Three pH points, a thousand times the difference
The pH scale looks like an ordinary ruler running 0 to 14, and that is where it misleads. It is logarithmic: each step of 1 point multiplies acidity by 10. Two neighbouring numbers hide an order of magnitude — and three neighbouring numbers hide a thousandfold.
1. Lemon and coffee
Lemon juice sits around pH 2. Brewed coffee is close to 5. That is three points apart on a scale that runs to 14. How many times more acidic is the lemon?
2. The ruler that is not a ruler
pH is the negative logarithm of the hydrogen-ion concentration: pH = −log₁₀[H⁺]. Drag it and watch what happens to the concentration — the acidity bar explodes while the pH number creeps down:
Hydrogen-ion concentration as a function of pH, on a logarithmic scale.
Between pH 7 (pure water) and pH 0 (battery acid) there is a ten-million-fold difference in H⁺ concentration. The scale compresses all of that into seven notches — which is exactly what it is for, and also exactly why it fools people.
3. Where everyday things land
| Substance | Approximate pH | H⁺ concentration |
|---|
The most surprising row is normal rain: it is already acidic, around pH 5.6, because carbon dioxide in the air dissolves in water and forms carbonic acid. So "acid rain" at pH 4 is not twice as acidic — it is about 40 times ordinary rain.
4. Why "just add water" does not work
If every pH point is worth 10 times, then raising it by 1 point takes a tenfold dilution. That is the math that breaks the instinct to fix acidity by pouring in water:
- To go from pH 3 to pH 4: dilute 10×.
- To go from pH 3 to pH 5: dilute 100×.
- To go from pH 3 to pH 7: dilute 10,000× — one liter of solution into ten thousand liters of water.
And in practice even that does not settle it: real solutions are buffered — dissolved salts that hold the pH and resist change. That is why human blood stays locked between 7.35 and 7.45 regardless of what we eat, and why correcting the pH of a pool or a soil is done with a calculated chemical dose, not with a hose.
This lesson is about the math of the scale, not about health. Blood pH is controlled by the kidneys and lungs within an extremely narrow band and does not change with diet — "alkaline" diets do not alter blood pH. What food does change is urine pH, which is a different thing. In a lab or a pool, follow a reading from strips or a calibrated pH meter; mixing cleaning products of opposite pH (acid and base) can release toxic gases.
Where the numbers come from. Concentrations from [H⁺] = 10⁻ᵖᴴ at 25 °C. The pH values for substances are typical ranges and vary with origin, temperature and preparation — coffee runs 4.8 to 5.2, soft drinks 2.3 to 3.4.
Calculate pH
Conversion between pH, pOH and H⁺ / OH⁻ concentration, with the formula explained.
Open the pH Calculator →See also: Dilution · Molarity · Lesson: percentages don't add up