How to Calculate Percentage Increase and Decrease
Quick Answer
To know how to calculate percentage increase, use the percent change formula: (New Value / Old Value) * 100. A positive result is an increase, a negative result is a decrease. The formula is identical either way, only the sign flips. The part that actually causes mistakes isn't this basic formula, though. It's what happens when percentages stack on top of each other, or when you need to work backward from a final value to find the original. Both are covered in full below, along with the easily confused difference between a percentage change and a percentage point change. Run your own numbers instantly with our percentage calculator.
The single step percentage change formula is simple enough that most people get it right on the first try. Where things go wrong is almost always in what comes next: applying two percentage changes back to back, trying to reverse engineer an original value from a discounted price, or mixing up a percentage change with a percentage point change. These three situations account for the vast majority of real world percentage mistakes, and none of them are solved by the basic formula alone.
The Basic Formula Quickly
Percentage Change (%) = (New Value / Old Value) * 100
Example (increase): A salary rises from $50,000 to $56,000. (56,000 / 50,000) * 100 = 6,000 / 50,000 * 100 = 12% increase
Example (decrease): A price drops from $80 to $68. (68 / 80) * 100 = -12 / 80 * 100 = -15%, i.e. a 15% decrease
The negative sign on a decrease isn't an error. It's the formula correctly telling you the value went down. Drop the sign and state it as a decrease in plain language.
Compounding Percentage Changes: Why They Do Not Simply Add Up
This is where most people go wrong, and it's more common than it sounds: a product goes up 20%, then down 20% the following month. It's tempting to assume those cancel out and you're back to the original price. They don't.
Why: the second percentage change is calculated against the new value, not the original one.
Worked example: A $100 product.
- After a 20% increase: $100 * 1.20 = $120
- After a 20% decrease (applied to $120, not $100): $120 * 0.80 = $96
You end up at $96, not $100, a net 4% loss, even though the two percentages look like they should offset.
The General Formula for Stacked Percentage Changes
For any sequence of percentage changes, convert each one to a decimal multiplier (a 20% increase is *1.20, a 10% decrease is *0.90), multiply them all together, then convert the result back to a percentage:
Combined Change (%) = [(1 + r₁) * (1 + r₂) * ... * (1 + rₙ) - 1] * 100
Worked example: Two successive store discounts: 30% off, then an extra 10% off the already discounted price.
- (1 - 0.30) * (1 - 0.10) = 0.70 * 0.90 = 0.63
- Combined change: (0.63 - 1) * 100 = -37%, not -40%
A shopper expecting "30% + 10% = 40% off" is actually only getting 37% off, a gap that retailers rely on more often than most customers realize.
Reverse Percentage: Finding the Original Value
Sometimes you have the final value and the percentage change, but need to work backward to the original. This is common when a price already includes a discount or a tax, and you need the pre-discount or pre-tax figure.
Original Value = New Value / (1 + percentage change as a decimal)
Worked example: A jacket is on sale for $72, after a 20% discount. What was the original price?
- A 20% discount means the new value is 80% of the original: multiplier = 1 - 0.20 = 0.80
- Original = 72 / 0.80 = $90
Common mistake: calculating 20% of $72 and adding it back ($72 + $14.40 = $86.40). This is wrong, because 20% of the final price is not the same as 20% of the original price. The division method above is the only correct way to reverse a percentage change.
Percentage Change vs. Percentage Point Change
This distinction trips up even experienced professionals, especially in finance and reporting contexts.
- Percentage change is relative. It's calculated against the original value.
- Percentage point change is absolute. It's simply the arithmetic difference between two percentages, with no division involved at all.
Example: An interest rate moves from 5% to 7%.
- As a percentage point change: 7 - 5 = 2 percentage points (a simple subtraction)
- As a percentage change: (7 - 5) / 5 * 100 = 40% increase (a relative change)
Both statements are correct and describe the same event, but "the interest rate rose 2 points" and "the interest rate rose 40%" sound like very different magnitudes to a reader, and mixing them up in a report or headline is a common source of misleading statistics.
Where This Matters in Practice
- Sequential discounts: understanding that stacked percentage off deals don't simply add together.
- Salary and inflation comparisons: a raise needs to be compared against inflation as a percentage change, not a flat point difference, to know if real purchasing power actually went up.
- Reversing a tax inclusive price: finding the pre tax value from a final price that already includes a known tax percentage uses the exact same reverse percentage formula as the discount example above.
- Reading financial and political reporting: rate and polling changes are frequently reported in percentage points, while headlines sometimes convert them to percentage change (or vice versa) without being clear which one is being used.
For straightforward percentage calculations, finding what a number is as a percentage of another, or a single percentage change, our percentage calculator covers all three core formula types instantly. If you're working specifically with a sale price and want to go straight from original price to final discounted price (or the reverse), the discount calculator is built for that exact use case, and when a percentage problem is more naturally expressed as a fraction first, the fraction calculator handles the conversion.
Frequently Asked Questions
No. The second percentage is applied to the new, already changed value, not the original one, so the two do not cancel out. A $100 value that increases 20% to $120 and then decreases 20% (of $120) lands at $96, not $100.
Divide the new value by (1 + the percentage change as a decimal) for an increase, or (1 minus the percentage change as a decimal) for a decrease. Adding or subtracting the percentage directly from the new value, rather than dividing, is the most common mistake in reverse percentage calculations.
A percentage point change is a simple subtraction between two percentages (7% to 5% equals 2 points). A percentage change expresses that same difference relative to the original value. Both can describe the same event accurately, but they communicate very different magnitudes.
No. Two discounts of 30% and 10% do not combine to a 40% discount. The second discount applies to the already reduced price, so the actual combined discount is 37%, calculated by multiplying the two decimal multipliers together rather than adding the percentages.
Because the percentage change formula subtracts the old value from the new value. When the new value is smaller, that subtraction produces a negative result. The negative sign simply indicates direction (a decrease); the magnitude is read the same way regardless of sign.