pH is the negative base-ten logarithm of the hydrogen ion concentration. Every whole unit is a factor of ten.
A solution at pH 4 has a hydrogen ion concentration of 0.0001 mol/L. At pH 5 it is 0.00001. The gap that looks like one step on a fourteen point scale is a tenfold difference in the quantity that actually does the chemistry.
The scale compresses an enormous range
That compression is the reason the scale exists. Hydrogen ion concentrations in ordinary solutions span from around 1 mol/L down to 10 to the power minus 14. Writing those out, or plotting them on a linear axis, is unusable. Taking a logarithm turns fourteen orders of magnitude into fourteen units.
The cost is that intuition about differences stops working. Lemon juice near pH 2 is about a hundred thousand times more acidic than pure water at pH 7, not two and a half times. The pH calculator converts in both directions precisely because the concentration is the figure that means something physically.
Small pH changes are not small
This is why apparently minor pH shifts matter so much in biology and environmental science.
Human blood is held between about 7.35 and 7.45. A drop to 7.2, which sounds trivial, represents roughly a 40 per cent increase in hydrogen ion concentration and is a medical emergency. Ocean pH falling by 0.1 since pre-industrial times corresponds to about a 30 per cent rise in acidity.
Neither of those numbers is intuitive from the pH figures alone. Both are obvious once converted back to concentration.
pH 7 is only neutral at 25 degrees
Neutral means equal hydrogen and hydroxide concentrations, not pH 7. The two coincide at 25 degrees Celsius because that is where water's ion product is exactly 10 to the minus 14.
Heat the water and the ion product rises. At 50 degrees, neutral water has a pH near 6.6. That water is not acidic; it has equal concentrations of both ions and is neutral by definition. The number moved because the reference moved.
The scale does not stop at 0 and 14
Those bounds describe ordinary dilute aqueous solutions, not a limit. Concentrated strong acids have negative pH values and concentrated bases exceed 14. The simple logarithmic relationship becomes unreliable there, because at high concentration the effective activity of the ions diverges from their concentration, but the scale itself does not stop.
Buffers work on the same logarithm
The Henderson-Hasselbalch equation gives buffer pH as the pKa plus the log of the base to acid ratio. Because that term is logarithmic, a tenfold change in the ratio moves the pH by only one unit.
That insensitivity is the whole mechanism. A buffer absorbs added acid or base by shifting a ratio a long way while the pH barely moves, which is exactly what blood does to stay inside its 0.1 unit window. The Henderson-Hasselbalch calculator shows how flat that response is.
For acid strength on the same logarithmic scale, see the pKa calculator. For how much a buffer can absorb before it gives way, see the buffer capacity calculator.