Lemon juice, black coffee, and drain cleaner sit at wildly different points on the same 0-to-14 scale that tells you, in a single number, how acidic or basic a solution is. That number is pH, and it's built from a logarithm — which is exactly why a "small" change in pH represents a huge change in actual chemistry.
How to Use the pH Calculator
Choose whether to solve for pH from a known hydrogen-ion concentration, or for concentration from a known pH, then enter the known value. The calculator returns pH, hydrogen-ion concentration in moles per liter, pOH, and hydroxide-ion concentration, so you get the complete acid-base picture from a single input.
Working Backward From pH to Concentration
If you're given a target pH — say, a recipe or protocol calling for a solution at pH 5 — and need to know how much acid to add, solve for concentration instead: [H⁺] = 10^(-pH). For pH 5, that's 10⁻⁵ mol/L, a hundred times more dilute than the pH-3 example above. This reverse direction comes up constantly in buffer preparation, where a chemist needs to hit a specific pH target and has to work out the corresponding ion concentration before calculating how much of a given acid or base solution actually delivers it.
The pH Formula
pH = -log₁₀[H⁺]
pH equals the negative base-10 logarithm of hydrogen-ion concentration, written in brackets to denote "concentration of." The calculator's default example uses a hydrogen-ion concentration of 0.0001 mol/L, or 10⁻⁴ mol/L: taking the negative log of 10⁻⁴ gives exactly 4, so the solution has a pH of 4 — solidly acidic, in the range of orange juice or tomato juice.
pOH and the Water Equilibrium
pOH = 14 - pH
At 25°C, pure water maintains a constant equilibrium between hydrogen ions and hydroxide ions, described by the water dissociation constant Kw = 1.0 × 10⁻¹⁴. That constant is what fixes the relationship between pH and pOH — they always sum to 14 at this standard temperature. Using the calculator's default example, a pH of 4 gives a pOH of 10, and converting that back to hydroxide-ion concentration with 10^-10 gives 10⁻¹⁰ mol/L — a tiny number, confirming the solution is overwhelmingly dominated by hydrogen ions rather than hydroxide ions, consistent with it being acidic.
Why the Logarithm Makes Small Numbers Feel Big
Because pH is a logarithmic scale, each single-unit drop in pH represents a tenfold increase in hydrogen-ion concentration — a solution at pH 3 isn't "a bit more acidic" than pH 4, it's ten times more acidic in terms of actual hydrogen-ion concentration. That's why battery acid (around pH 0-1) and stomach acid (around pH 1-2) are so much more aggressive than vinegar (around pH 2-3), even though they're separated by only a couple of points on the scale — those couple of points represent a hundred-fold or thousand-fold difference in concentration.
Reading the Acid-Base Scale
At 25°C, pH 7 is neutral (pure water), values below 7 are acidic, and values above 7 are basic, also called alkaline. Common examples span the whole range: battery acid near pH 0, stomach acid around pH 1.5-2, coffee around pH 5, pure water at pH 7, seawater around pH 8, baking soda solution around pH 9, ammonia around pH 11, and drain cleaner or lye solutions above pH 13. Biological systems are extremely sensitive to pH — human blood, for instance, is tightly regulated between about 7.35 and 7.45, and even small deviations outside that narrow window are medically serious.
