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pH Calculator

Calculators · Added

pH from a concentration, for a strong or weak acid or base — or the concentrations back from a pH. The weak modes solve the equilibrium quadratic rather than using the √(Ka·C) shortcut, and show you what the shortcut would have given. Temperature is an input because pKw is 14.00 only at 25 °C, and neutral moves with it.

What are you working from?
mol/L

Scientific notation works — 1e-3 is fine.

°C

pKw is 14.00 only at 25 °C, and neutral moves with it.

How to use the ph calculator

  1. 1Choose what you have: a strong acid or base, a weak one, or a pH to work backwards from.
  2. 2Enter the concentration in mol/L, and for a weak acid or base its Ka or Kb.
  3. 3Set the temperature if it is not 25 °C.
  4. 4Read the pH, pOH and both ion concentrations, with the working shown.

Examples

A strong acid

Input
0.01 mol/L HCl at 25 °C
Result
pH 2.00 exactly — a strong acid dissociates fully, so [H⁺] is what you poured

A weak acid

Input
0.1 mol/L acetic acid, Ka 1.8e-5
Result
pH 2.87, with 1.33% of it dissociated

The √(Ka·C) shortcut agrees here. It stops agreeing as the solution gets dilute.

Neutral is not always 7

Input
Pure water at 60 °C
Result
pKw 13.03, so neutral is pH 6.52 — and a solution at pH 7 is basic at that temperature

A calculator that hardcodes 14 calls that acidic, which is wrong.

About the ph calculator

The logarithm is the whole difficulty

pH is −log₁₀ of the hydrogen ion concentration, and almost every misunderstanding of it comes from forgetting the log. pH 4 is not twice as acidic as pH 8: it is ten thousand times. A change of one unit is a factor of ten in concentration, which is why moving a lake from pH 6 to pH 5 is a serious event and why blood is held within about 0.05 of 7.4.

The logarithm is also why the scale exists. Hydrogen ion concentrations in ordinary solutions span roughly fourteen orders of magnitude, from about 1 mol/L down to 10⁻¹⁴. Writing those as decimals is unreadable; taking the negative logarithm turns them into numbers between 0 and 14 that fit on a strip of indicator paper.

Strength and concentration are different things

A strong acid is one that dissociates completely; a concentrated acid is one with a lot of it per litre. The two are independent, and conflating them is the most common error in an exam answer. Dilute hydrochloric acid is strong and weak-tasting; glacial acetic acid is concentrated and weak.

The practical consequence is in buffering rather than in pH. A weak acid holds a reservoir of undissociated molecules, so adding a little base converts some of them and the pH barely moves. A strong acid has no reservoir: what you add is what you get. That is why every biological buffer is built from a weak acid and its conjugate base, and why blood chemistry is a carbonic acid system rather than a hydrochloric one.

What this cannot do

Buffers, which need both members of a conjugate pair and the Henderson-Hasselbalch relation rather than a single equilibrium. Polyprotic acids past their first proton — sulfuric, carbonic and phosphoric each have a second and sometimes a third dissociation with its own constant, and the later ones interact.

It also uses concentration where the definition calls for activity. Above roughly 0.1 mol/L, ions crowd each other and the effective concentration falls below the nominal one, so a real meter reads differently from this arithmetic — increasingly so as the solution concentrates. For coursework and bench estimates that gap is irrelevant; for anything being reported, a calibrated meter is the measurement and this is the prediction.

Frequently asked questions

Why is neutral not always pH 7?
Because neutral means equal H⁺ and OH⁻, which is pKw ÷ 2, and pKw depends on temperature. Water's self-ionisation absorbs heat, so hot water ionises more: pKw is about 14.94 at 0 °C, 14.00 at 25 °C and 13.03 at 60 °C. Neutral water at 60 °C sits at pH 6.52 and is not acidic — it has exactly as many hydrogen ions as hydroxide ions, which is the definition.
Can pH go below 0 or above 14?
Yes. The 0-to-14 range is a convention describing dilute aqueous solutions, not a limit. A 10 mol/L strong acid has a negative pH by this arithmetic, and concentrated bases exceed 14. What does break down at those concentrations is the assumption that concentration stands in for activity, so the number becomes less meaningful before it becomes impossible.
What is the difference between a strong and a weak acid here?
How much of it dissociates. A strong acid gives up essentially every proton, so [H⁺] equals the concentration you started with and pH is a single logarithm. A weak acid reaches an equilibrium set by Ka, and finding [H⁺] means solving x² + Ka·x − Ka·C = 0. Strength is not concentration: a concentrated weak acid and a dilute strong one can reach the same pH by different routes.
Why show the √(Ka·C) shortcut separately?
Because it is what most textbooks teach and it is wrong in a specific, predictable direction. It assumes the amount that dissociates is negligible against the starting concentration, which holds for a concentrated solution of a genuinely weak acid and fails as either of those stops being true. The tool solves the quadratic exactly and shows the shortcut beside it, so you can see how much the assumption costs on your numbers instead of taking it on trust.
Why does a very dilute acid stop making sense?
Below about 10⁻⁶ mol/L, water's own ionisation supplies more hydrogen ions than the acid does. This model ignores that, so it will happily report pH 8 for a 10⁻⁸ mol/L strong acid — which would mean adding acid made the solution basic. The result carries a warning at that point; the correct treatment includes water's contribution in the charge balance.

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