How to calculate pH

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pH Calculator

Calculate pH, pOH and Ka for strong and weak acids

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What does pH measure?

pH measures how acidic or basic (alkaline) a solution is, by the concentration of hydrogen ions in it. The USGS describes the usual range as 0 to 14, with 7 neutral: below 7 is acidic and above 7 is basic. The more hydrogen ions, the lower the pH. Strong acids and bases can go below 0 or above 14, but those are unusual.

The scale is logarithmic. A solution at pH 5 has ten times the hydrogen ion concentration of one at pH 6, and a solution at pH 3 has 100 times that of pH 5. The Danish chemist Søren Sørensen introduced the pH scale in 1909.

Rain is slightly acidic because carbon dioxide from the air dissolves in it, according to the USGS. Blood normally stays between 7.35 and 7.45, as MedlinePlus notes, and the body works hard to keep it there.

How to calculate pH: step by step

1. Find [H⁺], the hydrogen ion concentration in mol/dm³. For a strong acid, this comes straight from the acid's concentration. For a weak acid or a base, it takes an extra step (below).
2. Take the log: press log on your calculator and enter [H⁺].
3. Change the sign: pH is the negative of that log, so it comes out positive for most solutions.
4. Round sensibly: pH is usually given to 2 decimal places.

Example 1: a strong acid

Hydrochloric acid is a strong acid: it ionises completely in water, so each HCl gives one H⁺. What is the pH of 0.050 mol/dm³ HCl? [H⁺] = 0.050, so pH = −log(0.050) = 1.30.

Example 2: from pH back to concentration

A solution has a pH of 4.5. What is its hydrogen ion concentration? Reverse the formula:

Example 3: a strong base

Bases are measured by their hydroxide ions, OH⁻. In water at 25 °C, the ionic product of water links the two: [H⁺][OH⁻] = 1.0 × 10⁻¹⁴, which means pH + pOH = 14, where pOH = −log[OH⁻].

Sodium hydroxide is a strong base. For 0.020 mol/dm³ NaOH, [OH⁻] = 0.020, so pOH = −log(0.020) = 1.70, and pH = 14 − 1.70 = 12.30.

Example 4: a weak acid

A weak acid only partly ionises, so [H⁺] is much less than the acid's concentration. If you know the acid dissociation constant, K_a, then for a weak acid on its own:

Ethanoic acid (acetic acid, in vinegar) has K_a of about 1.8 × 10⁻⁵ mol/dm³. For a 0.10 mol/dm³ solution: [H⁺] = √(1.8 × 10⁻⁵ × 0.10) = 1.34 × 10⁻³ mol/dm³, so pH = −log(1.34 × 10⁻³) = 2.87. A strong acid at the same concentration would have pH 1.00.

How dilution changes pH

Diluting a strong acid ten times divides [H⁺] by 10, which raises the pH by exactly 1. So 0.10 mol/dm³ HCl has pH 1.00, and diluting it to 0.010 mol/dm³ gives pH 2.00. Diluting more and more brings an acid closer to 7, but never past it: water's own ions take over. The Dilution Calculator works out the new concentrations.

Measuring pH in the lab

• Universal indicator: a mixture of dyes that turns red in strong acid, through orange, yellow and green near neutral, to blue and purple in strong base. Quick, but only gives a rough value.
• Litmus paper: red in acid and blue in alkali, so it only tells you which side of 7 you are on.
• pH meter: an electrode that measures pH electronically to one or two decimal places. It must be calibrated with buffer solutions of known pH.

In titrations, the pH changes sharply near the end point. You can watch a pH curve form in the Titration Lab.

Why small pH changes matter

Because the scale is logarithmic, a small change in pH is a big change in acidity. NOAA reports that the ocean's average pH has fallen from about 8.2 to 8.1 since the Industrial Revolution, as it absorbs carbon dioxide, which NOAA describes as about a 30% increase in acidity. With more precise values, about 8.21 falling to 8.10, the hydrogen ion concentration has risen by a factor of 10^0.11 ≈ 1.29. More acidic water makes it harder for shellfish and corals to build their shells and skeletons.

Common mistakes

• Forgetting the minus sign. log(0.01) is −2, so pH = −(−2) = 2.
• Using the acid concentration for a weak acid. Weak acids only partly ionise, so [H⁺] is far smaller. Use K_a.
• Taking the log of [OH⁻] and calling it pH. That gives pOH. Subtract from 14 to get pH.
• Thinking pH 4 is twice as acidic as pH 2's half. Each unit is a factor of 10, so pH 2 has 100 times the [H⁺] of pH 4.
• Assuming neutral is always 7. It is 7 at 25 °C. At other temperatures, water's ionic product changes and so does neutral pH.

Read next

Chemistry · Acids and basespH calculator: strong and weak acids, bases and buffersFree pH calculator: the pH of strong and weak acids and bases from molarity, buffers by Henderson-Hasselbalch, and Ka from a measured pH, with steps.