pH Calculator
Convert hydrogen ion concentration [H⁺] in mol/L into a pH value using pH = −log₁₀[H⁺]. The standard measure of acidity used in chemistry, biology, environmental science, and any application where solution acidity matters.
About this calculator
pH is defined as the negative base-10 logarithm of the hydrogen ion concentration: pH = −log₁₀([H⁺]), where [H⁺] is the molar concentration of H⁺ in mol/L (M). Equivalently, [H⁺] = 10^(−pH). The pH scale typically runs 0–14 in aqueous solutions at 25 °C: 0 is very acidic (1 M strong acid), 7 is neutral (pure water at 25 °C, where [H⁺] = 10⁻⁷ M), 14 is very basic (1 M strong base, where [H⁺] = 10⁻¹⁴ M). Because the scale is logarithmic, each unit change represents a 10-fold change in [H⁺]: pH 3 is 10× more acidic than pH 4, 100× more than pH 5. The scale extends beyond 0–14 in extreme cases — concentrated 12 M HCl has pH ≈ −1.08, and concentrated NaOH solutions can reach pH 15+. The neutral point shifts with temperature because the water-autoionisation constant K_w changes: at 0 °C neutral pH is 7.47; at 25 °C, 7.00; at 100 °C, 6.13. The −log formulation arose because H⁺ concentrations span an enormous dynamic range (10⁻¹⁵ to 10¹), and the log compresses this into a convenient 0–14 scale. Edge cases: [H⁺] = 0 gives undefined pH (mathematically infinity), reflecting that pure water always has some H⁺ from autoionisation. [H⁺] = 1 M gives pH = 0; [H⁺] > 1 M gives negative pH, which is physically valid for concentrated acids. The pH value here is for [H⁺] activity, which approximates concentration only in dilute solutions; at high ionic strength (above ~0.1 M) ionic interactions cause activity to deviate from concentration, and a more refined treatment uses an activity coefficient.
How to use
Example 1 — pH of stomach acid. Gastric fluid contains roughly 0.1 M HCl, a strong acid that fully dissociates: [H⁺] = 0.1 M = 10⁻¹ M. Enter concentration = 0.1. pH = −log₁₀(0.1) = 1.0. ✓ A pH of 1 is strongly acidic — about 1,000,000 times more acidic than pure water — which is why stomach lining produces protective mucus and the stomach has evolved to handle continuous exposure to this much acid. Example 2 — pH of blood. Healthy human blood is tightly buffered at [H⁺] ≈ 4 × 10⁻⁸ M (40 nM). Enter concentration = 4e-8 or 0.00000004. pH = −log₁₀(4 × 10⁻⁸) = 8 − log₁₀(4) ≈ 8 − 0.602 = 7.398 ≈ 7.4. ✓ A pH of 7.4 is the precise value the body maintains via the bicarbonate buffer system; even small deviations (pH 7.35 acidosis, pH 7.45 alkalosis) are clinically dangerous. The ~6.5× shift in [H⁺] between pH 7.3 (50 nM) and pH 7.5 (32 nM) seems small numerically but is enough to disrupt enzyme function — the tight buffering of blood pH is one of the most critical homeostatic mechanisms in physiology.
Frequently asked questions
Why is the pH scale logarithmic instead of linear?
Hydrogen-ion concentrations in solutions of practical interest range from about 10 M (concentrated strong acid) to 10⁻¹⁵ M (concentrated strong base) — a span of sixteen orders of magnitude. A linear scale would need huge numbers at one end and microscopic numbers at the other, with no way to compare them. The log scale compresses all of that into a clean 0–14 range that fits on a strip of pH paper or a single axis on a graph. The chemical justification is just as strong: chemical equilibria depend exponentially on concentration ratios through expressions like K = [products]/[reactants], so the natural mathematical object is log(concentration). Buffering, enzyme kinetics, and acid-base equilibria all simplify dramatically when expressed in log form. The pH scale was introduced by Søren Sørensen in 1909 specifically because it made acid-base chemistry tractable for the brewing industry, where Sørensen worked at Carlsberg.
How does pH relate to pOH and the water ionisation constant?
In pure water at 25 °C, autoionisation produces equal amounts of H⁺ and OH⁻: H₂O ⇌ H⁺ + OH⁻, with K_w = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴. Taking −log₁₀ of both sides gives pH + pOH = 14.00 at 25 °C. So in pure water at 25 °C, [H⁺] = [OH⁻] = 10⁻⁷ M, giving pH = pOH = 7.00 (neutral). In any aqueous solution at 25 °C, pH + pOH always equals 14: a solution at pH 4.2 has pOH = 9.8. This relationship lets you compute pH from a basic solution’s hydroxide concentration: for 0.01 M NaOH, [OH⁻] = 0.01 M, pOH = 2, so pH = 12. K_w changes with temperature: at 0 °C K_w ≈ 1.14 × 10⁻¹⁵ (neutral pH 7.47); at 100 °C K_w ≈ 5.5 × 10⁻¹³ (neutral pH 6.13).
How do I calculate the pH of a weak acid that doesn’t fully dissociate?
For a weak acid HA in water, only a fraction of molecules dissociate: HA ⇌ H⁺ + A⁻, with equilibrium constant K_a = [H⁺][A⁻]/[HA]. Actual [H⁺] is less than the formal acid concentration, so you can’t just enter the acid concentration here. Instead, set up the equilibrium: if initial [HA] = C and dissociation extent = x, then at equilibrium [HA] = C − x, [H⁺] = x, [A⁻] = x, and K_a = x²/(C − x). For weak acids (K_a < 10⁻³), the approximation x ≪ C gives x ≈ √(K_a · C). For acetic acid (K_a = 1.8 × 10⁻⁵) at C = 0.1 M: x ≈ √(1.8e-5 × 0.1) ≈ 1.34 × 10⁻³ M, so pH ≈ −log(1.34e-3) ≈ 2.87. Plug that [H⁺] = 1.34e-3 into this calculator and you get the same answer. For strong acids (HCl, H₂SO₄, HNO₃) the assumption [H⁺] = C is fine; for weak acids the dissociation step is essential.
What are the most common mistakes people make with pH?
The first is forgetting the minus sign and computing log₁₀([H⁺]) instead of −log₁₀([H⁺]), giving negative pH for ordinary solutions. The second is treating pH as a linear quantity — moving from pH 5 to pH 4 isn’t a 20% increase in acidity, it is a 10× increase. The third is plugging acid concentration directly into the pH formula for weak acids, ignoring partial dissociation; for weak acids you need to solve the equilibrium expression first to find the actual [H⁺]. The fourth is forgetting that pH depends on temperature through K_w — at body temperature (37 °C) neutral pH is 6.81, not 7.00. The fifth is assuming pH = pOH at all temperatures — pH + pOH = 14 only at 25 °C, and the relationship shifts at other temperatures. Finally, people often use pH paper or rough indicators where pH precision matters (pharma, biochemistry) — for accurate work you need a calibrated pH meter with at least two-point calibration on standard buffers.
When should I not use this calculator?
Skip it for weak acids and bases without first computing the actual [H⁺] from the equilibrium expression — entering the formal acid concentration directly gives the wrong pH for incompletely dissociated acids. Avoid it for high-ionic-strength solutions (above ~0.1 M total ionic concentration) where activity coefficients differ noticeably from 1 and the simple −log([H⁺]) calculation diverges from the experimentally measured pH (which is technically −log of H⁺ activity, not concentration). It is the wrong tool for non-aqueous solvents — pH in DMSO, methanol, or ethanol has a different operational definition and a different neutral point. Do not use it for buffered systems without computing buffer behaviour — the Henderson-Hasselbalch equation is more appropriate for pH-buffered solutions. Skip it for very high or very low pH at temperatures different from 25 °C without correcting for the temperature-dependent K_w. And for industrial process control or biomedical applications where pH precision matters, use a calibrated pH meter and the measured value, not an estimate from H⁺ concentration.