pH Calculator
pH, pOH and ion concentration for strong and weak acids and bases.
About
pH Calculator
pH compresses hydrogen ion concentrations spanning fourteen orders of magnitude onto a scale running from 0 to 14. That compression is the point: writing 0.0000001 mol/L every time water comes up would be unbearable, and pH 7 says the same thing.
The definition
pH = -log10[H+], and running it backwards, [H+] = 10-pH
The p stands for the negative base-10 logarithm, which is why pOH, pKa and pKw all work the same way. Pure water at 25 °C has [H+] = 1.0 × 10-7 mol/L, so its pH is 7.
The negative sign means a lower pH is a higher acidity. It also means the numbers run backwards from intuition, which is worth holding onto when reading a change.
Each unit is a factor of ten
This is the part that is easy to state and hard to feel.
| pH | [H+] mol/L | Against pure water |
|---|---|---|
| 1 | 1 × 10-1 | 1,000,000 times more |
| 3 | 1 × 10-3 | 10,000 times more |
| 5 | 1 × 10-5 | 100 times more |
| 7 | 1 × 10-7 | the same |
| 9 | 1 × 10-9 | 100 times less |
| 11 | 1 × 10-11 | 10,000 times less |
Lemon juice at pH 2 carries a hundred thousand times the hydrogen ion concentration of pure water. A soil moving from pH 6 to pH 5 has become ten times more acidic, which is why a one-unit change in a lake or a soil sample is treated as a serious event rather than a small one.
pOH and the water constant
Water dissociates slightly into H+ and OH-, and the product of the two is fixed at any given temperature. At 25 °C:
Kw = [H+][OH-] = 1.0 × 10-14, so pH + pOH = 14
A solution at pH 3 has pOH 11, and [OH-] of 10-11 mol/L. Adding acid pushes the hydroxide concentration down, since the product cannot change. The two are locked together.
The neutral point moves with temperature
That 14 is only correct at 25 °C. Water dissociates more readily when warm, so Kw rises and pKw falls.
| Temperature | pKw | Neutral pH |
|---|---|---|
| 0 °C | 14.94 | 7.47 |
| 25 °C | 14.00 | 7.00 |
| 50 °C | 13.26 | 6.63 |
| 100 °C | 12.26 | 6.13 |
Water at 100 °C sits at pH 6.13 and is still neutral. It has not turned acidic; both ion concentrations rose together and stayed equal. Neutral means equal concentrations of the two ions, not pH 7, and only at 25 °C do the two definitions coincide.
Strong acids and bases
A strong acid dissociates completely, so the hydrogen ion concentration equals the acid concentration. 0.01 M hydrochloric acid gives [H+] = 0.01 and pH = 2.00.
This breaks down at very low concentrations, where water's own contribution stops being negligible. Take 1 × 10-8 M HCl: the naive answer is pH 8, which would make an acid alkaline. The real answer is 6.98, because the water is supplying most of the hydrogen ions and the acid is nudging the balance slightly. Below about 10-6 M the full treatment is needed, and this calculator uses it.
Weak acids
A weak acid only partly dissociates, and how far depends on its acid dissociation constant Ka and on how dilute it is.
Acetic acid has Ka = 1.75 × 10-5. At 0.01 M the equilibrium gives [H+] = 4.10 × 10-4, so pH = 3.39 and only 4.1% of the acid has dissociated. Compare that with 0.01 M HCl at pH 2.00: same concentration, a factor of 24 difference in hydrogen ions.
The usual shortcut, [H+] = √(Ka × C), assumes the dissociated fraction is small enough to ignore. It works well for dilute solutions of genuinely weak acids and drifts as the acid gets stronger or more dilute. This calculator solves the quadratic exactly instead, so the answer holds across the whole range.
Buffers
A buffer holds pH nearly steady when acid or base is added, using a weak acid alongside its conjugate base. The Henderson-Hasselbalch equation describes it:
pH = pKa + log10([A-] ÷ [HA])
When the two concentrations are equal the log term is zero and the pH equals the pKa. Acetic acid has pKa 4.76, so an equal mixture of acetic acid and acetate buffers around pH 4.76. Buffers work best within about one pH unit either side of their pKa, which is why blood uses a carbonate system rather than an acetate one.
Measuring pH
Three methods, with very different precision. Indicator paper gives a colour change accurate to roughly half a pH unit, which is fine for confirming something is acidic and useless for anything finer.
A glass electrode meter reads to about 0.01 units and needs calibrating against buffer solutions at two or three known points, usually pH 4.01, 7.00 and 10.01. Calibration drifts, so a meter used daily needs it daily. Temperature affects both the electrode response and the sample itself, which is why good meters compensate automatically and why the sample temperature should be recorded alongside the reading.
Indicator dyes in solution, such as phenolphthalein or methyl orange, change colour over a narrow band and are used for titration endpoints rather than for measuring a value.
pH in the body and the environment
Human blood is held between pH 7.35 and 7.45, a range corresponding to hydrogen ion concentrations of 44.7 down to 35.5 nanomoles per litre. Moving outside it in either direction is a medical emergency, and the carbonate buffer system together with the lungs and kidneys is what holds it there.
Stomach acid sits near pH 1.5, which is 0.0316 mol/L of hydrogen ions, roughly a million times the concentration in blood and separated from it by a few millimetres of tissue.
Ocean surface pH has fallen from about 8.2 to 8.1 since the industrial revolution. That reads as a small change and is a 26% increase in hydrogen ion concentration, because the scale is logarithmic. Shell-forming organisms respond to the ion concentration rather than to the pH number, which is why a tenth of a unit is treated as significant.
How concentration shifts a weak acid
Diluting a weak acid raises the fraction that dissociates while lowering the total hydrogen ion concentration, so the pH still rises.
| Acetic acid | pH | Dissociated |
|---|---|---|
| 0.1 M | 2.88 | 1.3% |
| 0.01 M | 3.39 | 4.1% |
Diluting tenfold moved the pH by 0.51 rather than the full unit a strong acid would give, because more of the acid dissociated to partly make up the difference. This resistance is the same behaviour that makes a weak acid useful in a buffer.
Common mistakes
Treating a weak acid like a strong one. 0.1 M acetic acid is not pH 1. It is pH 2.88.
Assuming pH 7 is always neutral. True at 25 °C only.
Averaging pH values. The scale is logarithmic, so mixing pH 3 and pH 5 does not give pH 4. Convert to concentrations, average those, then convert back.
Expecting pH to stay between 0 and 14. It can go outside. Concentrated 12 M HCl has a negative pH, and the 0 to 14 range is a convention rather than a limit.
Common questions
Frequently asked questions
The concentration of hydrogen ions in a solution, expressed as a negative base-10 logarithm. A pH of 4 means 0.0001 mol/L of hydrogen ions. The logarithm is used because the concentrations involved span fourteen orders of magnitude.
Because at 25 degrees celsius pure water contains equal concentrations of hydrogen and hydroxide ions, both at 1e-7 mol/L. Neutral means those two are equal, and pH 7 is where that happens at that temperature. At 50 degrees celsius neutral sits at 6.63.
Yes. Concentrated hydrochloric acid at 12 M has a pH below zero, and concentrated sodium hydroxide can exceed 14. The 0 to 14 range covers ordinary dilute solutions, which is why it became the familiar scale, but the definition places no limit.
A strong acid dissociates completely in water, so its hydrogen ion concentration equals its concentration. A weak acid only partly dissociates. At 0.01 M, hydrochloric acid gives pH 2.00 while acetic acid gives pH 3.39, with only 4.1% of it dissociated.
Subtract the pOH from pKw, which is 14.00 at 25 degrees celsius. A solution with pOH 5 has pH 9. At other temperatures use the pKw for that temperature, since the two do not always add to 14.
Because water supplies its own hydrogen ions at 1e-7 mol/L, and once the acid concentration drops near that level the water dominates. A 1e-8 M solution of hydrochloric acid has pH 6.98, not the 8 the simple formula gives, since an acid cannot make water alkaline.
A weak acid together with its conjugate base, which resists pH change when acid or base is added. The pH sits at the pKa when the two are present in equal amounts, and buffering works well within about one unit either side of that.
Not directly, because the scale is logarithmic. Mixing equal volumes of pH 3 and pH 5 gives roughly pH 3.3, not pH 4, because the more acidic solution carries a hundred times more hydrogen ions. Convert to concentrations first, average those, then convert back.