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Everyone learns that pH 7 is neutral, lower is acidic and higher is basic. Fewer people learn what the number actually is — and that gap is why pH calculations feel mysterious. Once you know that pH is just a compact way of writing a tiny concentration, the rest falls into place.
What pH measures
pH measures the concentration of hydrogen ions — strictly, hydronium ions, H₃O⁺ — in a water-based solution. Chemists write this concentration in square brackets, [H⁺], in moles per litre.
The trouble is that these concentrations are inconveniently small and span an enormous range. Stomach acid has [H⁺] around 0.01 M. Pure water has 0.000 000 1 M. Household bleach has about 0.000 000 000 000 1 M. Nobody wants to compare numbers like that.
So in 1909 the Danish chemist Søren Sørensen, working at the Carlsberg brewery’s laboratory, proposed writing them as a power of ten and keeping only the exponent:
pH = −log₁₀[H⁺]
- [H⁺] = 10⁻² M → pH 2
- [H⁺] = 10⁻⁷ M → pH 7
- [H⁺] = 10⁻¹³ M → pH 13
The minus sign is there so that everyday pH values come out positive.
The scale is logarithmic
Because each pH unit is a power of ten, a change of 1 pH unit is a tenfold change in hydrogen-ion concentration.
- pH 3 is 10 times more acidic than pH 4.
- pH 3 is 100 times more acidic than pH 5.
- pH 2 (lemon juice) is about 100 000 times more acidic than pH 7 (pure water).
This is why small-looking pH changes can be a big deal. Human blood is held between about 7.35 and 7.45; a drop to 7.0 would be life-threatening, even though “0.4” sounds tiny.
Where does 7 come from?
Water itself splits very slightly into ions:
H₂O ⇌ H⁺ + OH⁻
At 25 °C, the product of the two ion concentrations is always 1.0 × 10⁻¹⁴. This is called Kw, the ion product of water:
[H⁺][OH⁻] = 1.0 × 10⁻¹⁴
In pure water the two concentrations are equal, so each is 10⁻⁷ M, giving pH 7. Neutral means [H⁺] = [OH⁻], and at 25 °C that happens to be pH 7. (At body temperature, Kw is larger and neutral is about pH 6.8 — neutral isn’t always exactly 7.)
pOH and the pH + pOH = 14 rule
The same logarithm trick works for hydroxide ions:
pOH = −log₁₀[OH⁻]
Taking the logarithm of the Kw equation gives the most useful shortcut in the topic:
pH + pOH = 14 (at 25 °C)
So if you know any one of pH, pOH, [H⁺] or [OH⁻], you know all four.
Worked examples
From concentration to pH. A solution has [H⁺] = 3.2 × 10⁻⁴ M. What is its pH? pH = −log(3.2 × 10⁻⁴) = 3.49
From pH to concentration. Black coffee has a pH of about 5.0. What is [H⁺]? [H⁺] = 10⁻⁵·⁰ = 1.0 × 10⁻⁵ M
From hydroxide to pH. A cleaning solution has [OH⁻] = 0.0050 M. pOH = −log(0.0050) = 2.30, so pH = 14 − 2.30 = 11.70
A strong acid. What is the pH of 0.025 M HNO₃? Nitric acid is a strong acid and releases all its H⁺, so [H⁺] = 0.025 M. pH = −log(0.025) = 1.60.
Weak acids need a bit more work, because they don’t fully ionize — see strong vs. weak acids.
pH of everyday substances
| Substance | Approximate pH |
|---|---|
| Battery acid | ~0–1 |
| Stomach acid | 1.5–3.5 |
| Lemon juice | ~2 |
| Vinegar | ~2.5–3 |
| Cola | ~2.5 |
| Coffee | ~5 |
| Rainwater (unpolluted) | ~5.6 |
| Milk | ~6.5–6.8 |
| Pure water (25 °C) | 7.0 |
| Blood | 7.35–7.45 |
| Seawater | ~8.1 |
| Baking soda solution | ~8.3 |
| Household ammonia | ~11–11.5 |
| Bleach | ~12.5–13 |
| Drain cleaner (NaOH) | ~14 |
Unpolluted rain is slightly acidic because carbon dioxide from the air dissolves in it to form carbonic acid. Rain is only called “acid rain” when it falls well below that natural 5.6.
Can pH go below 0 or above 14?
Yes. The 0–14 range covers most solutions you’ll meet, but it isn’t a hard limit. A 2 M solution of hydrochloric acid has a calculated pH of about −0.3, and concentrated sodium hydroxide can go above 14. At those extremes the simple formula also becomes less exact, because ions stop behaving independently.
Quick answers
Is pH 0 the most acidic possible? No — negative pH is possible for very concentrated strong acids.
Does a higher pH mean stronger base? A higher pH means a higher hydroxide concentration. “Strong base” is a separate idea about how completely the base dissociates.
Why is the scale 0–14? Because pH + pOH = 14 at 25 °C, and a 1 M strong acid or strong base sits at roughly 0 or 14. It’s a practical range, not a fundamental limit.
Calculate pH
The pH calculator converts between pH, pOH, [H⁺] and [OH⁻], and finds the pH of strong and weak acid and base solutions from their concentration.
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