% Percentage Calculator

Percentage change is not symmetrical

This is the mistake that costs people the most, and it is entirely counter-intuitive. If a price falls by 50% and then rises by 50%, you are not back where you started — you are 25% down. The fall was 50% of the original number; the rise was 50% of the smaller one.

Same arithmetic, same trap: a share that drops 80% needs to rise 400% just to break even. Any time you see two percentage moves added together, check whether they were measured against the same starting number. Usually they were not.

Percent versus percentage points

If an interest rate goes from 2% to 3%, that is a rise of one percentage point — and a rise of 50 percent. Both are correct, and they sound wildly different. Whoever is presenting the number will pick whichever suits them, so the useful habit is to ask which one you are being shown.

Working backwards is not the same as subtracting

If a price includes 25% VAT, you do not find the pre-tax amount by taking 25% off. The tax was added to the smaller number, so you divide by 1.25 rather than multiplying by 0.75. On 1,000 the two methods differ by 50 — which is exactly the kind of error that survives a whole spreadsheet unnoticed.

A return without a period is not a number

"Up 30%" means something very different over one year than over five. The last tab converts a total return into an annual one, which is the only way to compare two of them fairly. It is also the question most investment claims quietly avoid answering — worth reading alongside the guide to AI and money, where several of the claims in circulation come apart on exactly this point.

For projecting growth forward instead of measuring it backwards, use the compound growth calculator.