pH Calculator

What pH is measuring

pH is the negative base-10 logarithm of the hydrogen ion (more precisely hydronium) concentration in mol/L:

pH = −log₁₀[H⁺]

The logarithm is what makes pH practical. Pure water at 25 °C has [H⁺] = 1 × 10⁻⁷ mol/L, so its pH is exactly 7. Cola has [H⁺] ≈ 1.8 × 10⁻⁴, giving pH ≈ 3.74. Gastric juice is around pH 1.5. These span three orders of magnitude, and the one-digit difference between them is the whole reason pH is measured rather than concentration.

Inverting gives the other direction:

[H⁺] = 10⁻ᵖᴴ

Worked example

A solution has [H⁺] = 1.8 × 10⁻⁴ mol/L.

pH = −log₁₀(1.8 × 10⁻⁴) = 4 − log₁₀(1.8) = 4 − 0.2553 = 4.74.

At 25 °C, K_w = 1 × 10⁻¹⁴, so [OH⁻] = 10⁻¹⁴ ÷ 1.8 × 10⁻⁴ = 5.6 × 10⁻¹¹ mol/L, and pOH = 14 − 4.74 = 9.26.

The pH + pOH = 14 identity only holds at 25 °C. Body temperature is 37 °C, where K_w is about 2.5 × 10⁻¹⁴ and neutral pH is 6.81, not 7. A solution that reads 7.00 on a meter is very slightly alkaline at 37 °C. This matters in physiology and in any high-temperature process.

Strong acids, weak acids and buffers

For a strong acid the concentration of the acid is [H⁺], so the calculation above applies directly. Hydrochloric, nitric and sulfuric (first proton) acids behave this way.

For a weak acid it does not: only a fraction of the molecules ionise, and the fraction depends on the K_a. A 0.1 M acetic acid solution has a pH near 2.9, not 1.0, because K_a ≈ 1.8 × 10⁻⁵ means roughly 1% dissociates.

A buffer resists pH change because a weak acid and its conjugate base are both present. The Henderson–Hasselbalch equation gives the working pH:

pH = pKa + log₁₀([A⁻] ÷ [HA])

This is the practical form: you can set a target pH by choosing the ratio, which is how buffer recipes are designed. Useful working points: buffer capacity is greatest when the ratio is 1:1, and it falls off by a factor of 10 for every unit of pH away from pKa — the "one unit either side" rule of thumb.

Reading a number honestly

Two digits in a pH means a factor of about 1.2 in concentration, so significant figures should match the measurement. A pH meter reading of "4.76" is reporting to about 1% accuracy at best, and electrode drift of a few hundredths of a pH unit per day is normal. Near neutral this matters most: 6.9 versus 7.1 is a genuine difference in hydrogen concentration, even though both look like "about 7".

Frequently asked questions

1. How do I calculate pH from concentration?

Take the negative base-10 logarithm of the hydrogen ion concentration in mol/L: pH = -log10[H+]. For 1.8e-4 mol/L that gives 4.74.

2. Why does pH plus pOH equal 14?

Because [H+] x [OH-] = Kw, and at 25 C Kw is exactly 1e-14. Taking logs of both sides gives pH + pOH = 14. The identity shifts with temperature - at 37 C neutral pH is 6.81.

3. What is the pH of pure water?

7.00 at 25 C, by definition, since the ionisation of water gives [H+] = [OH-] = 1e-7 mol/L. The value is temperature dependent, not a universal constant.

4. How is a buffer pH calculated?

Use the Henderson-Hasselbalch equation: pH = pKa + log10([A-]/[HA]). A ratio of 1:1 gives pH = pKa, which is where buffer capacity is greatest.