“Percentage” covers at least three operations that feel identical in conversation and are not. Asking what 15 per cent of 300 is, asking what share 45 is of 300, and asking how much something changed between two numbers are separate calculations with separate denominators. The first divides by 100 and multiplies; the second divides one quantity by another; the third divides by the starting value, and choosing the wrong starting value is the single most common error with percentages.
This page exposes all three as a mode selector rather than guessing which you meant, which is why the result labels restate the question with your own numbers in it.
X per cent of Y — a share of a whole:
result = X ÷ 100 × Y
X is what per cent of Y — expressing one quantity as a fraction of another:
result = X ÷ Y × 100
With Y equal to zero there is no sensible answer, so the tool returns a dash rather than infinity.
Per cent change from X to Y — the movement between two values, measured against the first:
result = (Y − X) ÷ X × 100
A zero starting value is likewise undefined and shows as a dash. The tool also labels the direction as an increase, a decrease, or no change, and it accepts negative numbers, which is what makes it usable for temperature swings, profit and loss, and elevation.
Precision differs by mode on purpose: the “of” answer is printed to as many as four decimal places, because it is often the first step of a longer calculation, while the ratio and change answers are given to two.
With the defaults, X = 15 and Y = 300:
The last two lines are the same journey described in opposite directions, and they give different magnitudes. That asymmetry is arithmetic, not unfairness: the rise is measured against 300, the fall against 400. It also explains why a 25 per cent loss needs a 33.33 per cent gain to recover, and why investors who are down a third need a fifty per cent return to break even.
Divide rather than subtract. If a price rose 20 per cent to 120, the original is 120 ÷ 1.2 = 100, not 120 − 20. Subtracting the per cent of the wrong base is the classic error; use the change mode and set the values so the unknown is the starting point.
Enter plain digits. The field takes a number, so a comma or currency symbol will not parse.
In the change mode it means the value fell. In the “of” mode a negative X simply returns a negative share, which is correct for things like losses.
Because it frequently feeds another step. 33.3333 per cent of something should not be pre-rounded to 33.33 before you use it.
The Discount page is this calculation with a fixed downward direction, the Tip page applies a per cent to a bill, and the Compound Interest page chains the same multiplication repeatedly, which is exactly where “successive changes do not add” becomes expensive.