Percentages Explained: Every Formula You Actually Need

Percent of a number, percent change, reverse percentages, percentage points and the discount stacking rule. Five formulas cover almost every percentage question anyone actually asks.

The short answer is that every common percentage question in one place: percent of a number, percent change, increase, decrease and reverse percentages. Everything below explains why, and where that answer stops being true.

Why it works this way

Understanding the mechanism matters more than memorising a result. Once you can see which quantity drives the outcome, you can sanity-check any number a tool hands you — including ours — and spot when an input is wrong before the answer misleads you.

A worked example

Open the Percentage Calculator with its default values, then change a single input and note the effect. Every common percentage question in one place: percent of a number, percent change, increase, decrease and reverse percentages.

Common mistakes

Three mistakes account for most wrong answers here: mixing units without converting, applying a rate for the wrong period (annual where monthly was needed, or the reverse), and rounding partway through instead of at the end. Each one is easy to make and easy to avoid once you are watching for it.

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Try it yourself

Work through the example with your own figures in the calculator below. Change one input at a time and watch which direction the result moves — that single habit builds more intuition than reading another explanation.