Percentage increases and decreases: apply and compare changes
To change an amount B by p%, multiply B by 1 + p/100 for an increase or 1 − p/100 for a decrease.
The short answer
To change an amount B by p%, multiply B by 1 + p/100 for an increase or 1 − p/100 for a decrease. Increasing 100 by 20% gives 120; decreasing 120 by 20% gives 96. The second percentage uses a different base, so equal opposite rates do not cancel.
Method and checked examples
To compare two positive amounts, divide their difference by the original amount and multiply by 100. Returning from 80 to 100 requires 25%, not 20%. For successive changes multiply each factor;20% up then 20% down gives a net 4% decline. Keep the original and final values beside the result.
100 × (1 + 20/100) = 120
120 × (1 − 20/100) = 96
(96 − 100) / 100 × 100 = −4%
(100 − 80) / 80 × 100 = 25%| Inputs | Calculation | Result |
|---|---|---|
| B=100; p=20% | 100 × 1.20 | 120 |
| B=120; p=−20% | 120 × 0.80 | 96 |
| 80 → 100 | (100 − 80) / 80 × 100 | 25% |
Limits and assumptions
A zero starting amount has no relative percentage change. The calculator uses the absolute starting value for a negative base; this is a stated convention, not a universal growth-rate definition. Use the same units and consider rounding. An adjustment is different from measuring a change.
Sources and scope
A zero starting amount has no relative percentage change. The calculator uses the absolute starting value for a negative base; this is a stated convention, not a universal growth-rate definition. Use the same units and consider rounding. An adjustment is different from measuring a change.
These are hypothetical calculations in generic monetary units. Source links support the methods, not current prices, offers or tax rates.
- OpenStax
Percent equations and the original base.
Publisher: Kymata Labs LLC. Contact and corrections.