pH Calculator
Enter any one of [H⁺], [OH⁻], pH or pOH — the calculator returns the other three at 25 °C, plus an acid/base classification.
pH
4.00 (acidic)
- pOH
- 10.00
- [H⁺] (hydrogen-ion concentration)
- 1.0000e-4 mol/L
- [OH⁻] (hydroxide-ion concentration)
- 1.0000e-10 mol/L
- Classification
- acidic
pH = −log₁₀[H⁺] and pOH = −log₁₀[OH⁻]. At 25 °C the ion-product of water Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴, so pH + pOH = 14. pH below 7 is acidic, above 7 is basic, exactly 7 is neutral.
How to use this calculator
Pick what you know — the [H⁺] concentration in mol/L, the [OH⁻] concentration in mol/L, the pH, or the pOH — and type the value. Concentrations are usually small numbers, so use scientific notation (for example 1e-4 for 0.0001 mol/L). pH and pOH are dimensionless and lie between 0 and 14 in ordinary aqueous solutions. The calculator assumes a temperature of 25 °C, where the ion-product of water Kw equals 1.0 × 10⁻¹⁴ — at this temperature pH + pOH = 14 exactly. Outputs are pH, pOH, both ion concentrations, and whether the solution is acidic, neutral or basic.
How the calculation works
pH is defined as the negative base-10 logarithm of the hydrogen-ion (more precisely, hydronium-ion) activity: pH = −log₁₀[H⁺]. The "p" prefix means "negative log of"; it converts the awkwardly small concentrations of H⁺ in water (often 10⁻¹ to 10⁻¹⁴ mol/L) into a friendly 0–14 scale. Each whole pH unit is a factor of ten in [H⁺] — pH 3 has ten times more H⁺ than pH 4, and a hundred times more than pH 5. The hydroxide scale pOH = −log₁₀[OH⁻] works the same way. In any aqueous solution at 25 °C the two are linked by water’s autoionisation, [H⁺][OH⁻] = Kw = 1.0 × 10⁻¹⁴, which gives pH + pOH = 14. So once you know any one of the four quantities the other three are fixed. Pure water has [H⁺] = [OH⁻] = 10⁻⁷ mol/L, so pH = pOH = 7 — the definition of neutral.
Worked example
A 0.01 mol/L solution of hydrochloric acid is a strong acid and dissociates completely, giving [H⁺] = 1.0 × 10⁻² mol/L. Choose "[H⁺] concentration" and enter 0.01. pH = −log₁₀(0.01) = 2. pOH = 14 − 2 = 12, so [OH⁻] = 10⁻¹² mol/L. The result is firmly acidic. Going the other way: a household ammonia solution might measure pH 11. Choose "pH" and enter 11. Then [H⁺] = 10⁻¹¹ mol/L, pOH = 3 and [OH⁻] = 10⁻³ mol/L — a basic solution about a million times richer in OH⁻ than pure water.
Frequently asked questions
What is the formula for pH?
pH = −log₁₀[H⁺], where [H⁺] is the molar concentration of hydrogen ions (more strictly, hydronium ions H₃O⁺) in mol/L. The negative sign and the logarithm together turn the tiny concentrations of H⁺ in water — anywhere from 1 mol/L for a strong acid down to 10⁻¹⁴ mol/L for a strong base — into the familiar 0 to 14 scale. The IUPAC operational definition uses the activity of hydrogen ions rather than the concentration, but at the dilutions of everyday chemistry the two are interchangeable.
Why is pH + pOH = 14?
At 25 °C water self-ionises, H₂O ⇌ H⁺ + OH⁻, with an equilibrium constant Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴. Taking −log₁₀ of both sides gives pKw = pH + pOH = 14. The number 14 is specific to 25 °C — Kw rises with temperature (water dissociates more), so at 100 °C pKw is about 12.5 and "neutral" pH is roughly 6.25, not 7. This calculator uses the 25 °C reference value, which is the convention for almost all textbook and lab chemistry.
What does each pH value mean — is pH 4 twice as acidic as pH 8?
The pH scale is logarithmic, so it is not "twice" anything in a linear sense. A drop of one pH unit means ten times more H⁺. pH 4 has 10⁴ = 10,000 times more H⁺ than pH 8, not twice. Rough reference points: stomach acid ≈ pH 1.5, lemon juice ≈ 2, vinegar ≈ 3, black coffee ≈ 5, pure water ≈ 7, blood ≈ 7.4, seawater ≈ 8.1, household ammonia ≈ 11, oven cleaner ≈ 13.
Can pH be negative or greater than 14?
Yes, in principle. The 0–14 range is the practical span for dilute aqueous solutions, but [H⁺] greater than 1 mol/L gives a negative pH (concentrated battery acid is about pH −1) and [OH⁻] greater than 1 mol/L gives a pH above 14 (saturated NaOH is around pH 15). At those concentrations the simple −log[H⁺] formula loses accuracy because the activity of the ions diverges from the concentration; you need activity coefficients. This calculator restricts pH and pOH to 0–14 and concentrations to positive numbers, which covers everything you will meet outside specialist research.
I know the concentration of an acid — is that the same as [H⁺]?
Only for strong acids that dissociate completely. Hydrochloric (HCl), nitric (HNO₃), sulfuric (H₂SO₄, first proton), perchloric (HClO₄) and a handful of others ionise essentially 100 % in water, so for a 0.01 mol/L solution of HCl, [H⁺] = 0.01 mol/L. For weak acids — acetic (vinegar), citric, carbonic — only a small fraction dissociates, and you need the acid dissociation constant Ka to find [H⁺]. Use this calculator once you have computed [H⁺] from Ka, or for strong acids and bases directly.
What is a buffer and how does it relate to pH?
A buffer is a solution that resists changes in pH when small amounts of acid or base are added. It contains a weak acid and its conjugate base in comparable amounts; their equilibrium absorbs added H⁺ or OH⁻. The Henderson–Hasselbalch equation, pH = pKa + log₁₀([A⁻]/[HA]), gives the buffer pH from the acid’s pKa and the ratio of conjugate base to acid. Buffers are essential in biology — blood is buffered near pH 7.4 by the carbonic acid / bicarbonate system, and deviations of even 0.4 units are life-threatening.