Key takeaway
Compare two numbers as a percent change (relative) or as a ratio (relative size). Learn which reveals what, and why they're not interchangeable.
Scope and assumptions
Percent change shows relative shift from a base; a ratio shows relative size. Different questions. Illustrative.
Short answer: Compare two numbers as a percent change (relative) or as a ratio (relative size). Learn which reveals what, and why they're not interchangeable.
Quick navigation
- Convert ratio to percent → convert-ratio-to-percent
- Percentage difference formula → percentage-difference-formula
- Percent to ratio → percent-to-ratio
- The calculator → Percentage Calculator
Why the same two numbers can read two ways
Put 120 and 100 side by side and you can report them as a ratio (1.2× the size) or as a percent change (+20% from the base). Same pair, different question. Picking the wrong one doesn't just sound off — it can invert your message (a 1.2 ratio and a −16.7% change describe the same 120-vs-100 flip depending on which is the base).
1. The two comparisons
Ratio: A : B = A ÷ B — shows relative size, no time direction Percent change: (A − B) ÷ B × 100 — shows growth from a base B
The ratio needs no "before." The percent change always needs a starting value B to divide by.
2. Worked examples
| A | B | Ratio (A:B) | % change (B→A) |
|---|---|---|---|
| 120 | 100 | 120 ÷ 100 = 1.2 : 1 | (120−100)/100 × 100 = +20% |
| 100 | 120 | 100 ÷ 120 = 0.833 : 1 | (100−120)/120 × 100 = −16.7% |
| 150 | 50 | 150 ÷ 50 = 3 : 1 | (150−50)/50 × 100 = +200% |
Flip the base and the sign flips: 100 vs 120 is +20% going up, −16.7% coming back down.
3. Why they aren't interchangeable
A ratio answers "how many times bigger is A than B?" A percent change answers "how much did it grow from B?" The same 120 vs 100 reads 1.2× (ratio) or +20% (change) — both true, different questions.
4. Ratio order matters
A:B is not B:A. For 120 vs 100, the ratio is 1.2:1; reverse it and it's 0.833:1. Always state which is the "reference" number, or your reader will invert the meaning. In finance, "debt-to-equity" and "equity-to-debt" are opposites for this reason.
5. The percent-change base trap
Percent change divides by the starting value, not the ending one. A price going $50 → $75 is +50% (÷50), but $75 → $50 is −33.3% (÷75), not −50%. Same $25 move, different percent, because the base changed.
6. Common mistakes to avoid
- Using a ratio when you mean change — ratio has no direction; change does (+/−).
- Wrong base in percent change — always divide by the starting value B.
- Saying "1.2%" for a 1.2 ratio — a ratio of 1.2 is 120%, not 1.2%.
- Mixing ratio order — A:B differs from B:A.
- Thinking ±20% is symmetric — +20% then −20% doesn't return to start (see §5).
- Dropping the sign — "changed 20%" hides whether it went up or down.
7. Quick reference
| You want to say… | Use |
|---|---|
| A is how many times B | Ratio A÷B |
| How much it grew from B | (A−B)÷B × 100 |
| Compare sizes with no direction | Ratio |
| Show before/after movement | Percent change |
FAQ
Q: What's the difference between percent change and ratio? Ratio shows relative size (A÷B); percent change shows growth from a base ((A−B)÷B×100).
Q: Is 120 vs 100 a 1.2 ratio or 20%? Both — ratio 1.2:1 and +20% change from the base of 100.
Q: Which should I use? Use ratio for relative size; use percent change when there's a before/after.
Q: Can a ratio be a percent? Yes, a ratio of 1.2 equals 120%, but they answer different questions.
Q: Why is 100 vs 120 −16.7%? (100−120)/120 × 100 = −16.7% from the base 120.
Sources: Khan Academy — Ratios and rates; Maths is Fun — Ratio.
Disclaimer: Illustrative. Choose the comparison that matches your question; the same numbers can read differently. Informational only.
Sources and references
- Khan Academy — Ratios and rateshttps://www.khanacademy.org/math
- Maths is Fun — Ratiohttps://www.mathsisfun.com/numbers/ratio.html