Percentage Change Calculator

How to Calculate Percentage Change

Percentage change measures the relative difference between an old value and a new value, expressed as a proportion of the old value. The formula is: ((New - Old) / Old) × 100. A positive result means increase, negative means decrease. From 80 to 100: ((100 - 80) / 80) × 100 = 25% increase. From 100 to 80: ((80 - 100) / 100) × 100 = -20% decrease.

Notice something important in that example: going from 80 to 100 is a 25% increase, but going from 100 back to 80 is only a 20% decrease. This asymmetry trips up investors constantly. A stock that drops 50% needs to gain 100% to return to its original price. A 33% loss requires a 50% gain to recover. The deeper the loss, the more disproportionate the recovery needed — a 90% loss requires a 900% gain. This is why avoiding large losses matters more than chasing large gains.

Percentage Change vs Percentage Point Change

This distinction causes more confusion in news reporting than perhaps any other mathematical concept. If an interest rate moves from 5% to 7%, that is a 2 percentage point increase but a 40% increase. Both are correct, but they describe very different things. Saying "interest rates increased 40%" sounds alarming. Saying "rates increased 2 percentage points" sounds manageable. Politicians, journalists, and marketers choose whichever framing serves their argument — being able to calculate both protects you from manipulation.

Common Uses

Business: revenue growth, profit margins, year-over-year comparisons, market share changes. Finance: investment returns, inflation rates, price movements, portfolio performance. Science: experimental results, population changes, measurement differences. Academics: grade improvements, test score comparisons, enrollment trends. Health: weight change, blood pressure changes, medication dosage adjustments.

Why is a 50% loss not recovered by a 50% gain?

Because the percentage is calculated on a different base. If $100 drops 50% to $50, a 50% gain from $50 is only $25, bringing you to $75 — not $100. You need a 100% gain ($50 → $100) to recover. The base changes after the loss, making recovery mathematically harder than the original decline.

What is the difference between percentage change and percentage difference?

Percentage change compares a new value to an old value (directional — there is a clear before and after). Percentage difference compares two values without directionality, using their average as the base: |A - B| / ((A + B) / 2) × 100. Use percentage change for time-based comparisons and percentage difference for comparing two alternatives.