from 7.00 to about 6.63. For temperature-sensitive work (industrial process water, biological samples), this correction matters.
Strong Acids and Bases
For a strong acid such as hydrochloric acid (HCl), nitric acid (HNO₃), or sulphuric acid (H₂SO₄), dissociation in water is essentially complete. This means a 0.01 mol/L HCl solution has [H+] = 0.01 mol/L and pH = −log₁₀(0.01) = 2.0. Similarly, a 0.001 mol/L NaOH solution has [OH−] = 0.001 mol/L, pOH = 3, and pH = 14 − 3 = 11. The pH calculator above handles both directions: enter [H+] to find pH, or enter pH to find [H+] and [OH−].
Weak Acids and the Henderson-Hasselbalch Equation
Weak acids — acetic acid, carbonic acid, citric acid, and the amino-acid side chains in proteins — do not fully dissociate. Their pH is governed by the acid dissociation constant Ka and the ratio of conjugate base to acid in the buffer. The Henderson-Hasselbalch equation captures this elegantly: pH = pKa + log₁₀([A−] / [HA]). When [A−] = [HA] the log term is zero and pH equals pKa. For acetic acid, pKa = 4.76 at 25 °C, which is why a 50/50 acetate buffer holds pH at 4.76 — well-buffered against small acid or base additions. Buffer capacity is highest within ±1 pH unit of pKa, which is why phosphate buffer (pKa2 = 7.2) is the workhorse for biological work near physiological pH.
Worked Example: pH of a Diluted Strong Acid
Suppose you have 100 mL of 0.10 mol/L HCl and dilute it with 900 mL of pure water. What is the resulting pH? The total moles of H+ are 0.100 L × 0.10 mol/L = 0.010 mol. The final volume is 1.000 L, so [H+] = 0.010 mol/L = 1 × 10⁻². Therefore pH = −log₁₀(1 × 10⁻²) = 2.0. The pH calculator above will give you this directly when you enter [H+] = 0.01 mol/L.
Worked Example: Adjusting Pool Water pH
A 50,000-litre pool reads pH 8.2; the target is pH 7.4. Each 1.0 pH unit roughly corresponds to a tenfold change in [H+], so going from pH 8.2 to pH 7.4 means raising [H+] from 6.3 × 10⁻⁹ to 4.0 × 10⁻⁸ mol/L — about a 6.3× increase. In practice, pool operators dose with sodium bisulphate (dry acid) or muriatic acid (HCl) using a chart that accounts for the pool’s total alkalinity, which buffers pH change. A typical dose is around 1 kg of sodium bisulphate per 50,000 L per 0.2 pH-unit drop, but always retest after 6 hours.
Where pH Calculations Matter
Beyond chemistry classrooms, pH calculations show up everywhere: in water treatment, where pH controls coagulation efficiency, chlorine disinfection (lower pH = more HOCl, the active germicide), and corrosion of distribution pipes; in swimming-pool chemistry, where pH 7.2–7.6 balances bather comfort and disinfection; in brewing and winemaking, where wort/must pH controls enzyme activity and final flavour; in soil science, where pH governs nutrient availability and crop selection; in blood gas analysis, where pH 7.35–7.45 is the narrow band compatible with life; and in industrial process water, where boiler feedwater pH directly controls corrosion of carbon steel. Each of these has linked calculators in the chemical dosing and chlorine dosing tools.
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