How to Calculate Percentage Increase and Decrease: Formulas + Examples

October 21, 2026 · 6 min read · By the DollarWise team

On this page

Percentages run the modern world — sale discounts, salary raises, investment returns, price hikes, tips. Yet most people can’t reliably compute a percentage change without a calculator, and plenty get it subtly wrong with one. Here’s the one formula that handles every case, plus the traps to avoid.

The One Formula

Percentage change = ((New Value − Old Value) ÷ Old Value) × 100

That’s it — increase and decrease are the same formula. Positive result = increase; negative = decrease.

Example 1 — increase: A jacket goes from $40 to $52. ((52 − 40) ÷ 40) × 100 = (12 ÷ 40) × 100 = 30% increase

Example 2 — decrease: A laptop drops from $80 to $56. ((56 − 80) ÷ 80) × 100 = (−24 ÷ 80) × 100 = −30%, i.e., a 30% decrease

Don’t want to do it by hand? Our free percentage calculator computes increase, decrease, and reverse percentages instantly.

Everyday Examples

Sale shopping. A $120 item marked “25% off”: discount = 120 × 0.25 = $30, so you pay $90. Or compute directly: 120 × (1 − 0.25) = $90. The reverse check: ((90 − 120) ÷ 120) × 100 = −25%. ✓

Salary raise. $52,000 to $55,640: ((55,640 − 52,000) ÷ 52,000) × 100 = (3,640 ÷ 52,000) × 100 = 7% raise.

Investment return. $5,000 growing to $6,250: ((6,250 − 5,000) ÷ 5,000) × 100 = 25% gain. If it fell to $4,000 instead: ((4,000 − 5,000) ÷ 5,000) × 100 = −20% loss.

Tipping. 18% on a $64 bill: 64 × 0.18 = $11.52. (For 20%, just move the decimal and double: $6.40 × 2 = $12.80.)

The Reverse Problem (Going Backwards)

This is where people stumble. A store raises prices 20%, then has a “20% off everything” sale. Are you back to the original price? No.

$100 → +20% → $120 → −20% → $96. The second 20% is taken from a bigger number.

To undo a percentage change, divide:

Undo a 20% increase: divide by 1.20 → $120 ÷ 1.20 = $100
Undo a 20% decrease: divide by 0.80 → $80 ÷ 0.80 = $100

General rule: to find the original value after a p% change, compute New ÷ (1 ± p/100) — plus for an increase, minus for a decrease.

Percentage Points vs. Percent: The Classic Trap

This distinction trips up journalists, politicians, and marketers daily:

Interest rate goes from 2% to 3% → that’s a 1 percentage point increase, but a 50% relative increase ((3−2)÷2).
A phone battery drops from 100% to 80% → 20 percentage points, 20% relative decrease. Same number, different meaning!

When someone says “increased by 5%,” always ask: 5% of what? Five percentage points, or five percent relative? The answers can differ wildly.

Compound Changes: When Percentages Stack

Real life rarely gives you one clean change. Prices rise 5% two years in a row — is that a 10% total increase? No: it’s 10.25%.

$100 → +5% → $105 → +5% → $110.25. Each increase applies to the new, larger base. The general rule: multiply the factors. Two 5% increases = 1.05 × 1.05 = 1.1025 → 10.25%.

This compounding is why “just” 3% annual inflation feels so much bigger over a decade: 1.03¹⁰ ≈ 1.344 → 34.4% cumulative price increase. And it’s the same math behind compound interest — the most important percentage in personal finance.

The Cruelest Percentage Trap in Investing

An investment falls 50%. How much must it gain to break even? Most people say 50%. The answer is 100%.

$100 → −50% → $50. To get back to $100, you need +$50 on a $50 base = +100%. In general, recovering from an x% loss requires a gain of x/(100−x) × 100:

Loss	Gain needed to recover
10%	11.1%
20%	25%
33%	50%
50%	100%
80%	400%

This asymmetry is why “avoid big losses” beats “chase big gains” in investing — the math punishes drawdowns brutally.

Percentage of a Percentage

“30% of 40%” trips people up, but it’s just multiplication: 0.30 × 0.40 = 0.12 → 12%. Real example: a store offers 40% off, then an extra 30% off the sale price. Total discount = 1 − (0.60 × 0.70) = 1 − 0.42 = 58% off — not 70%.

Reading Percentages in Headlines Critically

News headlines love percentages because big numbers get clicks — and they count on you not checking the base. “Crime up 200%!” might mean 3 incidents became 9. “Profits soar 500%!” might mean a startup went from $10k to $60k. Always ask: percent of what, and what was the starting number?

Also watch for the base-switch trick: “Prices fell 30%, then rose 30% — back to normal!” As you’ve learned, $100 → $70 → $91. Not normal. Anyone presenting stacked percentages without showing the underlying numbers is either innumerate or hoping you are.

Practice Problems (Answers Below)

A $240 jacket is 30% off. What’s the sale price?
Your $48,000 salary rises to $51,600. What percent raise?
A stock drops from $200 to $150, then rises 30%. Where is it now?
A restaurant bill is $85 before a 15% tip. What’s the total?

Answers: 1) $240 × 0.70 = $168. 2) ((51,600−48,000)÷48,000)×100 = 7.5%. 3) $150 × 1.30 = $195 — still below the original $200! 4) $85 × 1.15 = $97.75.

Quick Mental Math Shortcuts

10% of anything: move the decimal one place left ($240 → $24)
5%: half of 10% ($24 → $12)
15%: 10% + 5% ($24 + $12 = $36 on $240)
20%: double 10%
25%: divide by 4
1%: move the decimal two places left ($240 → $2.40) — then scale: 7% = 7 × $2.40 = $16.80

Frequently Asked Questions

What is the formula for percentage increase?

Percentage increase = ((New Value − Old Value) ÷ Old Value) × 100. Example: a price rising from $40 to $52 is ((52−40)÷40)×100 = 30% increase.

What is the formula for percentage decrease?

It’s the same formula: ((New Value − Old Value) ÷ Old Value) × 100 — the result just comes out negative. A price falling from $80 to $56 is ((56−80)÷80)×100 = −30%, i.e., a 30% decrease.

What is the difference between percent and percentage points?

A change from 20% to 25% is a 5 percentage point increase, but a 25% relative increase ((25−20)÷20). Mixing these up is the most common percentage mistake in news and marketing.

How do you reverse a percentage change?

Divide instead of multiply. To undo a 20% increase, divide by 1.20 (not subtract 20%). To undo a 20% decrease, divide by 0.80. Example: $120 after a 20% increase came from $120 ÷ 1.20 = $100.

#percentage #math #formulas #everyday

Written by the DollarWise team

We turn confusing money topics into plain-English guides for beginners. Every article is written to be actionable on day one — no jargon, no hype, no sales pitch.