Numbers
How to Calculate Percentage Increase and Decrease
The percentage change formula with everyday examples, how to add or remove a percentage, and why a 20% fall needs a 25% rise to recover.
By Team Vind · Updated · 4 min read
Prices went up, marks went down, sales grew: "by how much percent?" is one of the most common sums in daily life. It takes one formula, but there are a few traps: dividing by the wrong number, mixing up percent and percentage points, and expecting a fall and a rise of the same percent to cancel out.
The formula
Percentage change = (new − old) ÷ old × 100
A positive answer is an increase, a negative one a decrease. Always divide by the old (starting) value. Rent going from ₹18,000 to ₹20,500 is (20,500 − 18,000) ÷ 18,000 × 100 = 13.89% increase.
Worked examples
| Old | New | Change | |
|---|---|---|---|
| Petrol price (₹ per litre) | 94.72 | 101.5 | +7.16% |
| Rent (₹ a month) | 18,000 | 20,500 | +13.89% |
| Phone price after a sale (₹) | 24,999 | 19,999 | −20% |
| Monthly electricity units | 310 | 248 | −20% |
Try it: Percentage Change Calculator
Percentage Increase
Working
- % change = (new − old) ÷ |old| × 100
- = (300 − 250) ÷ 250 × 100 = 20%
Increasing or decreasing by a percentage
Increase by p%: x × (1 + p ÷ 100) · Decrease by p%: x × (1 − p ÷ 100)
₹850 plus 12% is 850 × 1.12 = ₹952. ₹2,400 less 15% is 2,400 × 0.85 = ₹2,040. Finding the original before a change is the reverse: if ₹1,120 is after a 12% rise, the original was 1,120 ÷ 1.12 = ₹1,000. That's exactly how you remove GST from a price.
Trap 1: ups and downs don't cancel
A share falls 20%, then rises 20%. You're not back where you started: ₹100 → ₹80 → ₹96. After a 20% fall, you need a 25% rise to recover, because the rise is worked out on a smaller number.
Trap 2: percent vs percentage points
If a loan rate goes from 8% to 9%, it rose by 1 percentage point, but by 12.5% in percent terms. News reports about interest rates, exam pass rates and vote shares usually mean percentage points.
Working out a raise? See how to calculate a salary hike. For any other percentage, use the percentage calculator.
Frequently asked questions
How do I calculate percentage increase?
Subtract the old value from the new one, divide by the old value, and multiply by 100. From 40 to 50 is 10 ÷ 40 × 100 = 25%.
How do I calculate percentage decrease?
Use the same formula; the answer is negative. From 50 to 40 is −10 ÷ 50 × 100 = −20%, a 20% decrease.
Why is a 50% loss not recovered by a 50% gain?
The gain is worked out on the smaller amount. ₹100 falls 50% to ₹50; a 50% gain brings it only to ₹75. You need 100% to get back to ₹100.
What is the difference between percent and percentage points?
Percentage points are the plain difference between two percentages (8% to 9% = 1 point). Percent change is that difference relative to the start (12.5%).
Sources
Last reviewed: 10 October 2026