pH Calculator
Convert between hydrogen-ion concentration and pH, with a visual acidity scale.
[H⁺] = 1.00e-4 mol/L · pOH = 10
To find pH, take the negative base-10 logarithm of the hydrogen-ion concentration: pH = −log₁₀[H⁺], with [H⁺] in mol/L. For [H⁺] = 1 × 10⁻³ mol/L, pH = −(−3) = 3, an acidic solution. Reverse it with [H⁺] = 10⁻ᵖᴴ.
What pH measures
pH is the negative base-10 logarithm of the hydrogen-ion concentration, written [H⁺] in moles per liter. Because it’s a log scale, a change of one pH unit means a tenfold change in acidity — pH 4 is ten times more acidic than pH 5, and a hundred times more acidic than pH 6.
[H⁺] in mol/L; reverse it with [H⁺] = 10⁻ᵖᴴ
Worked example
Find the pH of a solution with [H⁺] = 1 × 10⁻³ mol/L.
- 1 Write the concentration in scientific notation. [H⁺] = 1 × 10⁻³ mol/L, so the exponent is −3.
- 2 Take the base-10 logarithm. log₁₀(1 × 10⁻³) = −3, since log₁₀ of a power of ten is just the exponent.
- 3 Negate the result. pH = −(−3) = 3 — an acidic solution. Its pOH is 14 − 3 = 11 at 25 °C.
pH of common solutions
Approximate values at 25 °C; pH below 7 is acidic, above 7 is basic.
| Solution | Approx. pH | Nature |
|---|---|---|
| Battery acid | 0–1 | Strongly acidic |
| Lemon juice | 2 | Acidic |
| Black coffee | 5 | Weakly acidic |
| Pure water | 7 | Neutral |
| Baking soda | 9 | Weakly basic |
| Household bleach | 12–13 | Strongly basic |
When the simple formula applies
Strong acids and bases. For a strong acid like HCl that fully dissociates, [H⁺] equals the acid’s molarity, so pH = −log(molarity) directly.
Weak acids need Ka. A weak acid only partly dissociates, so [H⁺] is smaller than the molarity — you must work from its Ka first. For a weak acid mixed with its conjugate base, use the buffer pH calculator instead.
Common mistakes. Dropping the minus sign, confusing pH with pOH, and assuming pH 7 is always neutral — neutrality is exactly 7 only at 25 °C, because the water-ionization constant shifts with temperature.