A pH 3 solution — lemon-juice range
[H⁺] = 10⁻³ = 0.001 mol/L, [OH⁻] = 10⁻¹¹ mol/L, clearly acidic.
pH and hydrogen-ion concentration calculator
Result
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How it works
pH is a logarithmic scale: pH = −log₁₀[H⁺], compressing a concentration that spans many orders of magnitude (from about 1 mol/L in a strong acid to 10⁻¹⁴ mol/L in a strong base) into a manageable 0–14 range. Each one-unit drop in pH means a tenfold increase in [H⁺].
At 25 °C, water’s own ionisation fixes the relationship [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ (Kw), which is why pH + pOH always equals 14 at this temperature — knowing one of the four quantities (pH, pOH, [H⁺], [OH⁻]) gives the other three.
Formulas used
pH from concentration
pH = −log₁₀[H⁺]
Concentration from pH
[H⁺] = 10^(−pH)
Relationship to pOH
pH + pOH = 14 (at 25 °C)
Worked examples
A hydrogen-ion concentration of 2.5 × 10⁻¹⁰ mol/L
pH = −log₁₀(2.5 × 10⁻¹⁰) ≈ 9.60, a mildly basic solution — in the range of baking soda in water.
Assumptions and limits
- Temperature is 25 °C, the standard reference for Kw = 1.0 × 10⁻¹⁴.
- Activity coefficients are ignored — concentration is treated as equal to activity, which is accurate for dilute solutions only.
Frequently asked questions
Why does pH 0 to 14 not cover every possible solution?
The 0–14 range corresponds to [H⁺] between 1 and 10⁻¹⁴ mol/L, which covers dilute-to-moderate acids and bases. Concentrated strong acids or bases can technically fall outside this range (negative pH or pH above 14) — the formula still applies, but the simple relationship with pOH becomes less reliable at very high concentrations.
Does temperature affect this?
Yes. Kw depends on temperature (it roughly doubles for every 10 °C rise), so "neutral" is only exactly pH 7 at 25 °C. At body temperature (37 °C), for instance, neutral pH is closer to 6.8. This calculator assumes the standard 25 °C reference.
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