Percentage change tells you how much a value has increased or decreased relative to its starting point. It’s used everywhere β from stock market returns to salary negotiations to scientific data.
The Percentage Change Formula
% Change = ((New Value β Old Value) Γ· |Old Value|) Γ 100
- Positive result = increase
- Negative result = decrease
- Use absolute value (|Old Value|) so direction comes from the sign
Examples
Example 1 β Price Increase
A product goes from $80 to $96.
% Change = ((96 β 80) Γ· 80) Γ 100 = (16 Γ· 80) Γ 100 = +20%
A product goes from $80 to $96.
% Change = ((96 β 80) Γ· 80) Γ 100 = (16 Γ· 80) Γ 100 = +20%
Example 2 β Stock Drop
A stock falls from $150 to $127.50.
% Change = ((127.50 β 150) Γ· 150) Γ 100 = (β22.50 Γ· 150) Γ 100 = β15%
A stock falls from $150 to $127.50.
% Change = ((127.50 β 150) Γ· 150) Γ 100 = (β22.50 Γ· 150) Γ 100 = β15%
Example 3 β Salary Negotiation
You earn $55,000 and want $65,000.
% Change = ((65,000 β 55,000) Γ· 55,000) Γ 100 = (10,000 Γ· 55,000) Γ 100 = +18.2%
You earn $55,000 and want $65,000.
% Change = ((65,000 β 55,000) Γ· 55,000) Γ 100 = (10,000 Γ· 55,000) Γ 100 = +18.2%
Percentage Change vs Percentage Difference
These are often confused:
- Percentage Change β Compares a new value to an old value (direction matters: old β new).
- Percentage Difference β Compares two values with no “before/after” relationship. Formula: |A β B| Γ· ((A + B) / 2) Γ 100
Common Real-World Uses
- Investing β Calculate portfolio returns, stock gains/losses
- Retail β Percentage off, markup calculations
- Science β Percent error between experimental and theoretical values
- Business β Revenue growth, year-over-year comparisons
- Fitness β Track weight loss or strength gains over time
Common Mistakes to Avoid
- β Using the new value instead of the old value in the denominator
- β Forgetting that a 50% drop followed by a 50% gain does NOT return to the original value
- β Confusing percentage points with percentage change (interest rate going from 3% to 5% = 2 percentage points, but a 66.7% increase)
Related Math Calculators