How to calculate percentage change

“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.

The one formula you need

Percentage change from an old value to a new value: ((new − old) / old) × 100%. The old value always goes in the denominator. That’s the whole thing.

$80k → $100k: (100 − 80) / 80 = 0.25 = 25%. Revenue grew 25%. If you’d divided by 100 instead, you’d get 20%, which answers a different question (“the increase is what fraction of the new total?”) and is not growth rate.

Increases vs decreases — same formula, watch the sign

$100k → $80k: (80 − 100) / 100 = −0.20 = −20%. A 20% decrease. Note: a 25% increase followed by a 20% decrease lands you back at the starting value — that’s not symmetry, it’s multiplicative math. To undo a percent change, you need a larger percent change in the opposite direction.

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%:

It rose by 1 percentage point (absolute difference). It also rose by 25 percent (relative change, using the formula above). Both are correct; they describe different things. “Mortgage rates rose 25%” and “mortgage rates rose 1 point” are the same event described two ways. When precision matters, use “points.”

Year-over-year (YoY) growth

Same formula, applied across calendar years. April 2025 revenue vs April 2024 revenue: (2025_april − 2024_april) / 2024_april. YoY naturally controls for seasonality, which is why retail reports Q4 against Q4 instead of Q4 against Q3.

Compound growth (CAGR)

For multi-period growth where you want a single “average” rate: CAGR = (ending / starting)^(1/years) − 1. A portfolio that grew from $10k to $20k over 5 years has a CAGR of (20000/10000)^(1/5) − 1 = 1.1487 − 1 = 14.87% per year. Not 100%/5 = 20%. That linear math ignores compounding.

The compound interest calculator solves this in both directions — give it a start, end, and timeframe and it returns the implied rate.

A worked table

Some intuitions to pin down before reaching for a calculator:

10 → 11 is +10%. 11 → 10 is −9.09%, not −10%. 100 → 150 is +50%. 150 → 100 is −33.3%. 50 → 200 is +300%, not “4× growth means 400%.” The word “4×” means multiply by 4, which is a 300% increase, because the starting value is already counted once.

When “X% more” gets misquoted

“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.

“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.

Quick-check the calculator

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.

Use the percentage calculator for the five standard percentage questions, and the compound interest calculator when you need CAGR or multi-period growth.