pH calculator
Enter a concentration or a pH, get the rest.
How do I calculate pH?
pH = −log₁₀[H⁺], with the hydrogen ion concentration in moles per liter. [H⁺] = 0.001 M gives pH 3.
How do I get pH from hydroxide concentration?
Find pOH = −log₁₀[OH⁻], then pH = 14 − pOH at 25 °C. [OH⁻] = 0.0001 M is pOH 4, so pH 10.
What pH is neutral?
7 at 25 °C, where [H⁺] = [OH⁻] = 10⁻⁷ M. Below 7 is acidic, above 7 basic.
Why does one pH unit matter so much?
The scale is logarithmic: pH 3 has ten times the hydrogen ions of pH 4 and a hundred times those of pH 5.
Is pH + pOH always 14?
Only at 25 °C, where the water constant Kw is 1.0 × 10⁻¹⁴. At other temperatures the sum shifts a little.
Can a pH be negative or above 14?
Yes. A strong acid more concentrated than 1 M has a pH below zero: a pH of −1.07 corresponds to [H⁺] = 12 M (OpenStax Chemistry 2e, section 14.2, Example 14.5 practice problem). In the same way a strong base above 1 M has a pOH below zero and a pH above 14. The calculator accepts any pH or pOH.
How many decimal places should a pH have?
As many decimal places as the concentration has significant figures (OpenStax Chemistry 2e, section 14.2). Stomach acid at [H⁺] = 1.2 × 10⁻³ M has two significant figures, so its pH is 2.92, not 2.9208. The calculator shows extra digits for you to round.
How do I find the pH of a weak acid?
Not by typing its concentration as [H⁺]. A weak acid ionizes only partly, so [H⁺] is far below the amount of acid you dissolved. For 0.10 M acetic acid (Ka = 1.8 × 10⁻⁵) solving x² ÷ (0.10 − x) = Ka gives [H⁺] = 0.0013 M and a pH near 2.9; treating it as a strong acid would give 1.0. The ICE table calculator solves the equilibrium; enter its [H⁺] here for the pOH and [OH⁻].
How the calculation works
The calculator applies three relations from OpenStax Chemistry 2e, section 14.2. The pH is the negative base-10 logarithm of the hydronium ion concentration in moles per liter, and the pOH is the same for hydroxide. At 25 °C the water constant Kw = [H⁺][OH⁻] equals 1.0 × 10⁻¹⁴, so taking logarithms gives pH + pOH = 14.00. To go the other way, [H⁺] = 10−pH and [OH⁻] = 10−pOH. Because the scale is logarithmic, each unit of pH is a factor of ten in concentration. The calculator assumes 25 °C: the 14 is built in. Pure water at 80 °C has [H⁺] = 4.9 × 10⁻⁷ M, a pH of 6.31, and is still neutral, so “neutral is pH 7” is a 25 °C rule.
Worked example
A 0.0125 M potassium hydroxide solution. KOH is a strong base, ionizing essentially completely (OpenStax section 14.3), so [OH⁻] = 0.0125 M. Then pOH = −log₁₀(0.0125) = 1.903, and pH = 14 − 1.903 = 12.10. Choosing “[OH⁻]” in the calculator and entering 0.0125 returns the same numbers, which match OpenStax Example 14.6. Working back, a pH of 12.10 means [H⁺] = 8 × 10⁻¹³ M, which is Kw divided by 0.0125.
Common mistakes
The most frequent error is entering the concentration of a weak acid or weak base as [H⁺] or [OH⁻]: only strong acids and bases give an ion concentration equal to the amount dissolved. A second is forgetting the number of hydroxide ions per formula unit, so 0.010 M Ca(OH)₂ gives [OH⁻] = 0.020 M, not 0.010 M. A third is rounding the concentration before taking the logarithm; round only the final pH, to the decimal places described above. Last, pH + pOH = 14 does not hold for a solution at, say, 80 °C without correcting Kw.
Sources: OpenStax Chemistry 2e, section 14.2 “pH and pOH” (definitions, Kw = 1.0 × 10⁻¹⁴ at 25 °C, significant figures in logarithms, Examples 14.4 to 14.6 and the pure-water value at 80 °C) and section 14.3 “Relative Strengths of Acids and Bases” (strong versus weak, Ka of acetic acid). Related: ICE table calculator, buffer pH calculator, molarity calculator and dilution calculator.