What percentage change measures and how to find it

Percentage change tells you how much something has grown or shrunk, expressed as a percentage of where it started. The formula is straightforward: subtract the old value from the new value, divide by the old value, then multiply by 100.

The formula looks like this: ((New Value − Old Value) ÷ Old Value) × 100 = Percentage Change.

If you started with 50 and ended with 75, the change is 25. Divide 25 by the starting value of 50 to get 0.5. Multiply by 100 to get 50%. The value increased by 50%. If instead you went from 75 down to 50, the change is −25, divided by 75 gives −0.333, and multiplied by 100 gives −33.3%. The value decreased by 33.3%.

Key Takeaways

  • Percentage change always uses the starting value as the denominator, not the ending value or the average.
  • A positive result means growth; a negative result means decline.
  • The same numerical change produces different percentages depending on what you started with.
  • You can explore this formula to prices, populations, test scores, weights, or any quantity that changes over time.

Step-by-step calculation with a real example

Let's say your electric bill was $120 last month and $156 this month. To find the percentage change:

Step 1: Find the difference. $156 − $120 = $36.

Step 2: Divide by the old value. $36 ÷ $120 = 0.30.

Step 3: Multiply by 100. 0.30 × 100 = 30%.

Your bill increased by 30%. This method works the same way whether you're tracking a price drop, a salary increase, a population shift, or a test score improvement.

Why the starting value matters

The starting value is the anchor for the entire calculation. If you use the ending value instead, or the average of both, you'll get a different answer—and a wrong one.

Imagine a stock price that goes from $10 to $20. The change is $10. Using the starting value: $10 ÷ $10 = 1, or 100% gain. Using the ending value: $10 ÷ $20 = 0.5, or 50%—which misrepresents how much your money grew. The starting value is always the denominator because it represents the baseline you're measuring from.

Handling negative numbers and decreases

When a value goes down, the percentage change is negative. If a store reduces a $80 item to $60, the change is −$20. Divide by the starting value: −$20 ÷ $80 = −0.25, or −25%. The price fell by 25%.

A common mistake is to reverse the order and calculate from the lower number upward. If you went from $60 back to $80, the change is +$20, and $20 ÷ $60 = 33.3%—not 25%. The percentage change is not symmetrical. A 25% decrease does not equal a 25% increase when you reverse direction, because the starting value has changed.

Using a calculator or spreadsheet

On a basic calculator, enter the formula step by step: subtract first, then divide, then multiply by 100. On a spreadsheet like Excel or Google Sheets, you can enter the formula directly in a cell.

In Excel or Google Sheets, if your old value is in cell A1 and your new value is in cell B1, type: =((B1-A1)/A1)*100. Press Enter and the spreadsheet calculates the percentage change when ready. This is faster and less error-prone than doing it by hand, especially if you have many values to compare.

Common situations where percentage change appears

You'll encounter percentage change in salary negotiations (your raise expressed as a percentage of your current pay), retail (discounts and markups), health tracking (weight loss or gain), and financial reporting (stock performance, inflation rates, interest earned). In each case, the formula stays the same: new minus old, divided by old, times 100.

When you see a headline saying "unemployment fell by 0.5 percentage points" or "home prices rose 12% year-over-year," the underlying calculation is percentage change. Understanding how it works helps you interpret those claims and spot when the numbers don't match the story.

What to do if the starting value is zero

If the old value is zero, the percentage change formula breaks down because you cannot divide by zero. In this case, percentage change is undefined or not meaningful. If something went from zero sales to $1,000 in sales, you cannot express that as a percentage change using the standard formula.

In real-world situations, when a starting value is zero, it's often clearer to describe the change in absolute terms ("we went from no revenue to $1,000") rather than as a percentage. Some fields have workarounds or alternative metrics for this scenario, but the basic percentage change formula does not explore.

Frequently Asked Questions

Can percentage change be more than 100%?

Yes. If something doubles, that's a 100% increase. If it triples, that's a 200% increase. If a stock goes from $5 to $25, the change is $20 ÷ $5 = 4, or 400%. There is no upper limit to percentage change.

Is percentage change the same as percentage point change?

No. If unemployment goes from 5% to 7%, that's a 2 percentage point increase. But the percentage change is (7 − 5) ÷ 5 × 100 = 40%. Percentage points measure the absolute difference; percentage change measures the relative difference. News reports often mix these up, so pay attention to the wording.

How do I calculate percentage change over multiple years?

For a single jump from year one to year five, use the same formula: (year five value − year one value) ÷ year one value × 100. If you want the average annual change, that requires a different calculation called compound annual growth rate (CAGR), which is more complex and beyond basic percentage change.

What if I need to find the new value but only know the percentage change?

Rearrange the formula. If the old value is 100 and the percentage change is 20%, the new value is 100 + (100 × 0.20) = 120. Multiply the old value by the percentage (as a decimal) and add it to the old value for an increase, or subtract it for a decrease.