Percentage changes
made simple

The percentage change formula

Percentage change shows how far a value moved relative to where it started. Use it for price rises, salary hikes, exam marks, weight loss, anything with a before and an after.

1. 1Subtract the old value from the new value.
2. 2Divide that difference by the old value.
3. 3Multiply by 100 to turn the decimal into a percentage.

Dividing by the old value is the key choice. It anchors the answer to your starting point, so the same rule works for prices, populations, scores or anything else you can measure twice.

Increase versus decrease

A fall works the same way. A price dropping from ₹500 to ₹425 gives (425 − 500) ÷ 500 × 100 = −15%, a 15% decrease.

The starting value matters. ₹50,000 to ₹55,000 is +10%, but ₹55,000 back to ₹50,000 is −9.09%, because the second change is measured against the larger number. Likewise, 80 to 100 is a 25% increase, while 100 back down to 80 is a 20% decrease.

Percentage answers rarely come out even. −9.0909…% is normally written as −9.09%. Two decimals suit most purposes, and whole numbers are fine for a quick comparison.

Why +50% then −50% does not get you back

Each percentage applies to a different base. Start with ₹1,000. A 50% rise makes it ₹1,500. A 50% fall is then half of ₹1,500, which is ₹750, so you finish 25% below where you began. The same arithmetic is why a 50% loss on any amount needs a 100% gain to break even.

To recover from a fall you need a bigger percentage rise, because the base is now smaller:

A neat way to chain changes is with multipliers. A rise of x% multiplies by 1 + x ÷ 100 and a fall multiplies by 1 − x ÷ 100, so +50% then −50% is 1.5 × 0.5 = 0.75, a 25% fall. Even small equal moves leave a gap: +10% then −10% on ₹1,000 gives ₹990, a net 1% fall. Never add percentages that come from different bases.

Percentage points versus percent

When the quantity is itself a percentage, such as an interest rate, there are two valid ways to describe a move. A rate going from 6% to 8% is up 2 percentage points, the plain difference. It is also a 33.33% increase relative to 6%, from (8 − 6) ÷ 6 × 100.

Both statements are correct but answer different questions, so say which one you mean. Another example: a deposit rate moving from 6.5% to 7% is up 0.5 percentage points, or about 7.69% in relative terms. Headlines often say “up 2%” loosely, so check whether the figure is in points or in percent before you compare it with anything.

Working backwards: reverse percentages

Sometimes you know the result after a change and need the original. Divide by the multiplier rather than adding the percentage back:

• After a 20% discount the multiplier is 0.80. If the sale price is ₹1,600, the original price is 1,600 ÷ 0.80 = ₹2,000.
• After adding 18% GST the multiplier is 1.18. If the bill is ₹11,800, the price before GST is 11,800 ÷ 1.18 = ₹10,000.
• After a 12% price rise, the multiplier is 1.12. If an item now costs ₹2,800, it cost 2,800 ÷ 1.12 = ₹2,500 before.

The common slip is adding 20% of ₹1,600 (₹320) back to get ₹1,920. That is wrong because the 20% was taken from the original price, not from the sale price.

Finding a percentage of a number

The simplest percentage task is finding a share of a number: divide the percentage by 100 and multiply.

• 15% of ₹2,400 = 0.15 × 2,400 = ₹360.
• 7.5% of ₹8,000 = 0.075 × 8,000 = ₹600.