Quick answer: pH = −log10[H+], where [H+] is the hydrogen-ion concentration in mol/L. Below 7 is acidic, 7 is neutral and above 7 is basic (at 25°C). This pH calculator converts between pH, [H+], pOH and [OH−] in one step.
Last reviewed: September 2026
Key facts
- pH = −log10[H+] and [H+] = 10−pH — the two directions of the same formula.
- pH + pOH = 14 at 25°C, since [H+][OH−] = 10−14.
- Each pH unit means a 10× change in acidity: pH 3 is ten times more acidic than pH 4.
- pH < 7 acidic, pH = 7 neutral, pH > 7 basic — valid for aqueous solutions at 25°C.
pH measures how acidic or alkaline a solution is on a logarithmic scale: pH = −log10[H+], where [H+] is the hydrogen-ion concentration in mol/L. This free pH calculator converts between pH, pOH, [H+] and [OH−] and instantly labels the solution acidic, neutral or basic.
Choose your known value, enter it, and get all four quantities with the acid/base verdict. No sign-up, works on mobile and desktop.
How to use this pH calculator
- Choose what you know: [H+], pH, [OH−] or pOH.
- Enter the value in the input box.
- Read the pH, [H+], pOH, [OH−] and the acidic/neutral/basic label.
- All conversions assume 25°C, where pH + pOH = 14.
Background: the birth of the pH scale
The pH scale was introduced in 1909 at the Carlsberg Laboratory in Copenhagen as a compact way to report hydrogen-ion concentrations in brewing research. The "p" denotes the negative base-10 logarithm and "H" the hydrogen ion — so pH 3 simply means [H+] = 10−3 mol/L. The modern formal definition (IUPAC) is pH = −log a(H+), the negative logarithm of hydrogen-ion activity, which matches concentration closely in dilute solutions.
Early measurement used cumbersome hydrogen electrodes; the glass electrode and the first practical electronic pH meters of the 1930s made routine measurement possible, and today's probes still rely on the same glass-electrode principle — which is why the definition and the everyday meter agree.
The pH formulas
| Term | Meaning |
|---|---|
| pH | Negative base-10 log of hydrogen-ion concentration; dimensionless. |
| [H+] | Hydrogen-ion concentration in mol/L (M). |
| pOH | Negative base-10 log of hydroxide-ion concentration. |
| [OH−] | Hydroxide-ion concentration in mol/L (M). |
The logarithm compresses an enormous range — from 1 M down to 10−14 M — into the familiar 0–14 scale.
Strong vs weak acids: why pH alone can mislead
A strong acid dissociates completely, so [H+] is essentially the acid concentration and pH = −log C works directly. A weak acid dissociates only partly, so its pH is always higher (less acidic) than −log C would predict — finding its [H+] requires its acid dissociation constant Ka and the equilibrium expression. Enter the actual free [H+] into this pH calculator, not the nominal acid concentration:
| Strong acid (e.g. HCl) | Weak acid (e.g. acetic acid) | |
|---|---|---|
| Dissociation | ~100%: [H+] ≈ C | Partial: [H+] < C |
| pH of a 0.1 M solution | 1.00 | ≈ 2.87 (Ka = 1.8 × 10−5) |
| Formula to use | pH = −log C | [H+] ≈ √(Ka × C), then pH = −log[H+] |
Check: for 0.1 M acetic acid, [H+] ≈ √(1.8 × 10−5 × 0.1) ≈ 1.34 × 10−3 M, so pH ≈ 2.87 — a hundred times less acidic than the strong-acid value. Mixtures of a weak acid with its conjugate base resist pH change (buffers); their pH is estimated with the Henderson–Hasselbalch equation, pH = pKa + log([base]/[acid]), a separate calculation this tool does not perform.
Temperature and the neutral point
Neutral pH is 7.0 only at 25°C, where Kw = [H+][OH−] = 10−14. Water's self-ionization increases with temperature, so the neutral point falls: about 6.14 at 100°C and about 7.47 at 0°C. The pH calculator assumes 25°C throughout, so pH + pOH = 14 always holds in its results.
Worked examples
[H+] = 0.001 M (1 × 10−3 M)
pH = −log10(0.001) = 3.00.
pH 3.00 — acidic. pOH = 11.00, [OH−] = 1.00 × 10−11 M.
pH = 11.5
[H+] = 10−11.5 = 3.16 × 10−12 M, pOH = 14 − 11.5 = 2.50.
Basic (alkaline). [OH−] = 3.16 × 10−3 M.
[OH−] = 1 × 10−5 M
pOH = −log10(10−5) = 5.00, so pH = 14 − 5.00 = 9.00.
pH 9.00 — basic. [H+] = 1.00 × 10−9 M.
Everyday pH reference
| Substance | Typical pH |
|---|---|
| Battery acid | ~0.5 |
| Lemon juice | ~2 |
| Vinegar | ~2.5–3 |
| Black coffee | ~5 |
| Pure water (25°C) | 7.0 |
| Blood | 7.35–7.45 |
| Soap solution | ~9–10 |
| Bleach | ~12.5 |
Limitations
- Assumes 25°C. The identities pH + pOH = 14 and [H+][OH−] = 10−14 hold at 25°C; at other temperatures the neutral point shifts (see above).
- Activity vs concentration. Strictly, pH is defined by hydrogen-ion activity (IUPAC), not concentration. The two agree closely in dilute solutions but diverge in concentrated ones.
- Input range 0–14. This pH calculator accepts the everyday range; concentrated strong acids and bases can fall outside it.
- Weak acids/bases need equilibrium first. For a weak acid, enter the measured or equilibrium [H+], not the nominal acid concentration — see the strong vs weak section.
Frequently asked questions
What is pH?
pH is a logarithmic measure of hydrogen-ion concentration: pH = −log10[H+], with [H+] in mol/L. Values below 7 are acidic, 7 is neutral and above 7 is basic (alkaline) for aqueous solutions at 25°C.
How do you calculate pH from [H+]?
Take the base-10 logarithm of the hydrogen-ion concentration and change its sign. Example: [H+] = 0.001 M gives pH = −log10(0.001) = 3.00, which is acidic.
How do you find [H+] from pH?
Raise 10 to the power of negative pH: [H+] = 10^(−pH). For pH 11.5, [H+] = 10^(−11.5) ≈ 3.16 × 10^(−12) M. Each pH unit is a tenfold change in concentration.
What is the relation between pH and pOH?
At 25°C, pH + pOH = 14, because [H+][OH−] = 10^(−14) in water. If you know one, subtract from 14 to get the other.
Can pH be below 0 or above 14?
Yes, in concentrated strong acids or bases the scale extends beyond 0–14, since pH is defined by the logarithm, not bounded by it. In everyday dilute solutions the 0–14 range covers almost everything.
Sources
- IUPAC Gold Book: pH — the formal definition of pH via hydrogen-ion activity
- OpenStax: Chemistry 2e — free college chemistry textbook covering acids, bases and pH
Key takeaways
- pH = −log10[H+]; [H+] = 10^(−pH).
- pH + pOH = 14 at 25°C.
- Each unit is a 10× acidity change; below 7 acidic, 7 neutral, above 7 basic.
- Strong acids give pH = −log C directly; weak acids need the Ka equilibrium.
- The calculator converts pH, pOH, [H+] and [OH−] in one step.
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