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MATH & SCIENCE

Hydrogen Ion Concentration to pH Calculator

Calculate pH from a hydrogen ion concentration in mol/L.

About this tool

Calculate pH from a hydrogen ion concentration, or work backward from a pH value to find the concentration it represents — using the actual definition, pH = −log₁₀[H⁺], not a lookup table.

pH is logarithmic for the same reason decibels are: hydrogen ion concentrations in real solutions span an enormous range (many orders of magnitude), and a logarithmic scale compresses that into the familiar, manageable 0-14 range. Each whole pH step represents a 10× change in hydrogen ion concentration — a solution of pH 4 has 10 times more hydrogen ions than pH 5, and 100 times more than pH 6, not merely "a bit more."

Pure water is neutral at pH 7 (concentration exactly 10⁻⁷ mol/L) — lower values are more acidic (higher hydrogen ion concentration), higher values are more basic/alkaline (lower hydrogen ion concentration).

Frequently asked questions

Why is each pH step a 10x change, not a small increment?

Because pH is a base-10 logarithm of concentration — log₁₀ increasing by 1 corresponds exactly to the underlying value increasing by a factor of 10, the same relationship behind the Richter scale for earthquakes or decibels for sound.

What counts as acidic vs basic?

Below pH 7 is acidic, above pH 7 is basic (alkaline), and exactly 7 is neutral (pure water) — the further from 7 in either direction, the stronger the acid or base.

Can pH go below 0 or above 14?

In theory yes, for extremely concentrated solutions, though the 0-14 range covers essentially every real-world substance people typically ask about — this tool accepts values outside that range too, it just covers the common cases most naturally.

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