Interactive tool
Percentage and growth toolkit
Percentage change, “what percent of”, and successive changes in one place — with the shortcut formula shown so you learn it, not just use it.
The formulas behind the toolkit
Percentage change from an old value to a new one:
change % = (new − old) ÷ old × 100
The base is always the old value. A rise from 80 to 100 is a 25% increase; a fall from 100 to 80 is a 20% decrease. Same gap, different base.
What percent is A of B:
A ÷ B × 100
Successive changes of a% followed by b%:
net change % = a + b + (a × b) ÷ 100
Use negative numbers for decreases. A 20% rise followed by a 20% fall gives 20 − 20 + (20 × −20) ÷ 100 = −4, a net 4% fall — not zero. For three changes, combine the first two, then combine that result with the third.
Fractions worth knowing by heart
Recognising these saves real time in quant and data interpretation:
| Fraction | Percentage |
|---|---|
| 1/2 | 50% |
| 1/3 | 33.33% |
| 1/4 | 25% |
| 1/6 | 16.67% |
| 1/7 | 14.29% |
| 1/8 | 12.5% |
| 1/9 | 11.11% |
| 1/11 | 9.09% |
| 1/12 | 8.33% |
| 1/16 | 6.25% |
Use the toolkit to check your working, not to replace it — the goal is to make these calculations automatic in your head.