pH Calculator

Free pH Calculator - Calculate pH from hydrogen ion concentration or vice versa.

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What pH measures and when to calculate it

pH is a logarithmic scale for the hydrogen ion concentration of an aqueous solution. Because concentrations of H+ span many orders of magnitude, from about 1 mol/L in strong acid down to 10-14 mol/L in strong base, a logarithm turns them into a compact scale that mostly runs from 0 to 14. Each drop of one pH unit means the hydrogen ion concentration has risen tenfold.

Use this calculator when you know the H+ concentration in mol/L and need the pH, for example when finishing a strong-acid homework problem, checking a dilution, or converting a titration result. It converts concentration to pH only. To go the other way, use [H+] = 10-pH on any scientific calculator.

Formula and variables

pH = −log10[H+]

  • [H+] is the molar concentration of hydrogen ions (strictly, hydronium activity) in mol/L.
  • log10 is the base-10 logarithm.

For a strong monoprotic acid that dissociates completely, [H+] equals the acid concentration. For a diprotic strong acid such as sulfuric acid, first-step dissociation is complete but the second is not, so you must work out [H+] yourself before using the tool. Reported pH values conventionally carry as many decimal places as the concentration has significant figures.

Worked example

A solution has [H+] = 2.5 × 10-4 mol/L.

  • log10(2.5 × 10-4) = log10(2.5) + (−4) = 0.39794 − 4 = −3.60206.
  • pH = −(−3.60206) = 3.60206.

Entering 0.00025 (or 2.5e-4) gives “pH: 3.60”, since the calculator rounds to two decimals. The result is acidic, and it is the same as saying the solution is about 103.4 times more acidic than neutral water at pH 7.

Common mistakes and how to interpret the result

  • Entering a pH or pOH instead of a concentration. The input must be [H+] in mol/L, a small positive number like 0.001.
  • Assuming very dilute acids follow the formula. A 1 × 10-8 M HCl solution is not pH 8; water’s own ionisation brings the true value to about 6.98.
  • Treating weak acids like strong ones. Acetic acid at 0.1 M does not release 0.1 M of H+; use the acid dissociation constant to find [H+] first.
  • Calling 7 neutral at any temperature. Neutral pH is 7.00 only near 25 °C, because the ion product of water changes with temperature.

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Frequently Asked Questions

Can pH be negative or above 14?
Yes. Concentrated strong acids above 1 M have negative pH values, and concentrated strong bases can exceed 14. The 0 to 14 range is a convenient guide for dilute solutions, not a hard limit.
How do I find [H+] from a known pH?
Raise 10 to the power of the negative pH. For pH 3.60, [H+] = 10^-3.60, which is about 2.5 x 10^-4 mol/L.
Why does the tool return an error message for zero?
The logarithm of zero is undefined, and a real solution always contains some hydrogen ions. Enter a concentration greater than zero.
How many decimal places should I report?
Match the decimal places of the pH to the significant figures in the concentration. A concentration of 2.5 x 10^-4 has two significant figures, so a pH of 3.60 is appropriate.