Percentage Change Formula: Calculate Increase and Decrease

Percentage change is one of the most useful tools in everyday math — it tells you how much something grew or shrank relative to where it started. Whether you are tracking a stock price, comparing quarterly revenue, or watching a population grow, the same formula turns a raw difference into a number you can actually compare. This guide breaks down the percentage change formula, walks through increase and decrease examples, and flags the mistakes that quietly produce wrong answers.

The percentage change formula

Every percentage change calculation comes back to one relationship: the difference between two values, divided by the value you started with. The formula is:

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

Subtract the old value from the new value, divide that difference by the old value, and multiply by 100 to convert the decimal into a percent. A positive result means the value grew; a negative result means it shrank.

The single most important detail is that you always divide by the old value — the starting point. That baseline is what the change is measured against. Swap it for the new value and the answer falls apart, even though the arithmetic feels close.

Want to skip the arithmetic? A percentage calculator handles the formula instantly once you plug in the two values, which is handy when the numbers are messy or you are checking several changes at once.

Percent increase: a worked example

A stock you hold climbs from $80 to $100. What is the percentage increase?

• Old value = $80
• New value = $100
• Difference = 100 − 80 = 20
• Divide by old value: 20 ÷ 80 = 0.25
• Multiply by 100: 0.25 × 100 = 25%

The stock rose 25%. That 20-point gain represents one-quarter of the $80 starting price, which is exactly what 25% means.

Percent decrease: the reverse move

Now flip it: another stock drops from $100 back down to $80. What is the percentage decrease?

• Old value = $100
• New value = $80
• Difference = 80 − 100 = −20
• Divide by old value: −20 ÷ 100 = −0.2
• Multiply by 100: −0.2 × 100 = −20%

That stock fell 20%. Notice the asymmetry: a move of $20 reads as a 25% increase one direction but only a 20% decrease the other. That is not a miscalculation — it is how percentage change works, because each calculation divides by a different starting value. A gain of 25% is not undone by a loss of 25%.

Common mistake: dividing by the new value

The single most frequent error in percentage change is dividing by the new value instead of the old one. Take the $80 to $100 move: the correct calculation divides 20 by 80 to get 25%. If you mistakenly divide by 100, you get 20% — the same number as the decrease in the reversed case, but applied to the wrong direction.

The error is easy to make because the new value is often the figure you are looking at. But change must always be measured against where you started. A quick sanity check: if a value doubles from 50 to 100, the change should be 100%. Dividing 50 by 50 gives 1, or 100% — correct. Dividing by 100 would give 50%, which is clearly wrong for a doubling.

Business examples: revenue growth and price changes

Percentage change is the standard way to report business performance because absolute dollar moves are hard to compare across companies of different sizes. A $2 million revenue increase means a lot for a $10 million company and almost nothing for a $2 billion one.

Revenue growth: a small business earns $240,000 in Year 1 and $288,000 in Year 2. The percentage change is ((288,000 − 240,000) ÷ 240,000) × 100 = (48,000 ÷ 240,000) × 100 = 20%. Year-over-year revenue grew 20%.

Price increase: a supplier raises the wholesale price of a component from $12.50 to $14.75. The change is ((14.75 − 12.50) ÷ 12.50) × 100 = (2.25 ÷ 12.50) × 100 = 18%. A procurement manager reporting this would say the component price increased 18% year-over-year.

Discount as percentage change: a product drops from $90 to $67.50. That is ((67.50 − 90) ÷ 90) × 100 = (−22.50 ÷ 90) × 100 = −25%, a 25% decrease. Sellers and buyers both translate discounts into percentages because they are comparable across products.

For anyone working through these regularly — say, a financial analyst juggling dozens of period-over-period comparisons — a percentage calculator removes the busywork and keeps the baseline straight. To go deeper on the business analytics behind these numbers, Coursera offers university-level courses in business analytics and financial reporting that cover growth metrics in a real-business context.

Population growth

Demographers use percentage change constantly to describe how populations shift over time. The U.S. Census Bureau, for instance, reports decade-over-decade growth as a percentage to make state-by-state comparisons meaningful.

Example: a city's population grows from 1.2 million to 1.38 million over ten years. The percentage change is ((1,380,000 − 1,200,000) ÷ 1,200,000) × 100 = (180,000 ÷ 1,200,000) × 100 = 15%. The city grew 15% over the decade, or roughly 1.4% per year if you average it out (though compounding makes the true annual rate slightly lower).

Population figures work the same way whether the baseline is a town of 8,000 or a country of 330 million — the percentage frames the change in comparable terms.

When to use percentage change (and when not to)

Percentage change is the right tool whenever you need to compare movement across different baselines. A few guidelines:

• Use it for growth and decline: revenue, prices, population, test scores — anything where the direction and relative size of the move matters more than the raw number.
• Watch small baselines: going from 2 to 4 is a 100% increase, but the absolute change is tiny. Percentages amplify small-base movements, which is why studies often report both the percentage and the underlying count.
• Don't mix it with percentage points: if mortgage rates rise from 6% to 7%, that is a 1 percentage point increase but a 16.7% increase in the rate (1 ÷ 6 × 100). The distinction matters in finance and policy reporting.
• Be careful averaging: a 50% gain followed by a 50% loss leaves you 25% below where you started, not back to even. Sequential percentage changes compound, not add.

Quick reference: the formula in one line

Keep this version handy for any percentage change problem:

((New − Old) ÷ Old) × 100

Positive is an increase, negative is a decrease. Always divide by the old value. The same formula covers percent increase, percent decrease, revenue growth, price changes, population growth, and any other "how much did this change" question.

To build the intuition behind this and other core formulas rather than just memorizing them, Brilliant offers interactive math and science courses that let you manipulate the variables and see why the formula behaves the way it does.

The bottom line

Percentage change converts a raw difference into a comparable, percentage-based measure of growth or decline. The formula — ((New − Old) ÷ Old) × 100 — works for increases and decreases alike; the sign tells you which. Divide by the old value every time, never confuse percentage points with percent change, and remember that sequential percentages compound rather than add. With those rules in place, you can work out revenue growth, price moves, and population shifts by hand — or reach for a percentage calculator when the numbers get messy.