pH Calculator

What is a pH calculator?

A pH calculator converts between the four ways of describing how acidic or basic a water-based solution is — pH, pOH, hydrogen ion concentration [H⁺] and hydroxide ion concentration [OH⁻]. Enter any one of them and it returns the other three, then labels the solution acidic, neutral or basic at 25°C. Students, lab technicians and chemistry teachers use it to check work fast.

What is the pH formula?

The core formula is pH = −log₁₀[H⁺], the negative base-10 logarithm of the hydrogen ion concentration. From there every other value follows. The symbols and their units are:

• pH — a unitless number, low for acids and high for bases.
• pOH — a unitless number measuring hydroxide instead of hydrogen.
• [H⁺] — hydrogen (hydronium) ion concentration in moles per litre (mol/L).
• [OH⁻] — hydroxide ion concentration in mol/L.

This tool computes pH first from whatever you supply, then fills in the rest:

• If you enter pH, it is used directly.
• If you enter pOH: pH = 14 − pOH
• If you enter [H⁺]: pH = −log₁₀[H⁺]
• If you enter [OH⁻]: pH = 14 − (−log₁₀[OH⁻])

Once pH is known, the remaining quantities come from these rearrangements:

• pOH = 14 − pH
• [H⁺] = 10^(−pH)
• [OH⁻] = 10^(−pOH)

pH and pOH are shown to 2 decimal places; concentrations are shown to 4 significant figures, switching to scientific notation when they are very small. Any concentration you enter must be greater than 0, because the logarithm of zero is undefined.

Worked examples

Each example below reproduces exactly what the calculator returns.

Example 1 — known [H⁺] = 1×10⁻³ mol/L (a dilute strong acid).

• pH = −log₁₀(1×10⁻³) = 3.00
• pOH = 14 − 3.00 = 11.00
• [OH⁻] = 10^(−11) = 1×10⁻¹¹ mol/L

Result: pH 3.00, acidic at 25°C.

Example 2 — known pH = 7 (pure water).

• pOH = 14 − 7 = 7.00
• [H⁺] = 10^(−7) = 1×10⁻⁷ mol/L
• [OH⁻] = 10^(−7) = 1×10⁻⁷ mol/L

Result: pH 7.00, neutral — hydrogen and hydroxide are equal.

Example 3 — known pOH = 2 (a dilute strong base).

• pH = 14 − 2 = 12.00
• [H⁺] = 10^(−12) = 1×10⁻¹² mol/L
• [OH⁻] = 10^(−2) = 1×10⁻² mol/L

Result: pH 12.00, basic at 25°C.

Example 4 — known [OH⁻] = 1×10⁻⁴ mol/L.

• pOH = −log₁₀(1×10⁻⁴) = 4.00, so pH = 14 − 4.00 = 10.00
• [H⁺] = 10^(−10) = 1×10⁻¹⁰ mol/L

Result: pH 10.00, basic. Notice that even though you entered hydroxide, the tool still reports the matching [H⁺] for you.

Example 5 — known pH = 4.50 (a non-whole value).

• pOH = 14 − 4.50 = 9.50
• [H⁺] = 10^(−4.5) = 3.162×10⁻⁵ mol/L
• [OH⁻] = 10^(−9.5) = 3.162×10⁻¹⁰ mol/L

Result: pH 4.50, acidic. Here the concentrations are not neat powers of ten, so the tool rounds them to 4 significant figures.

pH scale reference

This chart shows the relationship between pH, [H⁺] and [OH⁻] at 25°C. Each whole pH step changes [H⁺] by a factor of ten, so the scale is logarithmic, not linear.

pH	[H⁺] (mol/L)	[OH⁻] (mol/L)	pOH	Classification
0	1×10⁰	1×10⁻¹⁴	14	Strongly acidic
1	1×10⁻¹	1×10⁻¹³	13	Strongly acidic
3	1×10⁻³	1×10⁻¹¹	11	Acidic
5	1×10⁻⁵	1×10⁻⁹	9	Weakly acidic
7	1×10⁻⁷	1×10⁻⁷	7	Neutral
9	1×10⁻⁹	1×10⁻⁵	5	Weakly basic
11	1×10⁻¹¹	1×10⁻³	3	Basic
13	1×10⁻¹³	1×10⁻¹	1	Strongly basic
14	1×10⁻¹⁴	1×10⁰	0	Strongly basic

For context, lemon juice sits near pH 2, black coffee near pH 5, pure water at 7, baking soda solution near pH 9, and household bleach near pH 13.

Common uses

• Chemistry homework and exams — convert between pH, pOH and ion concentrations and verify each step.
• Lab work — sanity-check a meter reading or predict the pH of a prepared solution before titrating.
• Water and aquarium testing — interpret a test-kit [H⁺] or [OH⁻] reading as a familiar pH number.
• Teaching — demonstrate that one unit of pH equals a tenfold change in acidity.
• Engineering and process control — estimate acid or base strength when dosing or neutralising.

Tips and common mistakes

• Watch the units. Concentrations are in mol/L (molarity), not grams per litre. Convert mass to moles first.
• Enter concentration as a positive number. A value of 0 or below is rejected because log₁₀(0) is undefined — that is the division-by-zero of this tool.
• Mind the scientific notation. 1e-3 means 1×10⁻³ = 0.001 mol/L; dropping an exponent digit shifts the pH by a whole unit.
• pH and pOH always sum to 14 at 25°C. If your two numbers do not add to 14, recheck the input.
• Significant figures. A measured [H⁺] with one significant figure cannot honestly give a pH to many decimals; the tool rounds pH to 2 decimals, which is plenty for class work.
• Smaller pH means more acidic. A pH of 2 is ten times more acidic than 3, not “a little” more.

Limitations and accuracy

This calculator assumes a dilute, aqueous (water-based) solution at 25°C (298 K), where the ion product of water gives the familiar pH + pOH = 14. That constant shifts with temperature — at higher temperatures neutral water sits slightly below pH 7 — so results outside room temperature are approximate. The model also treats activity as equal to concentration, which is accurate for dilute solutions but less so for very concentrated ones, and it does not account for buffering or weak-acid dissociation equilibria. Treat it as an education and estimation aid rather than a substitute for a calibrated pH meter.

For more science tools, try the density calculator, the combined gas law calculator or browse the full chemistry and physics category.