How is pH calculated from concentration?

pH is the negative base-10 logarithm of the hydrogen-ion concentration in mol/L: pH = −log₁₀[H⁺]. For a strong monoprotic acid that fully dissociates, [H⁺] equals the acid concentration, so a 0.01 mol/L solution gives pH = −log₁₀(0.01) = 2.

How are pH and pOH related?

At 25 °C, pH + pOH = 14. This comes from the ion product of water, Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴. Take the negative log of both sides and you get pH + pOH = pKw = 14.

How do I find the pH of a strong base like NaOH?

A strong base sets [OH⁻] directly. For 0.01 mol/L NaOH, [OH⁻] = 0.01, so pOH = −log₁₀(0.01) = 2 and pH = 14 − 2 = 12. For Ca(OH)₂ set the OH⁻ count to 2, because each formula unit releases two hydroxide ions.

Why does a very dilute acid not reach pH 7 by simple subtraction?

Below about 10⁻⁶ mol/L, water's own self-ionisation contributes meaningfully to [H⁺]. This calculator solves the exact quadratic [H⁺]² − C[H⁺] − Kw = 0 instead of just taking −log(C), so a 10⁻⁸ mol/L acid correctly gives pH just under 7, never above it.

Can I enter scientific notation?

Yes. Type concentrations like 1e-3, 1E-3 or the decimal 0.001 — all are parsed in your browser. Results show ion concentrations in scientific notation to keep very small numbers readable.

Does temperature change the result?

Yes. Kw rises with temperature, so neutral pH falls below 7 in hot water (about 6.14 at 100 °C). This tool assumes 25 °C, where Kw = 1.0 × 10⁻¹⁴ and neutral pH is exactly 7. Weak acids and bases also need their Ka or Kb and are not covered here.

pH Calculator — Gera Tools

A complete pH calculator for chemistry homework, lab prep and titration planning. It does two jobs. First, it converts freely between pH, pOH, the hydrogen-ion concentration [H⁺] and the hydroxide-ion concentration [OH⁻] — give it any one and it returns the other three with an acidic / neutral / basic label. Second, it works out the pH of a strong acid or strong base directly from its molar concentration, handling multivalent species such as sulfuric acid or calcium hydroxide.

How it works

Every result rests on three relationships that hold for dilute aqueous solutions at 25 °C. The self-ionisation of water gives the ion product Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴. pH and pOH are defined as pH = −log₁₀[H⁺] and pOH = −log₁₀[OH⁻], and taking the negative log of the Kw expression yields pH + pOH = 14. Whatever you enter is first turned into [H⁺]; pH, pOH and [OH⁻] then follow from those three equations.

For the strong-acid/base mode, a strong monoprotic acid is assumed to dissociate fully, so [H⁺] ≈ C, where C is the analytical concentration. A diprotic acid (count = 2) contributes roughly 2C. A strong base supplies [OH⁻] ≈ n·C, where n is the number of hydroxide groups per formula unit. Rather than naively taking −log(C), the tool solves the exact quadratic [H⁺]² − C[H⁺] − Kw = 0. That matters for very dilute solutions: near 10⁻⁷ mol/L the water background dominates, and the exact solution keeps the pH on the correct side of 7 instead of crossing it — a classic textbook trap.

Worked example

Take 0.01 mol/L hydrochloric acid (HCl), a strong monoprotic acid. Because it fully dissociates, [H⁺] ≈ 0.01 mol/L. Then:

pH = −log₁₀(0.01) = 2 (acidic)
pOH = 14 − 2 = 12
[OH⁻] = Kw ⁄ [H⁺] = 10⁻¹⁴ ⁄ 10⁻² = 1 × 10⁻¹² mol/L

Switch the species to 0.01 mol/L NaOH and the symmetry shows: [OH⁻] = 0.01, pOH = 2, pH = 12, and [H⁺] = 1 × 10⁻¹² mol/L.

Input	pH	pOH	[H⁺] (mol/L)	[OH⁻] (mol/L)
0.01 M HCl	2	12	1×10⁻²	1×10⁻¹²
Pure water	7	7	1×10⁻⁷	1×10⁻⁷
0.01 M NaOH	12	2	1×10⁻¹²	1×10⁻²

Formula note

The defining constants and equations used here are Kw = 1.0 × 10⁻¹⁴ at 25 °C, pH = −log₁₀[H⁺], pOH = −log₁₀[OH⁻] and pH + pOH = 14. These describe strong acids and bases and simple ion conversions. Weak acids and bases reach equilibrium governed by their dissociation constants Ka and Kb and are not modelled by this tool.

Everything is computed in your browser — no numbers are uploaded or stored.