pH, pOH and the ion product of water
How pH and pOH connect through the water ion product Kw, why they add to 14 at 25C, and how to read concentrations from either scale.
The pH scale as a logarithm
pH compresses a huge range of hydrogen ion concentrations into a friendly scale by taking a logarithm. Because pH = -log10[H+], each whole step on the scale is a tenfold change in [H+]. A drop from pH 5 to pH 4 means ten times more hydrogen ions, and a drop to pH 3 means a hundred times more. That is why strong acids and bases sit only a few units apart despite an enormous difference in ion concentration.
Why pH and pOH add to 14
Water constantly splits into a small number of hydrogen and hydroxide ions. At 25 degrees Celsius the product of their concentrations, called Kw, is fixed at 1.0 x 10^-14. Taking the negative logarithm of that product gives pH plus pOH equal to 14. So if you know one scale you know the other by simple subtraction, which is exactly how this tool fills in a missing pOH from a pH.
Reading concentrations from the scale
To move from a pH back to a concentration you reverse the logarithm: [H+] equals ten to the power of negative pH. A pH of 3 gives 0.001 mol/L, and a pH of 7 gives 1.0 x 10^-7 mol/L for both ions, the balanced point of pure water. The hydroxide concentration follows the same rule with pOH. Keeping nine significant figures lets the tool show these tiny numbers without rounding them to zero.
Where the 25C assumption matters
The tidy value of 14 depends on temperature, because Kw grows as water warms. Near body temperature neutral water sits closer to pH 6.8, even though it holds equal hydrogen and hydroxide ions and is still chemically neutral. This calculator fixes the temperature at 25 degrees Celsius, the standard reference, so treat its verdicts as accurate for room-temperature chemistry and approximate elsewhere.