Last updated: 2026-06-14

Understanding pH

pH measures how acidic or basic a water-based solution is. It is defined as the negative base-10 logarithm of the hydrogen-ion concentration, so a small concentration of H⁺ gives a high pH and a large concentration gives a low pH. The scale runs from 0 to 14 at room temperature, with 7 marking a neutral solution.

The pH formula

$$\text{pH} = -\log_{10}[\text{H}^+]$$

Symbol	Quantity	Unit
pH	Acidity measure	unitless
[H⁺]	Hydrogen-ion concentration	mol/L (M)

The relationship reverses to give the concentration back:

$$[\text{H}^+] = 10^{-\text{pH}}$$

Because the scale is logarithmic, each whole pH unit is a tenfold change in [H⁺]. A pH 3 solution has ten times more hydrogen ions than pH 4 and a hundred times more than pH 5.

pH, pOH, and the ion product of water

Water self-ionizes slightly, and at 25 °C the product of the ion concentrations is constant:

$$[\text{H}^+][\text{OH}^-] = K_w = 1\times10^{-14}$$

Taking negative logarithms gives the companion relationship:

$$\text{pH} + \text{pOH} = 14$$

So a solution of pH 4 has pOH 10, and one of pH 11 has pOH 3. This calculator lets you start from any of [H⁺], [OH⁻], pH, or pOH and returns all four.

Worked example

A solution has a hydrogen-ion concentration of 2.5 × 10⁻⁵ M. What is its pH?

$$\text{pH} = -\log_{10}(2.5\times10^{-5}) = 4.60$$

Then pOH = 14 − 4.60 = 9.40, and [OH⁻] = 10⁻⁹·⁴⁰ ≈ 4.0 × 10⁻¹⁰ M. With a pH below 7, the solution is acidic.

The pH of everyday substances

Substance	Approx. pH	Type
Battery acid	0	Acidic
Lemon juice	2	Acidic
Black coffee	5	Acidic
Pure water	7	Neutral
Sea water	8	Basic
Baking soda	9	Basic
Household bleach	13	Basic

Strong vs. weak acids

This calculator relates pH directly to the concentration you enter, which is exact for strong acids and bases such as HCl and NaOH that dissociate completely. Weak acids and bases only partly dissociate, so their actual [H⁺] is lower than the nominal concentration and depends on the acid-dissociation constant Ka. For a weak acid, first calculate [H⁺] from Ka and concentration, then enter that hydrogen-ion concentration here.

Frequently Asked Questions (FAQ)

What is the formula for pH?

pH is the negative base-10 logarithm of the hydrogen-ion concentration: pH = −log₁₀[H⁺], with [H⁺] in moles per litre. For example, a solution with [H⁺] = 1×10⁻³ M has pH = −log₁₀(10⁻³) = 3. Reversing it, [H⁺] = 10^(−pH). Because the scale is logarithmic, each whole pH unit represents a tenfold change in hydrogen-ion concentration.

How are pH and pOH related?

At 25 °C, pH + pOH = 14. This comes from the self-ionization of water, where [H⁺] × [OH⁻] = Kw = 1×10⁻¹⁴. Taking the negative logarithm of both sides gives pH + pOH = 14. So a solution with pH 4 has pOH 10, and one with pH 11 has pOH 3. The constant 14 applies at 25 °C; it shifts slightly at other temperatures because Kw is temperature-dependent.

What does the pH scale mean?

The pH scale runs from 0 to 14 at 25 °C. A pH below 7 is acidic (more H⁺ than OH⁻), exactly 7 is neutral (equal amounts), and above 7 is basic or alkaline (more OH⁻ than H⁺). Familiar examples: lemon juice ≈ 2, black coffee ≈ 5, pure water = 7, baking-soda solution ≈ 9, and household bleach ≈ 13. Values below 0 or above 14 are possible for very concentrated strong acids or bases.

Why does this calculator assume strong acids and bases?

This calculator relates pH directly to the hydrogen-ion concentration you enter, which is exact for strong acids and bases that dissociate completely (HCl, NaOH, etc.). Weak acids and bases only partially dissociate, so their [H⁺] is lower than their nominal concentration and depends on the acid-dissociation constant (Ka). For weak acids you would first calculate [H⁺] from Ka and concentration, then enter that [H⁺] here.