What percent change means and why you need it

Percent change is a way to describe how much something has grown or shrunk, expressed as a percentage of what it started at. Instead of saying "rent went up by $200," you can say "rent went up by 15 percent." The percentage tells you the size of the change relative to the original amount, which makes it easier to compare changes across different situations.

You run into percent change constantly: wage increases, price hikes, population shifts, housing cost growth. The formula is the same every time, and once you know it, you can calculate it on paper or in a spreadsheet in under a minute.

Key Takeaways

  • Percent change uses a three-step formula: subtract the old number from the new number, divide by the old number, then multiply by 100.
  • A positive result means an increase; a negative result means a decrease.
  • The old number (the starting point) always goes in the denominator, even if it is smaller than the new number.
  • You can use this formula for any two numbers: prices, income, population, rent, utility bills, or any other measurement that changes over time.

The percent change formula and how to use it

The formula has three parts. Write it down or keep it handy:

Percent Change = ((New Number − Old Number) ÷ Old Number) × 100

Here is what each part does. Subtract the old number from the new number to find the actual change in dollars, people, or whatever you are measuring. Divide that change by the old number — this tells you how large the change is compared to where you started. Multiply by 100 to convert it to a percentage.

The order matters. The old number (your starting point) always goes on the bottom of the division. If you flip it, your answer will be backwards.

Working through a real example

Say your rent was $1,200 last year and is now $1,380. Plug those numbers in:

Step 1: Subtract the old from the new. $1,380 − $1,200 = $180.

Step 2: Divide by the old number. $180 ÷ $1,200 = 0.15.

Step 3: Multiply by 100. 0.15 × 100 = 15.

Your rent increased by 15 percent. That is the same increase whether your rent was $1,200 or $12,000 — the percentage captures the relative size of the change.

When the change is a decrease

The formula works exactly the same way for decreases. If your utility bill dropped from $120 to $90, subtract: $90 − $120 = −$30. Divide by the old number: −$30 ÷ $120 = −0.25. Multiply by 100: −0.25 × 100 = −25.

The negative sign tells you it is a decrease. Your utility bill went down by 25 percent. If you see a negative result, the amount has shrunk. If you see a positive result, it has grown.

Using a spreadsheet or calculator

You do not have to do this by hand. In Excel, Google Sheets, or any spreadsheet, put the old number in one cell and the new number in another. Then type a formula like =((B2-A2)/A2)*100, where A2 is the old number and B2 is the new number. Press Enter and the spreadsheet calculates it instantly.

On a standard calculator, follow the same steps: subtract, divide, multiply by 100. On a phone calculator, you can do the same thing. The math is simple enough that mistakes usually come from entering the numbers in the wrong order, not from the calculation itself.

Common mistakes to watch for

The most common error is putting the new number on the bottom instead of the old number. Remember: the old number (where you started) always goes in the denominator. If you reverse it, your percentage will be backwards.

Another mistake is forgetting to multiply by 100 at the end. If you stop after dividing, you will get a decimal (like 0.15) instead of a percentage (15). The multiplication by 100 is what converts the decimal into the percentage form people actually use.

A third mistake is misreading which number is old and which is new. If someone says "the price used to be $50 and now it is $75," the $50 is old and the $75 is new. Read the sentence carefully to figure out the direction of time.

Percent change in housing and income contexts

Percent change shows up constantly in housing decisions. When comparing rent increases across different apartments or neighborhoods, the percentage tells you which increase is steeper relative to the starting rent. A $100 increase on a $1,000 apartment (10 percent) is different from a $100 increase on a $2,000 apartment (5 percent), even though the dollar amount is the same.

The same applies to income. If your hourly wage went from $16 to $18, that is a 12.5 percent increase. If someone else's wage went from $32 to $36, that is also a 12.5 percent increase — the percentages are identical even though the dollar amounts differ. Percent change lets you compare apples to apples.

Frequently Asked Questions

What if the old number is zero?

You cannot divide by zero, so percent change does not work when the old number is zero. If something went from $0 to $100, there is no meaningful percent change — you cannot compare $100 to nothing. In that case, just describe the change in dollars instead.

Can percent change be more than 100 percent?

Yes. If something doubled, that is a 100 percent increase. If it tripled, that is a 200 percent increase. If rent went from $500 to $1,500, that is a 200 percent increase. Large percent changes are common when the starting number is small.

Do I need to round my answer?

Not unless someone asks you to. For most purposes, rounding to one or two decimal places is fine — "15.3 percent" instead of "15.333333 percent." For formal reports or official documents, check whether the organization has a rounding standard.

How is percent change different from percentage points?

Percent change measures how much something grew or shrank relative to its starting value. Percentage points measure the difference between two percentages. If unemployment was 5 percent and is now 7 percent, that is a 2 percentage point increase, but a 40 percent increase in the unemployment rate itself.