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How to Calculate a Percentage Increase or Decrease

Percentage increase and decrease are the two sides of comparing values over time — prices, populations, sales, test scores, anything that changes. The formulas look symmetric but behave asymmetrically, which is why a 20% gain followed by a 20% loss does not get you back to where you started. Here's how to calculate both correctly, the shortcuts that actually work, and the traps that flip your answers if you're not careful.

Last updated: July 15, 2026.

The percentage increase formula

When a value grows from an old number to a new number, the percentage increase is:

Percentage increase = ((new − old) / old) × 100

Three things to remember:

• The numerator is the absolute difference — how much the value changed in raw units.
• The denominator is always the old (original) value — the base you're measuring growth from.
• Multiply by 100 to turn the ratio into a percent. Without the ×100 you get a decimal like 0.3 instead of 30%.

Example: a stock price rises from $50 to $65. The percentage increase is ((65 − 50) / 50) × 100 = (15 / 50) × 100 = 30%. The stock grew by 30% of its original price.

The percentage decrease formula

When a value drops from an old number to a new number, the percentage decrease is:

Percentage decrease = ((old − new) / old) × 100

The structure is the same — numerator is the difference, denominator is the old value, multiply by 100. The only difference is the sign: you subtract the new value from the old, which produces a positive number for a decrease.

Example: a price falls from $80 to $60. The percentage decrease is ((80 − 60) / 80) × 100 = (20 / 80) × 100 = 25%. The price dropped by 25% of its original value.

You can also write both formulas as a single percent change formula: ((new − old) / old) × 100. A positive result means an increase, a negative result means a decrease. That's cleaner for general use, but when you specifically need to report "percentage decrease," you flip the numerator to keep the number positive.

Why percentage increase and decrease are not mirrors

This is the mistake that trips up nearly everyone: percentage increase and percentage decrease are not symmetric. A 20% increase followed by a 20% decrease does not get you back to your starting point.

Work it out on $100:

• Start: $100
• After +20%: $100 × 1.20 = $120
• After −20%: $120 × 0.80 = $96

You're down 4% from where you started. The asymmetry happens because the second percentage is applied to a different base — $120, not $100. When you lose 20% of $120, you lose $24, which is more than the $20 you gained in the first step.

The pattern holds for any percentage: a +X% move followed by a −X% move leaves you at (1 + X/100) × (1 − X/100) = 1 − (X/100)² of your starting value. For ±10% you lose 1%. For ±25% you lose 6.25%. For ±50% you lose 25%. The bigger the swings, the worse the asymmetry gets.

This is why volatile investments underperform even when the average return looks fine. A portfolio that alternates +30% and −30% every other year has an "average" return of zero but a compounded return of −9% per two-year cycle. Volatility has a cost, and it's baked into the multiplication.

Absolute change vs. relative change

These are two different ways of measuring the same event, and mixing them up creates confusion.

Absolute change is the raw difference in units: new − old. If a salary goes from $60,000 to $63,000, the absolute change is +$3,000.

Relative change is that difference expressed as a percentage of the starting value. The relative change is (3,000 / 60,000) × 100 = 5%.

Which one matters depends on context. A $3,000 raise feels very different if you're starting from $30,000 (that's 10%) versus $150,000 (that's 2%). News headlines routinely exploit this: "Home prices jump $50,000!" sounds alarming, but if the starting median was $400,000 that's only a 12.5% increase, which might be normal for a hot market.

The rule: when comparing things of different sizes, use relative change (percentages). When tracking your own money or measuring things of similar size, absolute change is often more useful. A retirement account that gains $10,000 in a year is progress regardless of whether that's 5% or 10% — you can spend the dollars, not the percentage.

Common shortcuts and when they work

There are a few mental-math tricks that come up often enough to memorize:

To find 10% of anything: move the decimal point one place left. 10% of $230 is $23. To find any multiple of 10%, multiply: 30% of $230 is 3 × $23 = $69.

To add a percentage increase without multiplying: find the percentage of the original, then add it. To increase $50 by 15%, find 15% of $50 (which is $7.50), then add: $50 + $7.50 = $57.50. This is slower than multiplying by 1.15 but easier to do in your head.

To reverse a percentage increase: divide by (1 + percentage/100). A price is $132 after a 10% markup, so the original was 132 / 1.10 = $120. Do not subtract 10% of $132 — that gives $118.80, which is wrong. The percentage was applied to a smaller base, so you need to divide to undo it.

To reverse a percentage decrease: divide by (1 − percentage/100). A price is $85 after a 15% discount, so the original was 85 / 0.85 = $100. Again, do not add 15% of $85 — that only gets you to $97.75, not $100.

Worked example: successive discounts

A coat is marked $200. The store applies a 25% discount, then runs a "take an additional 10% off sale prices" promotion. What's the final price, and what's the total discount?

You can't just add 25% and 10% to get 35% off. Work it step by step:

• Start: $200
• After 25% off: $200 × 0.75 = $150
• After another 10% off: $150 × 0.90 = $135

Total discount: ((200 − 135) / 200) × 100 = 32.5%, not 35%. Successive discounts always produce less than the sum of their parts, because each percentage is applied to a smaller base than the last.

The general formula: two successive percentage changes of X% and Y% combine to give (1 + X/100) × (1 + Y/100) − 1, where X and Y are negative for discounts. For this example: (1 − 0.25) × (1 − 0.10) − 1 = 0.75 × 0.90 − 1 = 0.675 − 1 = −0.325, or −32.5%.

Worked example: markup and margin

A retailer buys an item for $40 and marks it up by 50%. What's the selling price, and what's the profit margin?

Selling price: $40 × 1.50 = $60. The markup percentage is applied to the cost.

Profit margin: ((selling price − cost) / selling price) × 100 = ((60 − 40) / 60) × 100 = 33.3%.

Notice that a 50% markup produces a 33.3% margin. Markup is a percentage of cost (the denominator is what you paid). Margin is a percentage of selling price (the denominator is what the customer pays). They are not the same number, and confusing them is how retailers accidentally lose money on sales.

The relationship: margin = markup / (1 + markup). A 100% markup (doubling the price) is a 50% margin. A 25% markup is a 20% margin. A 300% markup is a 75% margin. Markup can exceed 100%; margin caps at 100% (which would be selling something you got for free).

When percentage increase and decrease mislead: the small-base problem

Percentages scale with the size of the base. A $10 increase is a huge percentage change when you're starting from $20 and negligible when you're starting from $10,000.

• $20 → $30 is a 50% increase.
• $10,000 → $10,010 is a 0.1% increase.

Same absolute change, wildly different relative change. This is why press releases about small startups lead with huge percentage gains ("revenue up 800%!") while burying the raw numbers ($5,000 became $45,000). It's also why "cases tripled!" might mean 2 became 6, which is technically correct but misleading without context.

The fix: whenever a percentage looks suspiciously large or small, ask for the absolute numbers. A 200% increase in risk sounds alarming; a risk that went from 0.1% to 0.3% might not be. Both are true; neither alone tells the full story.

Quick reference: reversing common percentage changes

These come up constantly in pricing and finance. Memorize the patterns.

• To reverse a 10% increase, divide by 1.10 (or multiply by 0.9091).
• To reverse a 20% increase, divide by 1.20 (or multiply by 0.8333).
• To reverse a 25% increase, divide by 1.25 (or multiply by 0.80).
• To reverse a 50% increase, divide by 1.50 (or multiply by 0.6667).
• To reverse a 10% decrease, divide by 0.90 (or multiply by 1.1111).
• To reverse a 20% decrease, divide by 0.80 (or multiply by 1.25).
• To reverse a 25% decrease, divide by 0.75 (or multiply by 1.3333).
• To reverse a 50% decrease, divide by 0.50 (or multiply by 2.00).

The pattern: to reverse a change of X%, divide by (1 + X/100) for increases and (1 − X/100) for decreases. Or multiply by the reciprocal if that's easier to type into a calculator.

Worked example: compounding percentage increases

A population grows by 3% per year for 5 years. If it starts at 10,000, where does it end?

You can't just add 3% five times to get 15%. Each year's growth is applied to a new, larger base. Work it year by year:

• Year 0: 10,000
• Year 1: 10,000 × 1.03 = 10,300
• Year 2: 10,300 × 1.03 = 10,609
• Year 3: 10,609 × 1.03 = 10,927
• Year 4: 10,927 × 1.03 = 11,255
• Year 5: 11,255 × 1.03 = 11,593

Total growth: ((11,593 − 10,000) / 10,000) × 100 = 15.93%, not 15%. The extra 0.93 percentage points come from compounding — each year's growth itself grows the next year.

The shortcut: for n periods at X% per period, the end value is starting value × (1 + X/100)ⁿ. Here: 10,000 × 1.03⁵ = 10,000 × 1.1593 = 11,593. That's the same calculation as compound interest, which is why the compound interest formula is really just a repeated percentage increase.

Frequently asked questions

Try it yourself

Pick two numbers you care about — a price last month and this month, your salary last year and this year, a stock price six months apart — and work out the percentage increase or decrease both ways. Watch what happens when you apply the percentage to different starting bases. The asymmetry becomes obvious once you run your own numbers through it, and it sticks better than reading examples ever does.

This article is for general education. Numbers here are illustrative, not financial advice.