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pH Calculator

Turn pH, pOH, [H₃O⁺] or [OH⁻] into the other three, with acidic, neutral or basic shown.

By Nitin Raturi · Last reviewed

Your worksheet

How to use the pH Calculator

Turn any one of pH, pOH, [H₃O⁺] or [OH⁻] into the other three.

  1. Choose what you know.
  2. Enter its value; use 1e-3 style for small concentrations.
  3. Read the pH and the other three values.

Good to know

  • Each pH step is a tenfold change in hydronium concentration.

pH = −log[H₃O⁺], and pH + pOH = 14 at 25 °C. Type small values as 1.2e-3.

You know

Which quantity you are entering.

How to fill it in

  • pH or pOH, or the hydronium [H₃O⁺] or hydroxide [OH⁻] concentration in mol/L.

Example

0.0125 M KOH has [OH⁻] = 0.0125 M, so pOH 1.903 and pH 12.10.

Value

The pH or pOH number, or the concentration in mol/L.

How to fill it in

  • pH or pOH: −2 to 16.
  • Concentration: above 0 to 20 mol/L; type 1.2e-3 or 1.2 × 10^-3.

Example

[H₃O⁺] = 1.2 × 10⁻³ M gives pH 2.92; pH 7.3 means [H₃O⁺] = 5.01 × 10⁻⁸ M.

pH

2.92

The solution has pH 2.92 and pOH 11.08, so it is acidic. [H₃O⁺] = 1.20 × 10⁻³ M and [OH⁻] = 8.33 × 10⁻¹² M.

pH
2.921
pOH
11.079
[H₃O⁺]
1.20 × 10⁻³ M
[OH⁻]
8.33 × 10⁻¹² M

At 25 °C, where pH + pOH = 14.00 (K_w = 1.0 × 10⁻¹⁴). Concentrations are treated as activities, which is fair for dilute solutions.

ChangelogHow we test this calculatorEmbed this calculator

How this calculator works

  1. Step 1pH−log₁₀[H₃O⁺]Lower means more acidic.
  2. Step 2WaterpH + pOH = 14At 25 °C.
  3. Step 3Back10^(−pH)Concentration from pH.

pH is the negative logarithm of the hydronium ion concentration. Because it is a logarithm, each step of 1 is a tenfold change.

In water at 25 °C the hydronium and hydroxide concentrations multiply to 1.0 × 10⁻¹⁴, so pH and pOH always add to 14.

Worked example: OpenStax Example 14.4

pH of a solution with [H₃O⁺] = 1.2 × 10⁻³ M
pH
−log₁₀[H₃O⁺]
  1. log₁₀(1.2 × 10⁻³)−2.92
  2. pH2.92
  3. pOH14 − 2.9211.08
  4. [OH⁻]8.33 × 10⁻¹² M

Read the result

  • pH 7.35.01 × 10⁻⁸ MSlightly basic: OpenStax Example 14.5.
  • 0.0125 M KOHpH 12.10pOH 1.903: OpenStax Example 14.6.

Pure water at 25 °C has pH 7.00, with [H₃O⁺] and [OH⁻] both 1.00 × 10⁻⁷ M.

Assumptions and limits

  • 25 °CpK_w changes with temperature.
  • DiluteConcentration stands in for activity.
  • No equilibriaWeak acids need Ka first.
  • LogarithmicOne pH unit is a factor of 10.

pH is a logarithm of concentration, so each step of one is a tenfold change.

To find the concentration first, use the molarity calculator. The log calculator shows the logarithm behind every pH value.

Common mistakes

  • Mistake: Using the acid’s concentration for a weak acid.

    Instead: Work out [H₃O⁺] from Ka first.

  • Mistake: Thinking pH 4 is twice as acidic as pH 8.

    Instead: It has 10,000 times more hydronium.

Checking the method

A separate script recomputes every value with 40-digit decimal logarithms and reproduces OpenStax Examples 14.4 to 14.6.

Read how we test our calculators, or browse more maths calculators.

Frequently asked questions

What is the pH of [H₃O⁺] = 1.2 × 10⁻³ M?

pH = −log(1.2 × 10⁻³) = 2.92, as in OpenStax Example 14.4.

What hydronium concentration has pH 7.3?

[H₃O⁺] = 10⁻⁷·³ = 5.01 × 10⁻⁸ M; OpenStax rounds it to 5 × 10⁻⁸ M.

What is the pH of 0.0125 M KOH?

[OH⁻] = 0.0125 M, so pOH = 1.903 and pH = 12.10.

Why do pH and pOH add to 14?

Because [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 °C. Pure water has pH 7.00.

Can I enter 1e-7?

Yes. Concentrations accept 1e-7, 1 × 10^-7 or 0.0000001.

Sources and methodology

The formulas are standard time-value-of-money results. We check every figure against golden values worked out independently, by closed form and by month-by-month simulation; see the methodology.

Written and maintained by Nitin Raturi, a software engineer (about the author). Last reviewed 4 Nov 2026; next review due by . Found an error? Tell us.

Changelog

  • : Initial release.