How To Calculate Percentage Change

The one formula you need

“Revenue went from $80k to $100k” — what’s the growth rate? It’s not 20% (that’s the absolute amount divided by the new value by mistake), and it’s not 25% if you run the formula backward. The answer is 25%, but only if you pick the right denominator. This guide covers the percentage-change formula, why “percent” and “percentage points” are not the same thing, and the math behind year-over-year and compound growth.

Increases vs decreases — same formula, watch the sign

Specifically: a 50% drop needs a 100% rise to recover ($100 → $50 → $100). A 90% drop needs a 900% rise. This is why portfolio crashes are so brutal and why the “average” return of a volatile investment isn’t what you actually earned.

Percent vs percentage points

These get used interchangeably in news coverage, and it changes the meaning. If an interest rate goes from 4% to 5%:

Year-over-year (YoY) growth

Some intuitions to pin down before reaching for a calculator:

Compound growth (CAGR)

“200% more” means triple — the original plus two more of the same. Headlines routinely use “200% more” when they mean “doubled” (which is +100%). When you see the phrase, substitute the absolute numbers before accepting the claim.

A worked table

“3× faster” means finishing in one-third the time, or equivalently a 200% speedup. “3× more,” read literally, means the gain is 3× the original (so the new value is 4× the original). Most writers mean “3× as much” but write the less-precise version.

When “X% more” gets misquoted

Before trusting any percent-change output, sanity-check with one line: is the answer bigger or smaller than the starting value? Then: roughly what fraction of the starting value? If the tool says “$80k → $100k is a 20% change,” you know immediately something’s wrong — $20k is a quarter of $80k, so the change is ~25%. Rough mental math catches sign errors and denominator-swap bugs before they propagate.

Quick-check the calculator