pH is a measure of how acidic or basic a solution is, defined as the negative base-ten logarithm of the hydrogen ion concentration in moles per litre. A solution with [H⁺] of 10⁻³ M has a pH of 3. Because it is logarithmic, each whole unit represents a tenfold change in concentration, so the scale compresses an enormous range of concentrations into numbers that are easy to compare.

How do I convert between pH and hydrogen ion concentration?

To get concentration from pH, raise ten to the negative pH: [H⁺] = 10⁻ᵖᴴ. A pH of 4.5 gives 3.16 × 10⁻⁵ M. Going the other way, take the negative logarithm: a concentration of 2.5 × 10⁻⁶ M gives pH 5.60. The same pair of operations relates pOH and hydroxide concentration.

What is pOH and how does it relate to pH?

pOH is the negative logarithm of the hydroxide ion concentration, and it complements pH: the two always add up to pKw, which is 14.00 at 25 °C. So a solution of pH 3 has pOH 11 at room temperature. The relationship exists because water's ion product [H⁺][OH⁻] is fixed at any given temperature, so pushing one concentration up necessarily pushes the other down.

Why is pH 7 not always neutral?

Because neutrality means equal concentrations of hydrogen and hydroxide ions, and the point at which that happens depends on temperature. Water ionises more readily when warm, so pKw falls from 14.94 at 0 °C to 14.00 at 25 °C and 12.26 at 100 °C. Neutral pH is always pKw divided by two, which gives 7.47, 7.00 and 6.13 at those temperatures. Pure water at 50 °C has a pH of about 6.63 and remains perfectly neutral.

How do I find the pH of a strong acid?

A strong acid dissociates completely, so at ordinary concentrations the hydrogen ion concentration equals the acid concentration and pH is simply its negative logarithm — 0.01 M hydrochloric acid gives pH 2. Below about 10⁻⁶ M that shortcut breaks down, because water's own ionisation contributes a comparable amount of hydrogen ions. This calculator solves the exact relationship at every concentration rather than switching between two approximations.

Why does 10⁻⁸ M acid not have a pH of 8?

Because that would make an acid alkaline, which cannot happen. At such dilution the acid supplies fewer hydrogen ions than water produces by itself, so both sources must be counted. Solving [H⁺]² − C[H⁺] − Kw = 0 gives about 1.05 × 10⁻⁷ M and therefore a pH of roughly 6.98 — just barely acidic, which is exactly what you would expect from a trace of acid in water. Adding any amount of acid can only lower the pH, never raise it.

Can pH be negative or greater than 14?

Yes. The 0 to 14 range is a convention that covers dilute aqueous solutions, not a physical limit. Concentrated hydrochloric acid at around 12 M has a pH near −1.08, and concentrated sodium hydroxide can exceed 15. The values become less meaningful at those extremes because pH is properly defined in terms of ion activity rather than concentration, and the two diverge in very concentrated solutions.

How is the pH of a weak acid different?

A weak acid only partially dissociates, so its hydrogen ion concentration is far lower than its overall concentration and you cannot simply take the negative logarithm. You need the acid dissociation constant Ka, and for a solution of concentration C the approximation [H⁺] ≈ √(Ka × C) works when dissociation is small. Acetic acid at 0.1 M, with Ka of 1.8 × 10⁻⁵, gives a pH near 2.87 rather than the 1.00 a strong acid would give.

How much difference does one pH unit make?

A factor of ten in hydrogen ion concentration, which is far more than the small number suggests. Moving from pH 6 to pH 5 means ten times more hydrogen ions; from 6 to 4 means a hundred times more. This is why apparently minor pH shifts matter so much in practice — a drop of 0.3 units in ocean pH represents roughly a doubling of acidity, and small changes in a swimming pool or an aquarium have effects out of all proportion to the number.

pH Calculator

Convert between pH, pOH, hydrogen ion concentration and hydroxide ion concentration, or work out the pH of a strong acid or base from its concentration. Enter whichever quantity you have and the calculator returns the other three, along with where the solution sits on the pH scale and how it compare...

pH = −log₁₀[H⁺]

WHAT DO YOU KNOW?

pH VALUE

TEMPERATURE — pKw = 14.00

Neutral is pH 7.00 at this temperature, not 7 — water splits more readily when warm.

COMMON CASES

3.000acidic

pOH

11.000

[H⁺]

1.000e-3 M

[OH⁻]

1.000e-11 M

10,000× more H⁺ than neutral water at 25 °C.

3.0000

pOH

11.0000

[H⁺]

1.000e-3 M

[OH⁻]

1.000e-11 M

pKw at 25 °C

14.00

Neutral pH here

7.000

STEPS

At 25 °C the ion product of water gives pKw = 14.00.

pH and pOH must sum to pKw, so pOH = 14.00 − 3.000 = 11.000.

[H⁺] = 10^−pH = 1.000e-3 M and [OH⁻] = 10^−pOH = 1.000e-11 M.

WHERE IT SITS

Each pH unit is a factor of ten. Lemon juice at pH 2.4 is not roughly twice as acidic as tomato juice at 4.2 — it holds about 63 times more hydrogen ions. That is why the scale is logarithmic, and why a change of half a pH unit in a swimming pool or a fish tank matters far more than the small number suggests.

HOW IT COMPARES

Neutral is not fixed at 7. Water splits into its own ions more readily as it warms, so pKw falls and the neutral point moves with it — 7.00 at 25 °C. Pure water at 50 °C has a pH near 6.63 and is still perfectly neutral, because [H⁺] and [OH⁻] remain equal.

Created with❤️byeaglecalculator.com

HOW TO USE

1
Choose what you already know — pH, pOH, hydrogen ion concentration, hydroxide ion concentration, or the concentration of a strong acid or strong base. The input field relabels itself to match.
2
Enter the value. For the concentration options pick a unit alongside — molar down to nanomolar. Very small values can be typed in scientific notation, such as 1e-8.
3
Set the temperature if you are not working at 25 °C. This changes pKw and therefore the neutral point, which is shown on the scale as a green marker that moves as you change it.
4
Read the results: pH, pOH and both ion concentrations, whether the solution is acidic, neutral or basic for that temperature, and how many times more or less hydrogen it holds than neutral water.

THE FORMULAS

pHpH = −log₁₀[H⁺]

pOHpOH = −log₁₀[OH⁻]

Hydrogen ions[H⁺] = 10^−pH

Hydroxide ions[OH⁻] = 10^−pOH

The two togetherpH + pOH = pKw

Ion product[H⁺][OH⁻] = Kw

Strong acid, exact[H⁺] = (C + √(C² + 4Kw)) / 2

Neutral pointpH = pKw / 2

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Last updated: July 29, 2026 · Formula verified · Eagle-eyed accuracy for every calculation.