How to Calculate Percentage Increase and Decrease, Step by Step
Learn the percentage change formula, how to reverse a discount, why +10% then −10% is not zero, and the difference between percent and percentage points.
Percentages show up everywhere: a raise at work, a price that went up at the grocery store, a sale tag, a stock that dropped overnight. The math is simple once you know which number to divide by, and that is exactly where most mistakes happen. This guide walks through the formulas with real numbers, then covers the traps that catch even people who are good with numbers.
The percentage change formula
To find how much something changed in percent, divide the difference by the original value and multiply by 100:
Percentage change = (New value − Old value) ÷ Old value × 100If the result is positive, it is an increase. If it is negative, it is a decrease. The key detail is the denominator: always divide by the value you started with, not the one you ended with.
Example 1: percentage increase
Your rent goes from $1,200 to $1,320 a month.
- Difference: 1,320 − 1,200 = 120
- Divide by the original: 120 ÷ 1,200 = 0.10
- Multiply by 100: 10% increase
Example 2: percentage decrease
A laptop drops from $900 to $765.
- Difference: 765 − 900 = −135
- Divide by the original: −135 ÷ 900 = −0.15
- Multiply by 100: 15% decrease
Why the direction matters: 80 → 100 is not the same as 100 → 80
Going from 80 to 100 is a 25% increase (20 ÷ 80). Going back from 100 to 80 is a 20% decrease (20 ÷ 100). The difference is 20 in both cases, but the starting point changes, so the percentage changes too. This is why a stock that falls 50% needs to rise 100% just to get back to where it was.
How to find X% of a number
Convert the percentage to a decimal (divide by 100) and multiply:
- 18% of $85 = 0.18 × 85 = $15.30 (a typical restaurant tip)
- 7.5% of $2,400 = 0.075 × 2,400 = $180
A useful shortcut: 10% of anything is just the number with the decimal point moved one place to the left. 10% of $85 is $8.50, so 20% is $17 and 5% is $4.25.
How to increase or decrease a number by a percentage
Instead of calculating the percentage and then adding or subtracting it, multiply by a single factor:
- Increase by 8%: multiply by 1.08. $50 × 1.08 = $54.
- Decrease by 30%: multiply by 0.70. $120 × 0.70 = $84.
This "multiplier" method is faster and is the same logic banks, spreadsheets and price tags use.
Reverse percentages: finding the original price
A jacket costs $64 after a 20% discount. What was the original price? Many people take 20% of $64 and add it back, which gives $76.80. That is wrong, because the 20% was taken from the original price, not from $64.
The right way is to divide by the multiplier:
Original price = Sale price ÷ (1 − discount)
Original price = 64 ÷ 0.80 = $80The same works for taxes. If a receipt shows $108 including 8% sales tax, the pre-tax price is 108 ÷ 1.08 = $100.
Why +10% then −10% does not bring you back
Start with $100. Increase by 10% and you have $110. Decrease that by 10% and you have $99, not $100. Successive percentage changes multiply, they do not add:
1.10 × 0.90 = 0.99 → a 1% net lossThis matters for investments, inflation and salary negotiations. Two years of 5% inflation is not 10%; it is 1.05 × 1.05 = 1.1025, or 10.25%.
Percent vs. percentage points
If a mortgage rate rises from 4% to 5%, it went up by 1 percentage point, but by 25 percent (1 ÷ 4). News headlines often mix the two. Percentage points describe the simple difference between two percentages; percent describes the relative change.
What percentage is X of Y?
Divide the part by the whole and multiply by 100. If you spend $450 of a $1,800 monthly budget on groceries, that is 450 ÷ 1,800 × 100 = 25% of your budget.
Quick reference
| What you want | Formula | Example |
|---|---|---|
| X% of a number | number × X ÷ 100 | 15% of 200 = 30 |
| X is what % of Y | X ÷ Y × 100 | 30 of 200 = 15% |
| Percentage change | (new − old) ÷ old × 100 | 200 → 230 = +15% |
| Increase by X% | number × (1 + X/100) | 200 + 15% = 230 |
| Decrease by X% | number × (1 − X/100) | 200 − 15% = 170 |
| Original before X% off | price ÷ (1 − X/100) | 170 after 15% off = 200 |
Tip: our free percentage calculator handles all five cases above and lets you choose how many decimal places to show, so you can copy the result straight into a spreadsheet or email.
Frequently asked questions
What is the formula for percentage increase?
Subtract the old value from the new value, divide by the old value and multiply by 100. For example, going from 50 to 60 is (60 − 50) ÷ 50 × 100 = 20%.
How do I calculate a percentage decrease?
Use the same formula. The result will be negative. Going from 60 to 45 is (45 − 60) ÷ 60 × 100 = −25%, a 25% decrease.
How do I find the original price before a discount?
Divide the sale price by (1 − discount as a decimal). A $45 item after 25% off was originally 45 ÷ 0.75 = $60.
Is a 100% increase the same as doubling?
Yes. A 100% increase adds the full original value again, so the result is twice the original. A 200% increase triples it.
Lawyer for almost 20 years, focused on digital law, and creator of CoringaWeb. He writes the guides and builds the tools on this site.
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