Why Percentage Increase and Decrease Trip People Up
Percentages look simple until you actually need to calculate a percentage increase and decrease for something that matters — a raise, a discount stack, a price hike, or a grade. Most of the confusion does not come from the math itself; it comes from picking the wrong starting number, or assuming that going up and coming back down by the same percentage cancels out. It does not. This guide walks through the formulas, the traps, and a few worked examples so you can check any percentage change with confidence, using our free Percentage Calculator to double-check your work.
The Basic Formula
Percentage change is always calculated the same way, as explained in Khan Academy’s percent word problems lesson:
Percentage Change = (New Value – Original Value) / Original Value x 100
If the result is positive, you have a percentage increase. If it is negative, you have a percentage decrease. The part people skip is dividing by the original value, not the new one, and that single choice changes the answer every time.
Example: a product priced at 80 dollars goes up to 100 dollars.
- Difference: 100 – 80 = 20
- Divide by the original: 20 / 80 = 0.25
- Multiply by 100: 25 percent increase
Now run it the other way. That same 100 dollar item drops back to 80 dollars:
- Difference: 80 – 100 = negative 20
- Divide by the original (now 100): negative 20 / 100 = negative 0.20
- Multiply by 100: 20 percent decrease
A 25 percent increase followed by a 20 percent decrease brings you right back to where you started, not zero net change on paper, but mathematically it works out because the base shifted. This is the single biggest source of percentage confusion, and it is worth sitting with until it clicks.
Common Mistakes That Throw Off the Result
1. Dividing by the New Value Instead of the Original
The original (starting) number is always the denominator. Swap it out for the new value and your percentage will be off, especially over large changes.
2. Assuming Increases and Decreases Are Symmetrical
As shown above, a 50 percent decrease needs a 100 percent increase to undo it, not another 50 percent. If a 200 dollar item drops 50 percent to 100 dollars, it takes a 100 percent increase, not 50 percent, to get back to 200 dollars.
3. Adding Multiple Percentage Changes Together
Two consecutive discounts, say 30 percent off followed by another 20 percent off, are not the same as a flat 50 percent off. Each discount applies to a shrinking base. 100 dollars at 30 percent off is 70 dollars; another 20 percent off 70 dollars is 56 dollars, a total discount of 44 percent, not 50 percent.
4. Confusing Percentage Change With Percentage Points
If a loan interest rate moves from 5 percent to 7 percent, that is a 2 percentage point increase, but a 40 percent percentage change relative to the original rate (2 / 5 x 100). Financial news headlines mix these up constantly, so always check which one is being reported.
5. Applying a Percentage to the Wrong Base
Before doing anything, identify what the whole actually is. A 15 percent tip on a 60 dollar dinner is different from 15 percent of a bill that already includes tax and a service charge, know your base before you calculate.
Working Backwards: Finding the Original Value
Sometimes you know the new value and the percentage change, and need to find the original. If a price increased by 20 percent to reach 120 dollars:
Original = New Value / (1 + Percentage Change as a decimal)
Original = 120 / 1.20 = 100 dollars
For a decrease, divide by (1 minus the decimal). If a price fell 20 percent to 80 dollars: Original = 80 / 0.80 = 100 dollars.
Key Takeaways
- Always divide by the original value, never the new one.
- Percentage increases and decreases are not mirror images of each other, the base changes each time.
- Stacked percentage changes (like sequential discounts) do not simply add up.
- Percentage change and percentage points measure different things, do not mix them up.
- When in doubt, run the numbers through a Percentage Calculator rather than doing mental math on anything that matters financially.
FAQ
Is a 50 percent decrease followed by a 50 percent increase back to the original value?
No. A 100 dollar item that drops 50 percent becomes 50 dollars. A 50 percent increase on 50 dollars only brings it to 75 dollars, not back to 100 dollars.
How do I calculate percentage change for a negative starting value?
The standard formula gets unreliable when the original value is negative or zero, since dividing by a negative number flips the sign in a way that can be misleading. In those cases, it is usually clearer to describe the change in absolute terms rather than as a percentage.
What is the difference between percentage change and percentage points?
Percentage points measure the raw difference between two percentages (7 percent minus 5 percent = 2 points). Percentage change measures that difference relative to the starting percentage (2 / 5 = 40 percent change).
Can I use this for grades, taxes, and tips too?
Yes, the same increase/decrease formula applies anywhere you are comparing a new number to an original one. Try our Percentage Calculator, or browse the full set of tools on our tools page.