Percent change
Also known as: percentage change, percent increase or decrease
Percent change measures how much a quantity grew or shrank relative to its starting value: (new − old) ÷ old, expressed as a percent. A positive result is an increase, a negative result is a decrease.
The formula is percent change = (new value − original value) ÷ original value × 100. The denominator is always the original value — that is the single most common place students lose points. If a price rises from $40 to $50, the change is (50 − 40) ÷ 40 = 0.25, a 25% increase. Falling from $50 back to $40 is (40 − 50) ÷ 50 = −0.20, a 20% decrease. The same $10 move produces different percentages because the starting points differ.
Working backward is just as common on tests. If a value after a 20% increase is 96, the original is not 96 × 0.8 — it is 96 ÷ 1.20 = 80. Set it up as original × (1 + rate) = new and divide. For a decrease, use original × (1 − rate) = new. Recognizing 1.20 and 0.80 as multipliers makes these problems fast.
Successive changes multiply rather than add. A 10% increase followed by a 10% decrease gives 1.10 × 0.90 = 0.99, a net 1% decrease, not a return to the start. Chaining multipliers also handles compound growth: three consecutive 5% increases give 1.05³ ≈ 1.158, about a 15.8% total increase.
Keep percent change distinct from percentage-point change. If an interest rate moves from 4% to 6%, that is a 2 percentage-point rise but a 50% relative increase — questions often exploit the ambiguity.
Percent change shows up throughout standardized math testing. The ACT covers it in intermediate algebra, the GRE tests it in arithmetic and again in data interpretation, where you read values off a chart before computing, and the Praxis Core Math exam includes it under ratios, proportions, and percents.
Key takeaways
- Percent change = (new − old) ÷ old × 100, always dividing by the original value.
- To recover the original value, divide the new value by the multiplier: 1 + rate for an increase, 1 − rate for a decrease.
- Successive percent changes multiply — a 10% gain followed by a 10% loss leaves you 1% below where you started.
- A percentage-point change is not the same as a percent change; 4% to 6% is 2 points but a 50% increase.