pH Calculator
pH is the negative base ten logarithm of the hydrogen ion concentration. That single logarithm is why a hundredfold change in concentration moves the scale by only two units.
pH
3
- pOH
- 11
- Hydroxide concentration in picomoles per litre
- 10
- Dilution factor
- 0.1
- pH after dilution
- 4
Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.
The formula this calculator uses
pH = -log10[H+]
- H+
- Hydrogen ion concentration in moles per litre
- pH
- Negative base ten logarithm of that concentration
- pOH
- 14 minus the pH at 25 degrees Celsius
- OH-
- Hydroxide ion concentration, equal to 10 to the minus pOH
How to check the result by hand
- 1
Write the concentration in moles per litre
The formula expects a molar concentration, not grams per litre or a percentage. Convert first if necessary, because the logarithm of a wrongly scaled number is simply wrong rather than obviously wrong.
- 2
Take the base ten logarithm
The logarithm of 0.001 is minus 3. Concentrations below one always produce a negative logarithm, which is exactly why the definition includes a minus sign in front.
- 3
Change the sign to get pH
Minus 3 becomes a pH of 3. If the answer comes out negative, the concentration was larger than one mole per litre, which is possible for very strong concentrated acids.
- 4
Subtract from 14 for the pOH
A pH of 3 leaves a pOH of 11. This step is free and gives a useful cross-check, because the two values must always add to 14 at room temperature.
- 5
Apply the dilution ratio when volumes change
Multiply the concentration by the sample volume divided by the total volume, then take the logarithm again. Each tenfold dilution adds one whole unit to the pH, so the shift is easy to sanity-check.
For worked examples, common mistakes and the limits of this formula, read the full How To Calculate pH page.