How to Calculate Percentage Increase and Decrease (With Real Examples)

Knowing how to calculate percentage increase and decrease is one of the most useful everyday math skills there is. It tells you how much a salary really grew, whether a "50% off" deal is as good as it sounds, and what return your investment actually earned. The formula is short — the trick is using the right starting number.

The percentage change formula

There is one formula for both increase and decrease:

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

If the result is positive, it is an increase. If negative, a decrease. The single most important rule: always divide by the OLD value, never the new one.

Worked example: a price increase

A product went from $80 to $100.

• New − Old = 100 − 80 = 20
• 20 ÷ 80 = 0.25
• 0.25 × 100 = 25% increase

Worked example: a price decrease

A product dropped from $100 to $80.

• New − Old = 80 − 100 = −20
• −20 ÷ 100 = −0.20
• −0.20 × 100 = 20% decrease

Notice the asymmetry: going from 80 to 100 is a 25% rise, but going from 100 back to 80 is only a 20% fall. Same $20 gap — different percentages, because the starting number changed. This catches people out constantly.

Real example: a salary raise

Your salary goes from $52,000 to $57,200.

• 57,200 − 52,000 = 5,200
• 5,200 ÷ 52,000 = 0.10
• A 10% raise.

To check an offer the other way — "they offered a 4% raise on $52,000" — multiply: 52,000 × 0.04 = $2,080, so the new salary is $54,080.

Real example: a discount

A jacket is marked "30% off $120." The decrease is:

• 120 × 0.30 = $36 off
• You pay 120 − 36 = $84

A faster route: 30% off means you pay 70%, so 120 × 0.70 = $84 directly.

Real example: investment returns

You invest $5,000 and it grows to $5,650.

• 5,650 − 5,000 = 650
• 650 ÷ 5,000 = 0.13
• A 13% return.

If it had fallen to $4,500 instead: (4,500 − 5,000) ÷ 5,000 = −0.10, a 10% loss.

Percentage points vs percent change

A common trap. If a savings rate rises from 4% to 6%, that is a 2 percentage point increase — but a 50% increase (because 2 is half of the original 4). "Percentage points" measures the gap between two percentages; "percent change" measures the relative size of that gap. News headlines mix these up all the time.

Mental shortcuts

You can estimate most percentage changes in your head:

• 10% of a number is that number with the decimal moved one place left.
• 5% is half of 10%.
• Build other percentages by combining: 15% = 10% + 5%, 25% = 10% + 10% + 5%.

For "is this change roughly X%?", compare the difference to 10% of the old value.

Frequently asked questions

What is the formula for percentage increase? Percentage change = ((New − Old) ÷ Old) × 100. A positive result is an increase; a negative result is a decrease.

Do I divide by the old or the new value? Always the old (original) value. Dividing by the new value gives the wrong answer.

Why is a 25% increase not cancelled by a 25% decrease? Because the decrease is applied to a larger number. A 25% rise then a 25% fall leaves you below where you started.

What is the difference between percentage points and percent change? Percentage points is the simple gap between two percentages. Percent change is that gap relative to the starting percentage.

How do I quickly find a percentage of a number? Find 10% (move the decimal left one place), then add or halve to build the percentage you need.

Calculate it instantly

Skip the arithmetic — the free Percentage Calculator handles percentage increase, decrease, and percent-of-a-number with step-by-step working, so you can check any salary raise, discount or investment return in seconds.