pH and pOH Calculator

What pH actually measures

pH is a logarithmic measure of how much hydrogen ion a solution contains: pH = −log₁₀[H⁺]. The logarithm exists for a practical reason. Hydrogen ion concentrations in ordinary aqueous chemistry span from about 1 mol/L in strong acid down to 10⁻¹⁴ mol/L in strong base — fifteen orders of magnitude. Compressing that onto a scale running roughly 0 to 14 makes the numbers usable, at the cost of a fact people constantly forget: one pH unit is a factor of ten. A solution at pH 4 holds a hundred times more hydrogen ion than one at pH 6.

Every aqueous solution contains both H⁺ and OH⁻, because water autoionises: 2 H₂O ⇌ H₃O⁺ + OH⁻. The equilibrium constant for that reaction is the ion product K_w = [H⁺][OH⁻], equal to 1.0×10⁻¹⁴ at 25 °C. Because the product is fixed, the two concentrations are locked together: push one up and the other falls. Take the negative logarithm of both sides and that relationship becomes the sum you already know, pH + pOH = 14.00 at 25 °C.

Strictly, the IUPAC definition of pH is built on hydrogen ion activity, not concentration. Activity accounts for the way ions screen one another in solution, and it drops below concentration as the solution gets more concentrated. In dilute work the difference is negligible; above roughly 0.1 mol/L it is not, which is why a calculated pH for a concentrated acid should be treated as an estimate and not as a substitute for a measurement.

The four conversions, and the one everybody gets wrong

Three of the four conversions this calculator performs are pure arithmetic. From pH you get [H⁺] = 10^−pH. From [OH⁻] you get pOH = −log₁₀[OH⁻] and then pH = pK_w − pOH. None of these require you to know anything about the solute; they are properties of the numbers.

The fourth conversion is the one that hides a trap. Going from the concentration of a strong acid to pH looks equally trivial — HCl dissociates completely, so surely [H⁺] equals the concentration you weighed out. That works down to about 10⁻⁶ M and then fails, because you have ignored the hydrogen ion the water itself supplies. Apply the shortcut to 1×10⁻⁸ M HCl and you get pH 8: an acid that is somehow basic.

The honest treatment writes a charge balance, [H⁺] = [OH⁻] + C, substitutes [OH⁻] = K_w/[H⁺], and solves the resulting quadratic:

$$\left[H^{+}\right]=\frac{C+\sqrt{C^2+4K_w}}{2}$$

This calculator uses that exact form always. At 0.01 M the 4K_w term is forty billion times smaller than C² and changes nothing; at 10⁻⁸ M it dominates, and the answer bends smoothly toward neutrality instead of crossing it. The same expression with C as the base concentration gives [OH⁻] for a strong base.

For a weak acid or weak base the dissociation is partial and the concentration alone is not enough — you need the equilibrium constant. Use the weak acid pH calculator or the weak base pH calculator for those.

Reading the result: what counts as acidic

Compare your pH against the neutral pH at your temperature, not against 7. Neutrality means [H⁺] = [OH⁻], which happens at pK_w/2. That equals 7.00 at 25 °C and nowhere else. Water at 50 °C has pK_w = 13.26, so neutral water is pH 6.63 — it is not acidic, it is neutral at a different number. Boiling water at 100 °C is neutral at pH 6.13 by the same arithmetic. This calculator reports the neutral point alongside your pH for exactly this reason.

Two further habits separate a careful answer from a sloppy one. First, significant figures in pH live only after the decimal point. The digits before the point encode the exponent, so 0.010 M HCl (two significant figures) gives pH 2.00, not pH 2.0000. A pH reported to three decimal places implies a hydrogen ion concentration known to about 0.2%, which no field electrode delivers. Second, a routine glass electrode calibrated with two buffers is good to roughly ±0.02 pH units at best, and drifts with temperature, junction potential and sodium error at high pH. Treat calculated and measured values as agreeing when they are within a few hundredths.

If your solution is a mixture of a weak acid and its conjugate base, none of the strong-electrolyte reasoning above applies — the pH is set by the ratio of the two species and barely moves when you add acid. That is the domain of the Henderson-Hasselbalch buffer calculator.

Reference: pKw, neutral pH and the pH scale

pKw values are tabulated data for pure water (CRC Handbook); Kw and neutral pH in this table are derived from them as 10^-pKw and pKw/2. The calculator interpolates linearly between these anchors.

Mistakes that produce a wrong pH

• Treating a weak acid as strong. 0.10 M acetic acid is not pH 1.00; with K_a = 1.8×10⁻⁵ it works out to pH 2.88, because only about 1.3% of it dissociates. Concentration alone never gives the pH of a weak acid.
• Forgetting the second hydroxide or proton. Ba(OH)₂ and Ca(OH)₂ deliver two OH⁻ per formula unit, so 0.0050 M gives pOH 2.00, not 2.30.
• Using the shortcut below 10⁻⁶ M. It produces an acid with a basic pH. Keep the water term, as this calculator does.
• Assuming neutral is always 7.00. Neutral is pK_w/2. At body temperature it is 6.81, and blood at pH 7.40 is therefore more basic relative to neutral than the number 7.40 alone suggests.
• Reporting too many significant figures. Only the mantissa of a pH carries significant figures; the integer part is an exponent.
• Ignoring activity in concentrated solutions. Above about 0.1 M the measured pH departs from the concentration-based value, and by 1 M the gap is large enough to matter for any quantitative claim.
• Diluting and expecting a proportional change. Ten-fold dilution of a strong acid moves the pH by exactly one unit, but only until the water term takes over, after which further dilution barely moves it at all.

Where pH sits among the other acid-base calculations

This calculator handles the strong-electrolyte and pure-conversion cases. Three other calculations pick up where it stops.

Partial dissociation. A weak acid only releases a fraction of its protons, set by K_a. Solving for that fraction is a quadratic in [H⁺], not a logarithm; see the weak acid pH calculator.

Mixtures that resist change. Combine a weak acid with its conjugate base and the pH is pinned near the pK_a. That is what makes blood, seawater and every biochemical assay behave the way they do.

Reaction to an endpoint. If you are titrating rather than mixing, the quantity you want is the volume at equivalence and the pH along the way; the acid-base titration calculator builds the whole curve.

Two housekeeping tools sit underneath all of these. Getting the concentration right in the first place is the job of the molarity calculator, and moving from a stock solution to a working one is the job of the solution dilution calculator. A pH computed from a mis-stated molarity is wrong no matter how careful the logarithm was.

Key terms

Autoionisation of water

The reaction 2 H₂O ⇌ H₃O⁺ + OH⁻, which occurs in every aqueous solution and sets the floor on how low either ion concentration can go.

Ion product Kw

The equilibrium constant [H⁺][OH⁻] for water autoionisation. It depends on temperature only, not on what is dissolved.

Strong acid or base

One that dissociates essentially completely in water, so the ion concentration equals the formal concentration times the number of ionisable units.

Activity

Effective concentration after accounting for ion-ion interactions. The formal IUPAC definition of pH uses hydrogen ion activity; concentration is a dilute-solution approximation to it.

Normality

Concentration expressed in equivalents per litre. For a strong acid it is molarity times the number of ionisable protons, which is what the pH calculation needs.