pH is the everyday language of acids and bases — one number that tells you whether something is sour battery acid or slippery drain cleaner. Behind that single digit sits a logarithm. This calculator turns any one of pH, pOH, [H⁺], or [OH⁻] into all four, computes the pH of a strong acid or base directly from its molarity, and shows where the solution lands on the 0–14 scale. This guide explains what the number means, why the scale is logarithmic, and where the simple model stops working.
What pH actually measures
pH is defined as the negative base-10 logarithm of the hydrogen-ion concentration: pH = −log₁₀[H⁺], with [H⁺] in moles per litre. The negative sign and the logarithm together turn the tiny, awkward numbers of real solutions — pure water has [H⁺] = 0.0000001 mol/L — into a friendly 0-to-14 range. A low pH means a high hydrogen-ion concentration and an acidic solution; a high pH means a low one and a basic (alkaline) solution. Because water self-ionises, every aqueous solution also contains hydroxide ions, and the two are linked: [H⁺] multiplied by [OH⁻] always equals the ion product of water.
The scale is logarithmic — each step is ten times
The single most important fact about pH is that it is logarithmic, so the steps are not evenly spaced in concentration. Going from pH 5 to pH 4 multiplies the hydrogen-ion concentration by ten; from pH 5 to pH 3 multiplies it by a hundred. That means lemon juice (pH 2) is not 'a bit more acidic' than coffee (pH 5) — it has a thousand times the hydrogen-ion concentration. This is why small pH changes matter so much in biology and the environment: a one-unit drop in ocean pH represents a tenfold rise in acidity, and a swing of a few tenths in blood pH can be fatal. The colour bar in the calculator spaces the numbers evenly, but remember each tick is a factor of ten in [H⁺].
pH, pOH, and the pH + pOH = 14 rule
Hydroxide ions get their own logarithmic measure, pOH = −log₁₀[OH⁻]. Because [H⁺][OH⁻] = Kw = 1.0 × 10⁻¹⁴ at 25 °C, taking the negative log of both sides gives the tidy relationship pH + pOH = 14. So a solution with pOH 2 has pH 12, and you never need to measure both. This calculator uses that relationship to fill in every quantity from a single input: give it a pH and it returns pOH, [H⁺], and [OH⁻]; give it an [OH⁻] and it works backwards to the pH. The '14' is specific to 25 °C — it is really 2 × 7, where 7 is −log₁₀ of the square root of Kw.
Strong acids and bases from molarity
For a strong acid such as hydrochloric (HCl) or nitric (HNO₃) acid, dissociation is essentially complete: every molecule releases its proton, so the hydrogen-ion concentration equals the concentration of acid you dissolved. A 0.01 M solution therefore has [H⁺] = 0.01 mol/L and pH = 2. Strong monobasic bases like sodium or potassium hydroxide behave the same way for hydroxide: [OH⁻] equals the molarity, giving the pOH directly and the pH by subtraction. The From Concentration tab does exactly this. It assumes a clean 1:1, fully-dissociating species — diprotic acids like sulfuric acid, or anything that only partly ionises, need a more detailed treatment.
Where the simple model stops: weak acids, dilution, and temperature
Three things break the straightforward calculation. First, weak acids and bases (acetic acid, ammonia, carbonic acid) only partially dissociate, so their pH depends on an equilibrium constant (Ka or Kb) and concentration together — you cannot read it off the molarity, and this calculator deliberately keeps that out of scope. Second, extreme dilution: a 10⁻⁸ M strong acid is not pH 8 (that would be basic!) because water's own ions dominate; near neutrality you must account for Kw, so trust the calculator most between about pH 1 and 13. Third, temperature: Kw rises as water warms, so neutral pH falls below 7 — around 6.6 at 50 °C — even though the water is still perfectly neutral. The calculator works at the standard 25 °C reference, which covers almost all everyday and classroom situations.