Percentage Increase Calculator

(Final − Starting) ÷ |Starting| × 100. The denominator is always the starting value — that's the whole trick, and the source of every classic confusion. Price went from $80 to $100: (100−80)÷80 = +25%. Went from $100 to $80: (80−100)÷100 = −20%. Same $20, different percentages, because the base changed. The calculator shows this arithmetic worked out under the result precisely so the formula sticks.

Because the second calculation runs on a smaller base. $100 drops 50% to $50; gaining 50% of $50 only brings you to $75. Getting back to $100 from $50 requires a 100% gain. This asymmetry is the most financially consequential fact about percentages — it's why volatile investments underperform their average return, and why 'it's down 80%, how much worse can it get?' can still lose another 100% of what remains.

When a rate moves from 10% to 15%: it rose 5 percentage points, or 50 percent. Both are correct sentences describing the same change, chosen by whoever benefits from the framing — 'interest rates jumped 50%!' sounds apocalyptic, '5 points' sounds mild. The rule: point language for differences between two rates; percent language for relative change. News about polls, interest rates, and taxes mixes these constantly, usually not by accident.

Change is directional — before → after, this calculator — and uses the starting value as the base. Difference compares two values with no time order (two prices, two test scores) and conventionally divides by their average, so it's symmetric. If your numbers have a 'before,' use change. If you're comparing two products' prices side by side, the difference convention avoids the arbitrary choice of which one counts as the base.