The formula
How to calculate pOH
pOH is the alkaline counterpart to pH, measuring hydroxide ion concentration on the same logarithmic scale. The two always sum to 14 in water at 25 °C, so either can be derived from the other.
That relationship comes from the ion product of water: [H⁺][OH⁻] = 1 × 10⁻¹⁴ at 25 °C. Taking negative logarithms of both sides gives pH + pOH = 14.
What to enter:
- Hydroxide ion concentration (mol/L)
Results appear immediately — there is nothing to submit. Changing a field rewrites the link, so you can share the exact scenario you are looking at.
Units matter more here than the arithmetic itself: the formula assumes a specific set of units for each input, stated next to the field, and converting into those units first is usually the difference between a correct result and one that is wrong by a clean power of ten.
Why pOH matters
The formula behind pOH is standard and appears in the same form across textbooks and reference material; what a calculator adds is speed and the ability to see instantly how the result responds to a change in any one of the inputs, which is far slower to do by hand.
This also functions as a reference implementation of the formula itself: where the exact form of an equation is in question, the one used on this page, stated in the formula section above, is the standard version found in the relevant textbooks and reference material.
This calculation sits in a long tradition of being done first by hand with tables and slide rules, then with a scientific calculator, and now with a page like this one — the underlying mathematics has not changed at any point in that history, only the speed and convenience of getting from the inputs to the answer. Understanding the formula itself, shown above, is still worth doing even when a tool computes it instantly, since it is what makes the result trustworthy rather than just fast.
Where a calculation like this one is part of a larger piece of work, it is generally worth running it with a round, easy-to-check set of numbers first — inputs of exactly 1, 10 or 100 — purely to confirm the formula is being applied correctly, before switching to the real measured values the actual result depends on.
Worked example
Work through the defaults on this page:
- Hydroxide ion concentration: 0.001 mol/L
That gives:
- pOH: 3
- pH: 11
- Hydrogen ion concentration, as 10^x: -17 mol/L
The figures above are the calculator's own default values, shown purely so the working is visible rather than hidden — the same steps apply exactly to your own numbers, entered in the fields at the top of this page.
Reading the result
A pOH of 3 means a strongly alkaline solution — pH 11 — such as household ammonia. Low pOH means high hydroxide concentration, which is the opposite direction to the intuition most people carry from pH.
Where this goes wrong. The sum of 14 holds only at 25 °C. At 60 °C the ion product rises and the two sum to about 13.02, so temperature has to be stated when precision matters.
A result that is wrong by an exact factor of ten, a hundred or a similar round number is almost always a units error rather than a mistake in the formula itself — checking each input against the unit stated beside it is the fastest way to track it down.
Subtract from 14 at 25 °C. A pOH of 3.5 corresponds to a pH of 10.5.
It is convenient when working directly with hydroxide concentrations, particularly with strong bases where the hydroxide concentration is known and the hydrogen ion concentration is vanishingly small.
The headline figure is pOH. With 0.001 mol/L hydroxide ion concentration, that comes to 3. Change any field and the figure moves with it.
Generally, no more than the least precise input justifies — a result reported to six decimal places from inputs measured to two significant figures is implying a precision the calculation does not actually have. The calculator shows full precision so you can round appropriately for your own use.
Yes — the equation shown in the formula section above is the standard form used in textbooks and reference material for this calculation, not a simplified or approximate version.
Yes, in the sense that it applies the correct standard formula and returns an accurate result for the inputs given — but check your own course or publication's requirements for how results should be rounded, presented and referenced, since those conventions vary and are not something a calculator can know on your behalf.