pH Calculator

Convert between pH, pOH, hydrogen ion and hydroxide concentration, or find the pH of a strong or weak acid or base from its concentration and Ka.


Concentrations are in mol/L. Scientific notation works, so 1.75e-5 and 0.0000175 mean the same thing. Ka and Kb only apply to the two weak options; switch the last box to pK to enter 4.76 instead.
pH
2.88
Acidic
pOH
11.12
[H+] mol/L
1.31 × 10−3
[OH−] mol/L
7.61 × 10−12
02468101214

Weak acid. Solved from x² + Kax − KaC = 0 in full rather than assuming x is small, so the answer holds even when the acid is strongly ionised.

The acid or base is 1.31% ionised at this concentration.

What pH measures

pH is the negative base ten logarithm of the hydrogen ion concentration, so pH = −log10[H+]. Because it is a logarithm, each whole step is a factor of ten: pH 3 is ten times as acidic as pH 4 and a hundred times as acidic as pH 5. In pure water at 25 °C, [H+] and [OH−] are both 1.0 × 10−7 mol/L, which is where the familiar neutral value of 7 comes from. That 7 is not a universal constant; it is the water autoionisation constant Kw at room temperature, and it shifts if the temperature does.

pH, pOH and the two concentrations

These four quantities are one number wearing four hats. Give any one of them and the other three follow from pH + pOH = 14 and [H+][OH−] = Kw = 1.0 × 10−14. The first four options in the menu do exactly that. A pH of 3.4 gives a pOH of 10.6, a hydrogen ion concentration of 4.0 × 10−4 mol/L and a hydroxide concentration of 2.5 × 10−11 mol/L, and the calculation runs the same way from whichever end you start.

Strong acids and bases

A strong acid dissociates completely, so a 0.01 mol/L solution of hydrochloric acid gives 0.01 mol/L of hydrogen ions and a pH of 2. The shortcut pH = −log10C works fine down to about 10−6 mol/L and then quietly fails: it says 10−8 mol/L HCl has a pH of 8, which would make an acid basic. This tool solves the full balance including the hydrogen ions water contributes on its own, giving pH 6.98 instead, which is very slightly acidic, as it should be.

Weak acids and bases

A weak acid only partly ionises, and how far it goes depends on its acid dissociation constant Ka. The equilibrium gives x² + Kax − KaC = 0, where x is the hydrogen ion concentration. Textbooks usually drop the middle term and use x = √(KaC), which is close enough when ionisation is under about 5 per cent, and noticeably wrong when it is not. This tool solves the quadratic in full and also reports the percentage ionised, so you can see for yourself whether the shortcut would have held. Enter Ka as a number like 1.75 × 10−5, or switch the last box to pK and type 4.76.

Worth knowing

  • pH is a logarithm, so a difference of one unit is a factor of ten in acidity, not a small step.
  • The neutral point is 7 only at 25 degrees Celsius; it drops to about 6.14 in water at 100 degrees.
  • pH values below 0 and above 14 are perfectly real, they just need very concentrated solutions.
  • Strong means fully dissociated, not dangerous. Hydrofluoric acid is weak and still highly corrosive.
  • Nothing is stored. The calculation runs on our server and the result is discarded once it is sent.

Frequently asked questions

Take the negative base ten logarithm of the hydrogen ion concentration in mol/L, so pH = −log10[H+]. If you have a concentration instead of an ion count, pick one of the solution options and the tool works [H+] out first, taking dissociation into account.

For anything above about 10−6 mol/L it is simply pH = −log10C, since a strong acid dissociates completely. Below that, water contributes enough hydrogen ions of its own to matter, so this tool uses the exact form [H+] = (C + √(C² + 4Kw)) / 2.

Raise ten to the power of the negative pH: [H+] = 10−pH. A pH of 4.5 is 3.2 × 10−5 mol/L. Choose pH in the menu and all four quantities come back together.

pOH is the same idea applied to hydroxide, pOH = −log10[OH−]. At 25 degrees Celsius the two always add to 14, because the product of the two concentrations is fixed at Kw = 1.0 × 10−14. So a pH of 9.2 is a pOH of 4.8.

A strong acid gives up essentially all of its protons, so its hydrogen ion concentration equals its concentration. A weak acid reaches an equilibrium instead, and only a fraction ionises. That fraction is set by Ka, which is why a weak acid needs one more number before its pH can be worked out.

Yes. The 0 to 14 range is a convention for dilute solutions, not a limit. Concentrated hydrochloric acid at 12 mol/L has a pH around −1.1, and concentrated sodium hydroxide goes above 15. This tool accepts values outside the usual range and simply pins them to the end of the scale bar.

Because x = √(KaC) drops a term. It assumes the amount that ionises is small next to the starting concentration, which is a good assumption while ionisation stays under about 5 per cent. This tool solves the quadratic in full, so for a dilute solution of a moderately strong weak acid it will read a little lower. The percentage ionised is shown so you can judge whether the approximation was safe.

Only at 25 degrees Celsius. Neutral means [H+] equals [OH−], and that point sits at half of pKw. Since Kw rises with temperature, neutral water at 100 degrees has a pH near 6.14 and is still neutral. This tool uses the 25 degree value throughout, which is the standard assumption in coursework.

How do you calculate pH?

pH is −log10[H+], and pH + pOH = 14. This calculator converts between pH, pOH, [H+] and [OH−], and works out the pH of a strong or weak acid or base from its concentration, solving the weak acid quadratic in full and reporting the percentage ionised.