Stepwise.

pH Calculator

Convert between pH, pOH and hydrogen ion concentration, and find the pH of a strong or weak acid or base from its concentration.

How to use this calculator

  1. 1Choose what you already know: a pH, a concentration, or an acid or base to work from.
  2. 2For a weak acid, enter its Ka — the calculator solves the equilibrium exactly.
  3. 3Read the pH, pOH and both ion concentrations.

How the calculation works

pH = −log₁₀[H⁺] [H⁺] = 10^(−pH) pH + pOH = 14 (at 25 °C) weak acid: Ka = x² ÷ (C − x)
[H⁺]
Hydrogen ion concentration in moles per litre
pOH
The same measure for hydroxide ions: −log₁₀[OH⁻]
Ka
Acid dissociation constant — how readily a weak acid gives up a proton
C
The nominal concentration of the acid before any dissociation
x
The concentration that actually dissociates, which equals [H⁺]

The scale is logarithmic. Each pH unit is a factor of ten in hydrogen ion concentration, so pH 3 is a thousand times more acidic than pH 6 — not twice.

A strong acid dissociates completely, so [H⁺] simply equals its concentration and pH follows directly. A weak acid needs the equilibrium solved, because most of it stays intact.

The weak-acid case is solved exactly by the quadratic rather than the textbook shortcut x ≈ √(Ka × C). That approximation assumes dissociation is negligible against C, and it drifts once dissociation passes about 5% — which happens at low concentrations.

pH + pOH = 14 is temperature-dependent, because the ion product of water is. At 25 °C it holds; at 50 °C the sum is about 13.26, and neutral pH is 6.63.

Worked example

0.01 M hydrochloric acid, a strong acid

  1. 1.HCl is a strong acid, so it dissociates completely.
  2. 2.Every molecule releases one H⁺, so [H⁺] = 0.01 mol/L exactly.
  3. 3.pH = −log₁₀(0.01) = −(−2) = 2.
  4. 4.pOH = 14 − 2 = 12.
  5. 5.[OH⁻] = 10⁻¹⁴ ÷ 10⁻² = 10⁻¹² mol/L.

Result: pH = 2.000

0.01 M acetic acid, a weak acid

  1. 1.Acetic acid has Ka = 1.8 × 10⁻⁵ — it only partly dissociates.
  2. 2.At equilibrium Ka = x² ÷ (0.01 − x), where x is [H⁺].
  3. 3.Rearranged: x² + (1.8 × 10⁻⁵)x − 1.8 × 10⁻⁷ = 0.
  4. 4.The quadratic gives x = 4.1536 × 10⁻⁴ mol/L.
  5. 5.pH = −log₁₀(4.1536 × 10⁻⁴) = 3.382.
  6. 6.Compare the strong acid at the same concentration: pH 2. The weak acid is about 24 times less acidic despite identical molarity.

Result: pH = 3.382 — only 4.15% dissociated

Why one pH unit is a bigger deal than it sounds

pH is a logarithm, so the numbers are compressed enormously. Moving from pH 7 to pH 6 is a tenfold increase in hydrogen ion concentration; from 7 to 4 is a thousandfold. The scale exists precisely because writing 0.0000001 mol/L is unwieldy, but the compression makes small differences look trivial when they are not.

Human blood is held between pH 7.35 and 7.45 — a range of 0.1 units, which sounds like nothing and represents about a 26% swing in hydrogen ion concentration. Outside roughly 6.8 to 7.8, enzymes stop functioning and the condition is rapidly fatal. That is why the body spends so much effort on buffering.

The same compression explains ocean acidification. A drop of 0.1 pH units since pre-industrial times sounds negligible and is a 30% increase in hydrogen ion concentration, which is enough to interfere with shell formation in marine organisms.

Strong and weak is not concentrated and dilute

A strong acid is one that dissociates completely in water; a weak acid only partly does. This is a property of the substance, not of how much you dissolve, and confusing it with concentration is the most common error in introductory chemistry.

The demonstration is direct. At the same 0.01 M concentration, hydrochloric acid gives pH 2 and acetic acid gives pH 3.38 — nearly 25 times less acidic, because only about 4% of the acetic acid molecules have released their proton at any moment. A concentrated weak acid can easily be less acidic than a dilute strong one.

This also explains why vinegar is safe to eat and dilute hydrochloric acid is not. It is not about how much acid is present but about how readily it releases hydrogen ions.

What this assumes, and where it stops

Assumptions

  • Aqueous solution at 25 °C, where the ion product of water is 1.0 × 10⁻¹⁴ and pH + pOH = 14.
  • Ideal behaviour, using concentrations rather than activities — accurate for dilute solutions.
  • Strong acids and bases are treated as completely dissociated.
  • Weak acids are treated as monoprotic, releasing one proton per molecule.

Limitations

  • Assumes 25 °C. The ion product of water rises with temperature, so pH + pOH = 14 and neutral pH = 7 both shift — at 50 °C neutral is about 6.63.
  • Uses concentrations, not activities. Above roughly 0.1 M, ionic interactions make the calculated pH drift from the measured one.
  • Monoprotic acids only. Sulfuric and phosphoric acid release multiple protons with separate dissociation constants and need stepwise treatment.
  • Does not model buffers, salt hydrolysis, or the autoionisation contribution that matters for very dilute solutions near pH 7.
  • Not a substitute for measurement. Real solutions contain other species, and a pH meter measures what is actually there.

Common questions

How do you calculate pH from concentration?

Take the negative base-10 logarithm of the hydrogen ion concentration: pH = −log₁₀[H⁺]. For a strong acid, [H⁺] equals the acid's concentration, so 0.01 M HCl gives pH = −log₁₀(0.01) = 2. Weak acids need the dissociation equilibrium solved first.

What is the difference between a strong acid and a concentrated one?

Strong describes how completely the acid dissociates; concentrated describes how much is dissolved. They are independent. At the same 0.01 M concentration, hydrochloric acid gives pH 2 while acetic acid gives pH 3.38, because only about 4% of the acetic acid releases its proton.

Is pH always between 0 and 14?

No. That range covers ordinary solutions, but concentrated strong acids can have negative pH — 10 M HCl is around pH −1 — and concentrated strong bases can exceed 14. The 0–14 range is a convention of convenience rather than a physical limit.

Why is neutral pH not always 7?

Because pH 7 as neutral depends on the ion product of water at 25 °C. Water's autoionisation increases with temperature, so at 50 °C neutral water has pH 6.63. It is still neutral — hydrogen and hydroxide concentrations are still equal — but the number moves.

Sources

Formula and content last reviewed on .

Results are estimates for information only, not professional advice.

Report an error

Related calculators

Tools people commonly use alongside the ph calculator.

See all science & engineering calculators →