🧪 pH and pOH

Written and maintained by the PhDino author · Last reviewed 21 September 2026 · Checked against 4 independent reference calculations · how PhDino checks its numbers

Converting a hydrogen or hydroxide ion concentration into the pH scale.

pH is a logarithmic scale describing how acidic or basic a solution is, based on the concentration of hydrogen ions (H⁺) in it. Because concentrations of H⁺ span such an enormous range — from about 1 molar in a strong acid down to 10⁻¹⁴ molar in a strong base — the logarithm compresses that range into the familiar 0–14 scale, where each whole step represents a tenfold change in H⁺ concentration.

Water itself supplies a fixed relationship between the two ends of the scale: at room temperature, the product of H⁺ and OH⁻ concentrations in any aqueous solution is a constant (10⁻¹⁴), which is why pH and pOH always sum to 14 — knowing one tells you the other directly.

Key formula

pH = −log₁₀[H⁺]
pOH = −log₁₀[OH⁻]
pH + pOH = 14 (at 25°C)
Strong acid or base of concentration C: [ion] = (C + √(C² + 4K_w)) / 2, with K_w = 10⁻¹⁴

How to use the pH Calculator calculator

Use this to convert the concentration of a strong acid or a strong base into pH and pOH. Choose whether you know the hydrogen-ion concentration (an acid) or the hydroxide concentration (a base), enter it in moles per litre, and the calculator returns both scales, which always add up to 14 at room temperature.

It treats the acid or base as fully dissociated, which is right for the common strong acids and bases such as hydrochloric acid and sodium hydroxide. It is not for weak acids like vinegar, which only partly dissociate.

Concentration [H⁺] or [OH⁻] (M)

The concentration in moles per litre of hydrogen ions (acid) or hydroxide ions (base). For a strong acid with one acidic hydrogen, such as HCl, it equals the acid concentration. Acids with more than one acidic hydrogen, such as sulfuric acid, need more care, because the second hydrogen dissociates only partly except in very dilute solutions.

Solution Type

Choose acid if the concentration you know is that of hydrogen ions, or base if it is that of hydroxide ions. The calculator finds the other from the water equilibrium.

Worked example: dilute hydrochloric acid

A solution contains 0.0025 mol/L of hydrochloric acid, a strong acid that fully dissociates. What are its pH and pOH?

Worked by hand:

1. Hydrogen-ion concentration. HCl dissociates completely, so [H⁺] = 0.0025 M.
2. pH. pH = −log₁₀[H⁺] = −log₁₀(0.0025) = 2.602.
3. pOH. Because pH + pOH = 14 at 25°C, pOH = 14 − 2.602 = 11.398.

The solution has a pH of about 2.60: strongly acidic, though not extremely so. Each pH unit is a tenfold change in hydrogen-ion concentration, so a solution ten times stronger, 0.025 M, would have a pH exactly one unit lower, near 1.6. The calculator also handles very dilute solutions correctly: a 10⁻⁸ M acid comes out at pH 6.98, never above 7, because the water's own ions are included.

Reading the result: a logarithmic scale

pH is a logarithmic scale, which is why the numbers feel small: a pH of 3 is not a little more acidic than a pH of 4, it is ten times more concentrated in hydrogen ions. Neutral water sits at 7 with equal hydrogen and hydroxide ions at 10⁻⁷ M, acids are below 7 and bases above.

• The result is only as good as the strong-electrolyte assumption. A weak acid such as acetic acid at 0.1 M has a pH of about 2.87, not the 1.0 that treating it as strong would give, because only a small fraction of its molecules dissociate.
• Polyprotic acids need care. Sulfuric acid releases its first hydrogen completely but its second only partly, so its [H⁺] lies between one and two times the acid concentration, approaching two only in very dilute solution; finding it exactly takes an equilibrium calculation this calculator does not include.
• The relation pH + pOH = 14 is exact only at 25°C. At other temperatures the water constant shifts, and neutral water is no longer exactly pH 7.
• Very concentrated solutions behave less ideally, and the measured pH can differ from the simple calculation, because activities differ from concentrations.

Notes & limitations

• For ordinary concentrations the ion concentration is simply C, but below roughly 10⁻⁶ M the hydrogen and hydroxide ions that water itself supplies can no longer be ignored: a 10⁻⁸ M strong acid has a pH of about 6.98, not 8, and no acid solution, however dilute, is ever basic. The calculator uses the exact expression above so this comes out right.
• This treats the acid or base as fully dissociating (a "strong" acid or base), where the concentration entered equals the ion concentration directly. A weak acid or base only partially dissociates, and needs its equilibrium (Ka or Kb) to find the actual ion concentration first — a separate, more involved calculation than a strong-acid/base pH reading.
• The 14 relationship between pH and pOH is specific to water at 25°C — the underlying constant shifts somewhat at other temperatures, though 25°C is the standard reference condition this and most general chemistry material assumes.

Common mistakes

• Applying the strong-acid formula to a weak acid such as vinegar. The result is far too acidic, and a weak-acid equilibrium calculation is needed.
• Entering the formal concentration of an acid with more than one acidic hydrogen. The hydrogen-ion concentration of sulfuric acid can be up to twice its formal concentration, and the exact value needs an equilibrium calculation.
• Entering a hydroxide concentration but leaving the type set to acid, which reports the wrong end of the scale.
• Forgetting that a difference of one pH unit is a factor of ten, not a small change.
• Assuming pH 7 is neutral at every temperature. It is neutral at 25°C and shifts with temperature.

Frequently asked questions

Papers worth reading

Measurement of pH. Definition, standards, and procedures (IUPAC Recommendations 2002) Buck, R. P. et al. (2002), Pure and Applied Chemistry. The IUPAC recommendation that defines pH in terms of hydrogen-ion activity rather than concentration and sets out the standards for measuring it.