Free pH Calculator – From [H⁺] to Buffer Chemistry

How the pH Calculator Works

pH is a number on a roughly 0-to-14 scale that tells you how acidic or basic a water-based solution is, and it is defined precisely as pH = −log₁₀[H⁺], where [H⁺] is the hydrogen-ion concentration in moles per litre. A student checking a titration, a home brewer watching mash pH, an aquarium keeper tracking tank water, or a lab tech calibrating a meter all reach for the same handful of conversions this calculator covers: [H⁺] to pH and back, pOH, strong acids and bases, weak acids and bases through their equilibrium constant, and buffers built from a weak acid and its conjugate base. For a strong acid or base that dissociates completely, the concentration you dissolved is the ion concentration, so pH is just −log₁₀(C) for an acid, or you find pOH first for a base and subtract from pKw. Weak acids are the harder case: HA breaks apart only partially, governed by Ka = [H⁺][A⁻] ÷ [HA]. The textbook shortcut assumes ionization is small enough that [HA] stays close to the starting concentration C, giving [H⁺] = √(Ka × C). That shortcut is only safe when C ÷ Ka is roughly 100 or higher. Below that ratio the mass-balance equation has to be solved exactly as a quadratic, [H⁺]² + Ka[H⁺] − KaC = 0, which rearranges to [H⁺] = (−Ka + √(Ka² + 4KaC)) ÷ 2. Buffers use a third relationship, the Henderson–Hasselbalch equation, pH = pKa + log₁₀([A⁻] ÷ [HA]), which holds well as long as the ratio of the two forms stays within about a factor of ten each way of 1, i.e. inside pKa ± 1. Take 0.1 M acetic acid with Ka = 1.8 × 10⁻⁵. The square-root approximation gives [H⁺] = √(1.8 × 10⁻⁵ × 0.1) = 1.3416 × 10⁻³ M, which rounds to pH 2.87 — matching both Omni Calculator and calculator.net. Solving the exact quadratic instead gives [H⁺] = 1.3327 × 10⁻³ M and pH 2.8753, a difference of about 0.003 pH units that barely matters at this concentration because C ÷ Ka here is 5,556, far above the 100 threshold. Percent ionization, [H⁺] ÷ C × 100, comes out to about 1.33% either way — a useful reminder that even a "weak" acid at 0.1 M is still almost 99% un-ionized. Students verifying a lab result use the weak-acid mode to check a measured pH against theory before writing it up. Home brewers and winemakers use the buffer mode to see how much a mash or must will resist a pH swing, since malt and grape must both behave like weak buffer systems. Aquarium and pond keepers use the strong/weak modes to translate a test-kit ppm reading into an expected pH range. Chemistry instructors use the temperature selector to show a class that pH 7 is only "neutral" at 25 °C — at human body temperature, 37 °C, neutral water actually sits at pH 6.81, and pure water at a rolling boil drops to pH 6.15, purely because Kw itself changes with temperature, not because the water became acidic. The one mistake worth watching for is trusting the square-root shortcut at a low concentration. Drop the same acetic acid down to 0.001 M and C ÷ Ka falls to 55.6 — the approximation now says pH 3.8724 while the exact quadratic says pH 3.9015, a gap of 0.03 pH units that a lab report would flag as wrong if the exact answer was expected. This calculator shows both numbers side by side specifically so that gap is visible instead of hidden. A second limitation worth stating plainly: everything here uses concentration, not chemical activity, so a real calibrated meter reading a solution above roughly 0.1 M ionic strength will read a little differently than the formula predicts, and polyprotic acids like phosphoric or citric acid are treated only through their first dissociation constant. Every calculation runs locally in your browser; nothing you type is sent anywhere.

pH Calculator Formula & Method

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