How to Calculate Percent Change
A stock rises from $50 to $80. That's a 60% increase. The next month, it falls from $80 back to $50. Is that a 60% decrease?
No. It's a 37.5% decrease. The price ended exactly where it started, yet the percentages don't match. Understanding why is the key to calculating percent change correctly, and to reading news headlines, investment reports and sales figures without being misled.
The Same Change Gives Different Percentages Depending on Direction
A $30 change is the same size in both directions. But percent change measures that change relative to the starting value, and the starting value is different:
- Up from 50: 30 ÷ 50 = 60%
- Down from 80: 30 ÷ 80 = 37.5%
The base always matters. That's why a stock that drops 50% needs to rise 100% to recover.
The Formula
Percent change = (New value − Old value) ÷ Old value × 100
- A positive result is an increase
- A negative result is a decrease
Step-by-Step Examples
Example 1: An Increase
Monthly website visitors grew from 12,400 to 15,500.
Change = 15,500 − 12,400 = 3,100
Percent change = 3,100 ÷ 12,400 × 100 = 25%
A 25% increase.
Example 2: A Decrease
A jacket's price dropped from $120 to $90.
Change = 90 − 120 = −30
Percent change = −30 ÷ 120 × 100 = −25%
A 25% decrease.
Example 3: Working Backward
Sales rose 40% to $56,000. What were they before?
Old value × 1.40 = 56,000
Old value = 56,000 ÷ 1.40 = $40,000
Don't subtract 40% from $56,000; that gives $33,600, which is wrong. Check calculations with the basic calculator.
Percent Change vs. Percentage Points
When the values themselves are percentages, be careful. An unemployment rate that rises from 4% to 5%:
- Rose by 1 percentage point (5 − 4)
- Rose by 25 percent ((5 − 4) ÷ 4 × 100)
Both are correct, and they describe different things. Headlines that say "unemployment rose 25%" and "unemployment rose 1%" can refer to the exact same change. Always check which one is meant.
Percent Change Over Multiple Periods
Percent changes don't add. If sales rise 10% one year and fall 10% the next:
Overall = 1.10 × 0.90 = 0.99 → a 1% decrease
To find the average yearly rate over several periods, use the compound annual growth rate (CAGR):
CAGR = (Final ÷ Initial)^(1/years) − 1
If an investment grows from $10,000 to $16,105 over 5 years:
CAGR = (16,105 ÷ 10,000)^(1/5) − 1 ≈ 0.10 → 10% per year
See the compound interest calculator for the same math applied to savings.
An Insider Reference: Why Economists Use Log Changes
Because ordinary percent changes aren't symmetric, economists and data scientists often use log changes:
Log change = ln(New ÷ Old) × 100
For 50 → 80: ln(1.6) × 100 ≈ +47.0. For 80 → 50: ln(0.625) × 100 ≈ −47.0. The up and down moves are exactly opposite, and log changes over multiple periods add up correctly.
For small changes they're nearly identical to percent changes: a 2% change is a log change of about 1.98. That's why central banks and statisticians frequently analyze inflation and growth in log terms. Try it with the logarithm calculator.
A third option is percent difference, used when neither value is the "starting" one, like comparing two stores' prices. It divides by the average of the two values: |80 − 50| ÷ 65 × 100 ≈ 46.2%.
Common Mistakes
1. Dividing by the new value. The base is always the old value.
2. Averaging percent changes. +50% then −50% doesn't average to 0%. The result is a 25% loss.
3. Starting from zero. Percent change from 0 is undefined, because you'd divide by zero. A company going from 0 to 5 customers has no meaningful percent growth. See Why Division by Zero Doesn't Work.
4. Negative starting values. Percent change from a negative number, like profits going from −$10 to +$5, gives misleading signs. Report the absolute change instead.
Two Concepts Worth Knowing
Relative Change
Relative change compares a change to a reference value, while absolute change is just the difference. "Up $30" is absolute; "up 60%" is relative.
Multiplier
A multiplier turns a percent change into one multiplication: +25% means × 1.25 and −25% means × 0.75. Chains of changes multiply their multipliers.
Quick Answer: How Do You Calculate Percent Change?
Subtract the old value from the new value, divide by the old value, and multiply by 100. For example, from 50 to 80: (80 − 50) ÷ 50 × 100 = 60% increase. A negative result is a decrease. Always divide by the original value, and remember that percent changes over several periods multiply rather than add.
Try Them Yourself
- Basic Calculator: compute percent changes quickly
- Compound Interest Calculator: growth rates over time
- Logarithm Calculator: calculate log changes
- Financial Formulas: CAGR and growth formulas
- How to Calculate a Percentage: the basics
- The Mathematics of Inflation: percent change in everyday prices
Look up the price of something you buy regularly from five years ago and today. Calculate the percent change, then the CAGR. Compare it with the official inflation rate.