Introduction: Why Math Class Failed You
Most people think they understand percentages until money is involved. You see a stock drop 50% and think, "Oh, it just needs to go up 50% to recover."
Wrong. It needs to go up 100%.
This is where "school math" meets "wallet reality." Whether you're calculating a raise, a discount, or a terrifying crypto crash, understanding the difference between Percentage Change, Percentage Difference, and Percentage Error isn't just academic—it's financial survival.
Part 1: The "New vs. Old" Formula (Percentage Change)
This is the one you'll use 90% of the time. You have an old value (last year's salary) and a new value (this year's salary). You want to know if you should celebrate or cry.
The Formula
Real-World Example
- Your rent went from $2,000 to $2,200.
- Difference: $200 (Ouch)
- Calculation:
- Result: 10% increase
Part 2: The "Crypto Trap" (Why Losses Hurt More)
This is the most important concept in investing. If you start with $1,000 and lose 50%, you have $500. To get back to $1,000, you need to gain $500.
But $500 is 100% of your current $500 balance.
| Loss % | Required Gain to Break Even |
|---|---|
| -10% | +11% |
| -20% | +25% |
| -50% | +100% |
| -90% | +900% |
Part 3: Percentage Difference (No "Start" or "End")
Use this when comparing two things where neither is the "original." Like comparing the height of two mountains or the price of the same laptop at two different stores.
The Formula
We divide by the average because math tries to be fair. It prevents bias towards one number or the other.
Quick Cheatsheet
Percentage Change
Growth or shrinkage over time.
Percentage Difference
Comparing two separate items.
Percentage Error
Comparing a guess to exact data.
Final Thoughts
Percentages are relative. A 10% raise on a minimum wage job buys groceries; a 10% raise for a CEO buys a yacht. The math is the same, but the impact is different.
Next time you see a "Huge 50% Off Sale" that brings the price down to... exactly what it cost last month before they inflated it? You'll know exactly how to check the math.