Percentage Calculator

These describe genuinely different comparisons even though both involve two percentages. A percentage-point difference is a simple subtraction of two percentage figures — if an interest rate moves from 4% to 6%, that is a 2 percentage-point rise, full stop. A percentage change, by contrast, measures that same movement relative to the original starting figure — the same move from 4% to 6% represents a 50% increase, because the 2-point rise is half again as large as the original 4% base it started from. Both descriptions are accurate simultaneously; they are simply answering different questions, which is exactly why conflating them — reporting a "6% increase" when a percentage-point change was meant, or vice versa — is one of the most common and consequential numerical errors in casual reporting on rates, taxes and interest.

Each percentage change is calculated against whatever the current value happens to be at that moment, not against some fixed original reference point, which means a sequence of percentage changes is not simply reversible by applying the inverse percentage. A value of 100 increased by 50% becomes 150; that same 150 decreased by 50% becomes 75 — not back to 100 — because the decrease was calculated against the new, larger base of 150 rather than the original 100. Reversing a 50% increase actually requires a decrease of 33.3%, not 50%, since the percentage needed to undo a change depends on which value it is being calculated against, and the base has shifted by the time the reversal is applied.

Recovering an original value from a final one after a percentage change — finding the pre-discount price from a sale price, or the pre-tax amount from a total that already includes it — requires dividing rather than the more intuitive-seeming approach of simply adding the percentage back onto the final figure, and this is the single calculation people most reliably get wrong. A £60 item after a 25% discount did not start at £60 plus 25% of £60 (£75) — it started at £60 divided by (1 − 0.25), which is £80. The distinction matters because the percentage discount was always calculated against the *original*, larger price, not against the smaller, already-discounted figure being worked backward from — adding the percentage to the wrong base systematically produces a value that is too low.

A bare number with no visible formula gives no way to spot a mistaken input or a misunderstood question — entering the wrong mode, or transposing which value is the "original" and which is the "new" one, produces a confidently wrong answer with nothing to flag that anything went astray. Showing the formula with the actual entered values substituted directly into it turns the result into something that can be checked by eye against the specific question being asked, rather than simply trusted at face value.