Working out a percentage increase and decrease sounds like the kind of math you learned once and never think about again — until you’re staring at a payslip, a sale sticker, or a spreadsheet and the numbers don’t add up the way you expected. The formula itself is short, but the way people apply it is where things go wrong, usually because they divide by the wrong number. This guide walks through the exact steps, a few worked examples, and the mistakes that trip up even careful spreadsheet users.
The Percentage Increase and Decrease Formula, Step by Step
Both calculations start from the same idea: compare how much a value changed to what it started at.
- Percentage increase = (New Value − Original Value) ÷ Original Value × 100
- Percentage decrease = (Original Value − New Value) ÷ Original Value × 100
Notice that in both cases, you always divide by the original value — never the new one. That single detail is where most percentage increase and decrease mistakes start.
The #1 Mistake: Using the Wrong Base Value
Say a product’s price rises from $80 to $100. The increase is $20, and $20 ÷ $80 = 25%, so that’s a 25% increase. Now imagine the price drops back from $100 to $80. It’s tempting to assume that’s also a 25% change, but it isn’t: $20 ÷ $100 = 20%, a 20% decrease. The dollar amount is identical both times, but the percentage isn’t, because the base value changed. This is exactly why a 25% increase followed by a 25% decrease never brings you back to where you started.
Percentage Increase and Decrease in the Real World
A few everyday examples where getting the base value right actually matters:
- Salary raises: A jump from ₹40,000 to ₹46,000 a month is a (46,000 − 40,000) ÷ 40,000 × 100 = 15% increase.
- Discounts: A ₹2,000 item marked down to ₹1,500 is a (2,000 − 1,500) ÷ 2,000 × 100 = 25% decrease — the same math a percentage calculator runs instantly when you’re checking a sale price.
- Weight or measurement changes: Tracking a drop from 82 kg to 78 kg is a (82 − 78) ÷ 82 × 100 ≈ 4.9% decrease.
If you’d rather skip the manual arithmetic, CheckMatter’s free Percentage Calculator handles percentage increase and decrease, percentage-of-a-number, and reverse-percentage calculations in one place. It pairs well with the GST Calculator if you’re also adding or removing tax from the same amount.
What Happens When You Apply Multiple Percentage Changes in a Row
Retail pricing often stacks more than one change on the same base item, and this is where people get tripped up a second time. If a $100 item is marked up 20% and then discounted 20% during a sale, you might expect to land back at $100 — you don’t. The markup brings it to $120, and the 20% discount applies to that new $120, not the original $100, so 20% of $120 is $24, leaving a final price of $96. Successive percentage changes compound on whatever the current value is at each step, not on the original number, which is the same “wrong base value” mistake described above, just applied twice in a row.
Percentage Points vs. Percentage Change — They’re Not the Same
Financial and economic reporting adds one more wrinkle: percentage points. If an interest rate moves from 5% to 7%, that’s a 2 percentage point increase, but a (7 − 5) ÷ 5 × 100 = 40% percentage change. Mixing these two up is one of the most common errors in reading financial news, and it’s worth double-checking which one a headline is actually reporting. Government statistical agencies are careful about this distinction — the U.S. Bureau of Labor Statistics, for instance, publishes detailed guidance on how it calculates percent changes for the Consumer Price Index, using the same original-value-in-the-denominator rule described above.
Quick Reference Table
| Change | Formula | Example |
|---|---|---|
| Increase | (New − Original) ÷ Original × 100 | 80 → 100 = 25% increase |
| Decrease | (Original − New) ÷ Original × 100 | 100 → 80 = 20% decrease |
Key Takeaways
- Always divide by the original (starting) value, not the new one.
- An X% increase followed by an X% decrease never returns you to the original number.
- Percentage points and percentage change measure different things — don’t confuse them.
- For quick, error-free results, CheckMatter’s Percentage Calculator does this math for you instantly — check out the rest of our blog for more calculator guides.
FAQ
Is a percentage rise and an equivalent percentage drop of the same number always equal in reverse? No — because the base value changes between the two steps, the percentages are different even when the dollar or unit change is identical.
How do I calculate percentage change quickly without a calculator? Subtract the original value from the new value, divide by the original value, then multiply by 100. Keeping the original value as your denominator is the part to double-check.
What’s the difference between percentage change and percentage points? Percentage points measure the raw difference between two percentages (7% − 5% = 2 points), while percentage change measures that difference relative to the starting percentage (40% change).
If a price goes up 10% and then down 10%, do I end up back where I started? No. The 10% increase is calculated on the original price, but the 10% decrease that follows is calculated on the new, higher price, so the final result is slightly lower than the original amount.