pH Calculator

pH = −log₁₀[H⁺] pOH = −log₁₀[OH⁻] pH + pOH = 14 at 25 °C

pH

The reading an electrode gives you: minus the base-ten logarithm of the hydrogen ion concentration. A change of one unit is a tenfold change in concentration, which is why the scale is worth converting rather than estimating

pOH

The same logarithm taken of the hydroxide ion concentration. At 25 °C it is what is left when pH is subtracted from 14, so the two always move in opposite directions

[H⁺]

The hydrogen ion concentration in moles per litre. It is what a titration or a dilution calculation gives you, and what the electrode reading stands for

[OH⁻]

The hydroxide ion concentration, also in moles per litre. In water the two are locked together: their product is 1 × 10⁻¹⁴ at 25 °C, so knowing one gives the other

Use it when a number arrives in one form and the next step needs another: an electrode gives you pH and the calculation wants a concentration, or a dilution gives you a concentration and the label wants a pH. The second reason to be here is to check your own work — a solution cannot be 0.001 mol/L in hydrogen ions and pH 5 at the same time, and entering both makes the page say so instead of quietly picking one. The pH scale runs from 0 to 14 here, which covers dilute aqueous solutions at 25 °C: strong acids and strong bases in concentrated form fall outside it.

1. Pure water, the one pH everybody knows

   1. pH 7 is given, so [H⁺] is 10⁻⁷ moles per litre
   2. Hydroxide is the same by symmetry: 10⁻⁷ moles per litre
   3. pOH is 14 − 7 = 7, which is the definition of neutral
   4. In micromoles per litre both concentrations read 0.1 µmol/L

   Neutral water is the one state where every row is easy to read: 0.0000001 mol/L in one row and 0.1 µmol/L in the next are the same number, written at two magnitudes. That is the whole reason the panel carries both — at pH 3.5 the hydroxide concentration is 0.00000000 mol/L in the first of those rows, and the micromole row is where it becomes legible again.

2. A strong acid, entered as a concentration

   1. 0.001 mol/L is 1 × 10⁻³ mol/L
   2. Take the negative logarithm: 10⁻³ gives pH 3 exactly
   3. pOH is what is left: 14 − 3 = 11
   4. Hydroxide is 10⁻¹¹ mol/L, or 0.00001 µmol/L
   5. The pH field was left empty and the answer came from the concentration

   One route in, four values out: the pH field is blank here, which is not an incomplete form — any single one of the four settles the state. The concentration is entered as millimoles by switching the unit selector, and it is converted to moles per litre before the logarithm is taken. This is the direction a dilution calculation leaves you in: you know what you made, and the meter is the thing you are predicting.

3. A strong acid at the edge of the range, where one row reads zero

   1. pH 1 means [H⁺] = 10⁻¹ = 0.1 mol/L — this is roughly bench hydrochloric acid
   2. pOH = 14 − 1 = 13
   3. Hydroxide is 10⁻¹³ mol/L, which is 0.00000000 at eight decimal places
   4. The micromole row carries it: 10⁻¹³ mol/L is 0.0000001 µmol/L

   The hydroxide row shows 0 here, and that is the display running out of decimal places rather than the ion being absent — water always has some. A tenth of a mole of hydrogen ions per litre is the strong end of what this page covers; push further and the activity of the ions stops equalling their concentration, which is the assumption the logarithm rests on.

Everything here assumes 25 °C. The ion product of water is a function of temperature — about 1 × 10⁻¹⁴ at 25 °C but closer to 5 × 10⁻¹³ at 100 °C — so pH plus pOH equals 14 only near room temperature, and neutral water near boiling point sits near pH 6.1. There is no temperature field because the standard curve of pK against temperature differs between references, and a wrong curve would be worse than a stated limitation. The formula is also defined on activity rather than concentration, and the two only agree in dilute solution, which is why pH is held to the 0 to 14 range: a concentrated acid has no meaningful electrode reading at all.

How do I calculate pH from a concentration?

Take the base-ten logarithm of the hydrogen ion concentration and change its sign. A concentration of 0.001 mol/L is 1 × 10⁻³, so the pH is 3; 0.0001 mol/L gives 4; 1 mol/L gives 0. Going the other way, raise ten to the power of the negated pH: pH 7 is 10⁻⁷ mol/L. The page accepts either direction, so you can enter the number you have and read off the one you need.

What does a pH of 3.5 mean for the hydroxide concentration?

It means 10⁻¹⁰·⁵ mol/L, which is 3.16 × 10⁻¹¹ mol/L — so small that the moles-per-litre row shows 0.00000000 and only the micromoles row still carries it, at 0.00003162 µmol/L. Both rows are true, and they are the same quantity written at two magnitudes. The zeros appear when the fixed number of decimal places runs out, not when the ion is absent.

Why is pH plus pOH always 14?

Because the product of the two ion concentrations is a constant at a given temperature. At 25 °C that constant is 1 × 10⁻¹⁴, and taking the negative logarithm of both sides turns a product into a sum: pH + pOH = 14. The constant is not really constant — at 100 °C it is near 5 × 10⁻¹³, so the sum becomes about 12.3 and neutral water sits near pH 6.1. Everything on this page is at 25 °C.

Can pH be negative or above 14?

In principle yes: a 10 mol/L solution of a strong acid would calculate out at pH −1. In practice the electrode cannot read it, because pH is defined on the activity of the hydrogen ion and activity stops tracking concentration once the solution is concentrated — in a 1 mol/L acid the activity coefficient is already around 0.8. This page holds pH to 0 to 14, which is the range over which the dilute-solution assumption holds, and a concentration that calculates outside it is refused.

What happens if two of the values I enter disagree?

The page reports the disagreement and refuses to answer, rather than picking one. Two values are allowed to differ by up to 0.05 pH units, which is about a 12% difference in concentration — the width of copying two or three significant figures by hand. Beyond that it is a real contradiction: pH 3 and 0.0005 mol/L differ by 0.30 units, six times the tolerance, and one of the two is a mistake. Enter a single value and no comparison is made.

• SI Units — Amount of Substance: the mole — National Institute of Standards and Technology (NIST)
• The International System of Units (SI Brochure) — Bureau International des Poids et Mesures (BIPM)
• IUPAC Gold Book — amount of substance — International Union of Pure and Applied Chemistry (IUPAC)