pH Calculator From Concentration: pH = −log[H+]

This calculator turns a hydrogen ion concentration in mol/L into a pH. Enter [H⁺], which for a strong monoprotic acid such as HCl or HNO₃ equals the acid molarity; you get the pH, the pOH and the hydroxide concentration [OH⁻] at 25 °C.

Formula

pH = −log₁₀[H⁺]; pOH = 14 − pH; [OH⁻] = K_w ÷ [H⁺].

• [H⁺]: hydrogen ion concentration in mol/L
• K_w = 1.0 × 10⁻¹⁴ at 25 °C, the ion product of water, so pH + pOH = 14 at that temperature
• For a strong monoprotic acid, [H⁺] = acid concentration (full dissociation)

Worked Example

A 0.0025 mol/L solution of hydrochloric acid, fully dissociated, so [H⁺] = 0.0025 mol/L.

1. log₁₀(0.0025) = −2.60206, so pH = 2.60
2. pOH = 14 − 2.60206 = 11.40
3. [OH⁻] = 1.0 × 10⁻¹⁴ ÷ 0.0025 = 4.000 × 10⁻¹² mol/L

Assumptions

• The acid is strong and monoprotic, so every acid molecule gives one H⁺. For a diprotic strong acid such as dilute H₂SO₄ the real [H⁺] lies between one and two times the acid molarity.
• The temperature is 25 °C, where K_w = 1.0 × 10⁻¹⁴; at other temperatures pH + pOH is not exactly 14.
• The concentration is at least 10⁻⁶ mol/L, so the H⁺ from water itself can be ignored.

How to read the result

Each step of one pH unit is a tenfold change in [H⁺]: 0.01 mol/L gives pH 2 and 0.001 mol/L gives pH 3, so 0.0025 mol/L lands between them. Below pH 7 the solution is acidic at 25 °C. The calculated pH is a starting point: the reading of a calibrated pH meter is the real check, and pH depends on temperature and ionic strength, so adjust with small additions of acid or base while you measure. For a buffer, use the Tris buffer pH calculator.

Limits and common mistakes

• A weak acid such as acetic acid is only partly dissociated, so its pH is higher than this calculator gives for the same molarity.
• Entering mmol/L as mol/L shifts the pH by 3 units.
• Near 1 mol/L, activity differs from concentration, so a measured pH will not match −log of the molarity.

Frequently Asked Questions

How do you calculate pH from concentration?

Take the negative base-10 logarithm of the hydrogen ion concentration in mol/L: pH = −log[H+].

What is the pH of 0.0025 M HCl?

About 2.60, with a pOH of 11.40 at 25 °C.

Why does pH + pOH equal 14?

Because the ion product of water, Kw = [H+][OH−], is 1.0 × 10^−14 at 25 °C; taking −log of both sides gives pH + pOH = 14.

Can I use it for a weak acid?

Only if you already know the hydrogen ion concentration; the acid molarity alone overestimates [H+] for a weak acid.

in h | Hydrogen ion concentration [H+] | mol/L | 0.0025 | 0.000001 | 1
out ph | pH | - | -log10(h) | 2
out poh | pOH at 25 °C | - | 14 - ph | 2
out oh | Hydroxide concentration [OH−] | mol/L | 1e-14 / h | 3