Percentage change appears in exam results, salary negotiations, sales reports and price comparisons. The formula is consistent — what changes is whether you're calculating an increase, a decrease, or working backwards to find the original.
The Formula
Percentage change = ((New Value − Old Value) ÷ Old Value) × 100
A positive result = increase. A negative result = decrease.
Percentage Increase: Examples
| Old value | New value | Calculation | Result |
|---|---|---|---|
| Rs 40,000 salary | Rs 46,000 | (6,000 ÷ 40,000) × 100 | 15% increase |
| 200 visitors/day | 260 visitors/day | (60 ÷ 200) × 100 | 30% increase |
| 85 marks | 91 marks | (6 ÷ 85) × 100 | 7.1% increase |
Percentage Decrease: Examples
| Old value | New value | Calculation | Result |
|---|---|---|---|
| Rs 3,500 price | Rs 2,800 price | (−700 ÷ 3,500) × 100 | 20% decrease |
| 500 units sold | 425 units sold | (−75 ÷ 500) × 100 | 15% decrease |
Finding the Original Value
If you know the final value and the percentage change, find the original:
After a 20% increase: Original = 1,200 ÷ 1.20 = 1,000 After a 15% decrease: Original = 850 ÷ 0.85 = 1,000
The Common Mistake
A 20% increase followed by a 20% decrease does not return to the original:
- Start: 1,000 → +20% → 1,200 → −20% → 960
This is because the decrease applies to the higher value. The percentage always acts on the current number, not the original. This matters in salary negotiations, pricing and investment calculations.
When to Use This
- Comparing this month's sales to last month.
- Calculating how much a product's price changed.
- Finding the real change behind a "percent off" claim.
- Tracking growth in website traffic, followers or conversions.
Use the Percentage Calculator for any of these calculations. For the basic percentage problems (finding X% of a number), see how to calculate percentages quickly.
When Percentage Change Misleads
A 100% increase sounds dramatic. It means the value doubled. A 50% increase then a 50% decrease doesn't return to zero — as noted earlier, sequential percentages aren't additive. In business reporting, also watch for the base effect: a 50% increase from 2 to 3 looks huge as a percentage but is one unit. Context (both the percentage and the absolute numbers) gives the complete picture. The Percentage Calculator handles all percentage change calculations, including the sequential compound cases.
Percentage Points vs Percentage Change
"The interest rate rose from 12% to 15%" — it rose by 3 percentage points, but the percentage change in the rate itself is (3 ÷ 12) × 100 = 25%. These are different things. "Percentage points" is the arithmetic difference; "percentage change" is relative change. In financial reporting and statistics, confusing the two leads to misinterpretation. Percentage Calculator handles both types of calculation.
