The Basic Formula for Percent Change

Percent change tells you how much something has grown or shrunk as a percentage of where it started. The formula is: (New Number − Old Number) ÷ Old Number × 100 = Percent Change.

The order matters. You always subtract the starting number from the ending number, then divide by the starting number. Multiply by 100 to turn the decimal into a percentage. If your answer is positive, the number went up. If it is negative, the number went down.

For example: if rent was $1,000 last year and is $1,100 now, the calculation is ($1,100 − $1,000) ÷ $1,000 × 100 = 10%. Rent increased by 10%. This same method works whether you are tracking housing costs, income, utility bills, or any other number that changes over time.

Key Takeaways

  • Percent change uses the formula (New − Old) ÷ Old × 100, and the starting number always goes in the denominator.
  • A positive result means an increase; a negative result means a decrease.
  • The same formula works whether you are tracking income, expenses, population, or any other number that changes over time.
  • Multiplying by 100 converts the decimal to a percentage; without this step, you get a decimal like 0.10 instead of 10%.
  • Percent change lets you compare changes of different sizes on the same scale, so a $50 increase to a $500 base is comparable to a $100 increase to a $10,000 base.

Working Through a Real Example Step by Step

Say your household income was $45,000 two years ago and is now $54,000. To find the percent change:

Step 1: Subtract the old number from the new number. $54,000 − $45,000 = $9,000.

Step 2: Divide that result by the old number. $9,000 ÷ $45,000 = 0.2.

Step 3: Multiply by 100 to convert to a percentage. 0.2 × 100 = 20%. Your income increased by 20%.

This three-step process is the same every time, regardless of what numbers you are working with. Once you have done it a few times, the pattern becomes automatic.

When the Number Decreases

The same steps work when a number goes down. If your utility bill was $150 last month and $120 this month, the calculation is ($120 − $150) ÷ $150 × 100 = −20%. The negative sign shows the bill decreased by 20%.

Do not drop the negative sign. It tells you the direction of change. A −5% change means something shrank; a +5% change means it grew. Some people write it as "decreased by 5%" instead of "−5%", but both mean the same thing. The negative sign is the clearest way to show that the number moved downward.

Common Mistakes to Avoid

The most frequent error is dividing by the wrong number. Always divide by the starting number, not the ending number. If you divide by the new number instead, you get a different (and wrong) answer. For instance, if you accidentally divide $9,000 by $54,000 instead of $45,000, you get 16.7% instead of 20%.

Another mistake is forgetting to multiply by 100. If you stop after dividing, you have a decimal (like 0.15) instead of a percentage (15%). The decimal is technically correct mathematically, but percentages are what people expect to see and what makes the number meaningful in conversation.

A third trap is mixing up which number is old and which is new. The old number is always your baseline — the point you are measuring change from. If a question asks "how much did it change from January to March," January is old and March is new, even if you are reading the question in reverse order.

Using Percent Change to Compare Different Situations

Percent change is useful because it lets you compare changes of different sizes on the same scale. A $100 increase sounds bigger than a $50 increase, but if the $100 increase happened to a $10,000 salary and the $50 increase happened to a $500 salary, the smaller dollar amount is actually the bigger change in percentage terms.

For instance, if one program's funding went from $1 million to $1.2 million (a 20% increase) and another went from $100,000 to $115,000 (a 15% increase), the percent change tells you which program grew faster, regardless of their starting sizes. This is why percent change appears so often in news reports, budget discussions, and policy comparisons — it puts different-sized numbers on equal footing.

Frequently Asked Questions

What if the old number is zero?

You cannot divide by zero, so percent change is undefined when the starting number is zero. If something went from $0 to $100, there is no meaningful percent change — you went from nothing to something, which is infinite growth in a mathematical sense. Describe it as "started from zero" instead.

Do I need a calculator?

For simple numbers, you can do it by hand. For messier numbers (like $47,382 to $51,904), a calculator or spreadsheet is faster and more accurate. Any basic calculator or phone calculator app works. Spreadsheets like Excel or Google Sheets have built-in functions, but the manual formula is just as reliable.

Can percent change be more than 100%?

Yes. If something doubled, that is a 100% increase. If it tripled, that is a 200% increase. If a program had 50 participants and now has 200, the percent change is (200 − 50) ÷ 50 × 100 = 300%. Large changes produce large percentages.

What is the difference between percent change and percentage point change?

Percent change uses the formula above and compares to the starting value. Percentage point change is just the difference between two percentages. If unemployment was 5% last year and 7% this year, the percentage point change is 2 points, but the percent change is 40% (because 7 is 40% higher than 5). The context tells you which one matters.